https://www.gregschool.org/new-blog daily 0.75 2019-03-23 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5905570a20099e96374aba67/1494816142860/cygx1_ill.jpg Articles https://www.gregschool.org/new-blog/super-intelligence-rise-of-the-machines-btkn7 monthly 0.5 2019-03-21 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c93094bfa0d60506bee0100/1543712186611/how-intelligent-will-aI-get-3%5B1%5D.jpg Articles - Super Intelligence: Rise of the Machines Infographic source: https://www.huawei.com/en/about-huawei/publications/winwin-magazine/ai/how-intelligent-will-ai-get https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c93094bfa0d60506bee010a/1543713651396/staircase2%5B1%5D.png Articles - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c93094bfa0d60506bee0110/1543769327376/central+dome+super+computer.jpg Articles - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c93094bfa0d60506bee0102/1543709544581/TrainingTime-Graph-171019-r01%5B1%5D.gif Articles - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c93094bfa0d60506bee00f6/5c93094bfa0d60506bee00f7/1551237763911/Savvycom-AI-Lab%5B1%5D.jpg Articles - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c93094bfa0d60506bee0108/1543713631011/staircase1%5B1%5D.png Articles - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c93094bfa0d60506bee00fe/1543701465710/lg-airport-robot-9.jpg Articles - Super Intelligence: Rise of the Machines The two robots above help clean the floor and give directions to passengers at the Seoul-Incheon International Airport. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c93094bfa0d60506bee00fa/5c93094bfa0d60506bee00fb/1543700155460/androids%5B1%5D.jpg Articles - Super Intelligence: Rise of the Machines Cover art from the Sci-Fi Masterworks edition of Do Androids Dream of Electric Sheep? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c93094bfa0d60506bee0104/1543709737491/Knowledge%252520Timeline%5B1%5D.gif Articles - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c93094bfa0d60506bee010e/1543768690328/1541094406003-Untitled%5B1%5D.jpg Articles - Super Intelligence: Rise of the Machines An example environment fed to the AI physicist. Here, the field of view is divided into four quadrants, each of which is governed by a different physical effect, such as gravity or an electromagnetic field. The dots and lines represent the ball’s trajectory through the environment. Based on how a ball moves through the environment, the AI must use the strategies it was given to describe the physical laws that are governing the ball’s motion. Image: Tegmark and Wu/arXiv https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c93094bfa0d60506bee010c/1543714992397/1541094535342-shutterstock_680929729%5B1%5D.jpg Articles - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c93094bfa0d60506bee0106/1543711783089/tumblr_inline_p95ps0lvcV1scxxly_500%5B1%5D.png Articles - Super Intelligence: Rise of the Machines https://www.gregschool.org/new-blog/robots-and-their-uses-br26w monthly 0.5 2019-03-22 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c95404b4192024774a14a7f/5c95404b4192024774a14a80/1545767693595/luis-dourado-670d7641531557-57a9f2970415e.jpg Articles - Robots and their Uses https://www.artstation.com/artwork/YxRbq https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c95404b4192024774a14a83/5c95404b4192024774a14a84/1545767693598/arcologies.jpg Articles - Robots and their Uses https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c95404b4192024774a14a87/5c95404b4192024774a14a88/1545767693602/iStock-660606914-804x1024%5B1%5D.jpg Articles - Robots and their Uses https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c95404b4192024774a14a8b/1545767693606/Atlas_from_boston_dynamics%5B1%5D.jpg Articles - Robots and their Uses Atlas from Boston Dynamics https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c95404b4192024774a14a8d/1545767693608/if-you-could-visualize-grahams-curiosity-number-your-head-would-6200771.png Articles - Robots and their Uses https://me.me/i/if-you-could-visualize-grahams-curiosity-number-your-head-would-3896085 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c95404b4192024774a14a7b/5c95404b4192024774a14a7c/1545767693571/neil-blevins-inc-the-robot-14-textured-poses1%5B1%5D.jpg Articles - Robots and their Uses https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c95404b4192024774a14a8f/1545767693610/any-sufficiently-advanced-technology-is-indistinguishable-from-magic-arthur-c-14468433.png Articles - Robots and their Uses https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c95404b4192024774a14a77/5c95404b4192024774a14a78/1545767693565/524246%5B1%5D.jpg Articles - Robots and their Uses Image retrieved from: https://wall.alphacoders.com/big.php?i=524246 https://www.gregschool.org/new-blog/rotational-inertia-nkczj monthly 0.5 2019-03-23 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c958be2f9619a337b7692f4/1507334209137/rotational+inertiaimg.jpg Articles - Rotational Inertia Figure 1: The rotational inertia of a hollow sphere is given by \(I=\frac{2}{3}MR^2\) and the rotational inertia of a solid ball is given by \(\frac{2}{5}MR^2\). Since the lever arms \(r\) (perpendicular distance from the axis of rotation) of each mass element in the solid sphere is smaller (because each mass is closer to the axis of rotation) than the lever arms in the hollow sphere (since each mass is farther away from the axis of rotation), the solid sphere must have a smaller rotational inertia. According to Equation (2), if \(r\) is smaller, then the function \(r^2\) that we are taking the area under is smaller. https://www.gregschool.org/new-blog/2019/2/7/leaving-the-solar-system-4aahb monthly 0.5 2019-02-17 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c69ae4815fcc00f43ca1f69/5c69ae4815fcc00f43ca1f6a/1549568114520/034-035_AAS_024%5B1%5D.jpg Articles - Leaving the Solar System: Introduction to the Outward Bound Series Infographic retrieved from: https://www.spaceanswers.com/issue-previews/5025/5025/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c69ae4815fcc00f43ca1f5f/5c69ae4815fcc00f43ca1f60/1549566783210/84v8X%5B1%5D.jpg Articles - Leaving the Solar System: Introduction to the Outward Bound Series https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c69ae4815fcc00f43ca1f63/1549578332475/WH-Phoebe-1024x599%5B1%5D.jpg Articles - Leaving the Solar System: Introduction to the Outward Bound Series Image retrieved from: https://crossingzebras.com/wormhole-space-after-phoebe/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c69ae4815fcc00f43ca1f65/1549567172244/quote-the-moral-landscape-is-the-framework-i-use-for-thinking-about-questions-of-morality-sam-harris-12-51-41%5B1%5D.jpg Articles - Leaving the Solar System: Introduction to the Outward Bound Series Quote by Sam Harris, author of the book, The Moral Landscape. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c69ae4815fcc00f43ca1f71/1549574245734/wright_brothers%5B1%5D.jpg Articles - Leaving the Solar System: Introduction to the Outward Bound Series The Wright brothers on the steps of their boyhood home at 7 Hawthorn St. in Dayton.\(^{[1]}\) Carillon Historical Park https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c69ae4815fcc00f43ca1f77/1549579569564/grav_lens_telescope%5B1%5D%5B1%5D.jpg Articles - Leaving the Solar System: Introduction to the Outward Bound Series A gravitational lens telescope, as envisioned by Claudio Maccone in his 2009 book Deep Space Flight and Communications. (Claudio Maccone) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c69ae4815fcc00f43ca1f73/5c69ae4815fcc00f43ca1f74/1549578964152/This-is-How-Earth-Moves-1.jpg Articles - Leaving the Solar System: Introduction to the Outward Bound Series This image illustrates the fact that the Sun is actually moving through space relative to the Milky Way galaxy; from this frame of reference, the Earth is moving in a spiral-shaped path. Of course, we can actually alter this path as well as the Sun’s speed using a type of megastructure known as a Shkadov thruster; you could, in fact, give the Sun (and the Earth which goes around it) a radically different path which heads off-course away from the galaxy. Image retrieved from: https://wordlesstech.com/this-is-how-earth-moves/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c69ae4815fcc00f43ca1f6d/5c69ae4815fcc00f43ca1f6e/1549568694721/every_thing_that_comes_to_end.jpg Articles - Leaving the Solar System: Introduction to the Outward Bound Series https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c69ae4815fcc00f43ca1f67/1549567431465/maxresdefault.jpg Articles - Leaving the Solar System: Introduction to the Outward Bound Series https://www.gregschool.org/new-blog/2018/5/23/preliminary-interstellar-missions-prelude-to-the-stars-336f8-saywf monthly 0.5 2019-02-22 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c6f634aa4222f0da6e6f10d/1549254809143/microwave-sail-starwisp-n.jpg Articles - Preliminary Interstellar Missions: Prelude to the Stars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c6f634aa4222f0da6e6f0ff/1549254809131/Stromatolites_in_Sharkbay%5B1%5D.jpg Articles - Preliminary Interstellar Missions: Prelude to the Stars The stromatolites shown in the photograph above are fossils which were produced by cyanobacteria 3.5 billion years in Shark Bay, Australia. Cyanobacteria - a simple, single-celled lifeform - produced large amounts of oxygen via photosynthesis causing the first major oxygenation even in Earth’s history. Photograph taken by Paul Harrison. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c6f634aa4222f0da6e6f101/1549254809133/Great+Oxidization+Event.jpg Articles - Preliminary Interstellar Missions: Prelude to the Stars Diagram of the evolution of atmospheric oxygen concentration during the history of the planet. © Ido, Pierre Sans-Jofre https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c6f634aa4222f0da6e6f0f1/5c6f634aa4222f0da6e6f0f2/1537289631769/grav_lens_telescope%5B1%5D.jpg Articles - Preliminary Interstellar Missions: Prelude to the Stars A gravitational lens telescope, as envisioned by Claudio Maccone in his 2009 book Deep Space Flight and Communications. (Claudio Maccone) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c6f634aa4222f0da6e6f107/1549254809139/013532_med%5B1%5D.jpg Articles - Preliminary Interstellar Missions: Prelude to the Stars Illustration of the James Webb Space Telescope, current as of September 2009. Top side. Image Source: https://web.archive.org/web/20100527230418/http://www.jwst.nasa.gov/images_artist13532.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c6f634aa4222f0da6e6f0f9/5c6f634aa4222f0da6e6f0fa/1549254809127/1280px-Artist%27s_impression_of_the_planet_Ross_128_b%5B1%5D.jpg Articles - Preliminary Interstellar Missions: Prelude to the Stars Artist's impression of the planet Ross 128 b, with the star Ross 128 visible in the background\(^{[1]}\) Credit: European Southern Observatory https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c6f634aa4222f0da6e6f103/1549254809135/50lys%5B1%5D.gif Articles - Preliminary Interstellar Missions: Prelude to the Stars The image above is a map of a small fraction of nearby stars in our stellar neighborhood. It is a map of 130 stars located within 50 lightyears of us which are visible with the naked eye. This map shows only a tiny percent of that stars within 50 lightyears away from the Sun. There are in fact 1,800 known stars within this volume of space. To eliminate the threat of nearby supernovae, our descendants will one day visit all of these stars, either directly in which case their species actually arrives at the star, or indirectly by sending spacecraft and robots to those stars. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c6f634aa4222f0da6e6f0fd/1549254809129/NASA-WhatBiosignaturesDoesLifeProduce-20180625%5B1%5D.jpg Articles - Preliminary Interstellar Missions: Prelude to the Stars The combination of certain molecules and the absence of certain molecules in an exoplanet’s atmosphere is only likely if life is inhabited on that world: such combinations are called disequilibrium mixtures. As the light emitted from a star passes through an exoplanet’s atmosphere, the molecules in that exoplanet’s atmosphere absorb only certain wavelengths. Given which wavelengths were absorbed, we can determine whether or not disequilibrium mixtures are present in that exoplanet’s atmosphere and, consequently, assess the likelihood that extraterrestrial life inhabits that world. NASA/Aaron Gronsta https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c6f634aa4222f0da6e6f0f5/1536791569946/3E58320900000578-0-image-a-2_1489702334064%5B1%5D.jpg Articles - Preliminary Interstellar Missions: Prelude to the Stars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c6f634aa4222f0da6e6f0f7/1549254809125/mars_hs-2016-15-a-full_tif%5B1%5D.jpg Articles - Preliminary Interstellar Missions: Prelude to the Stars “This Hubble Space Telescope image of Mars shows details 20 to 30 miles across. A solar gravitational lens telescope would get even sharper views of exoplanets up to 100 light years away.”\(^{[4]}\) (STScI/AURA), J. Bell (ASU), and M. Wolff) Source URL: https://www.airspacemag.com/daily-planet/ultimate-space-telescope-would-use-sun-lens-180962499/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c6f634aa4222f0da6e6f105/1549254809137/Welcome_to_the_Universe_by_Neil_deGrasse_Tyson%3B_book_cover.jpg Articles - Preliminary Interstellar Missions: Prelude to the Stars Welcome to the Universe: An Astrophysical Tour is a popular science book by Neil deGrasse Tyson, Michael A. Strauss, and J. Richard Gott, based on an introductory astrophysics course they co-taught at Princeton University. The book was published by the Princeton University Press on September 20, 2016.\(^{[6]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c6f634aa4222f0da6e6f109/5c6f634aa4222f0da6e6f10a/1549254809141/dvv.jpg Articles - Preliminary Interstellar Missions: Prelude to the Stars Infographic above is from Time Magazine April 10, 2000. https://www.gregschool.org/new-blog/spaceship-comets-and-highways-through-space-5ec48 monthly 0.5 2019-02-24 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881c6/5c73127ce79c704c50c881c7/1536859707540/Asteroid+Mining+Station+by+Bas+Ruhe%5B1%5D.jpg Articles - Spaceship Comets and Highways Through Space - Copy of Asteroid Mining Station Artist’s depicion of a colonized asteroid. Artwork by Bas Ruhe from Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881aa/5c73127ce79c704c50c881ab/1537229707309/790097132176630087%5B2%5D.jpg Articles - Spaceship Comets and Highways Through Space - Copy of Spaceship Asteroid “The concept of turning an asteroid into a spacecraft is not entirely new: conceptual designer Bryan Versteeg has been working with the Mars One Team to imagine how we could use large asteroids for mining, transportation and habitat.”\(^{[2]}\) Credit: http://www.spacehabs.com/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c73127ce79c704c50c881f6/1536901738138/yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy.png Articles - Spaceship Comets and Highways Through Space “Each of the hexagons in this figure represents one of the mirror farms shown in [previous image]. The dots are schematic representations of the habitats occupied by each twent-five-member “band.” in reality the habitats would probably be much too small to be seen on this scale.”\(^{[37]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c73127ce79c704c50c881f2/1536978228964/pale+blue+dottttttttttttttttttttttttttttttttttttttttttttttttttt.jpg Articles - Spaceship Comets and Highways Through Space In Carl Sagan’s book, Pale Blue Dot, he talked about the possibility of interstellar human communities living in comets in the Kuiper belt, the Oort cloud, and beyond. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c73127ce79c704c50c881f4/1536900915403/hexagonal+array.png Articles - Spaceship Comets and Highways Through Space “This hexagonal array of starlight mirrors might support a co-living group of twenty-five adults and children. Each of the mirrors is about the size of the continental United States, and the entire mirror “farm” is about 30,000 kilometers across.”\(^{[37]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881ba/5c73127ce79c704c50c881bb/1536896112581/Superlaser2.jpg Articles - Spaceship Comets and Highways Through Space - Copy of Death Star Artist’s depiction of a death star. By building a shell world of the kind described by the scientist Paul Birch around a faint dead star (i.e. a brown dwarf), the faint radiation which that star gives off could be collected and used to power a gigantic laser mounted on the surface of a shell world. Thus, as far fetched as the idea might seem, it isn’t totally implausable. Image retrieved from: Artist’s depiction of a comet being used as a spaceship. Image retrieved from: http://earth-chronicles.ru/news/2014-04-21-63940 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c8819c/5c73127ce79c704c50c8819d/1536986254211/lunar-mining-base.jpg Articles - Spaceship Comets and Highways Through Space The power requirements of buried human habitats and propellant production plants could be met by the widely spaced solar power panels shown above. Image: anna.j.nesterova@gmail.com https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c73127ce79c704c50c881a8/1536853434848/ephemeralizationnnnnn.jpg Articles - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c73127ce79c704c50c881d6/1537145174696/9780553373356-uk%5B1%5D.jpg Articles - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881d8/5c73127ce79c704c50c881d9/1536987150213/MarsAndTheSpaceElevator%5B1%5D.jpg Articles - Spaceship Comets and Highways Through Space “Here is a new montage showing the base of the space elevator on the tented town called "Sheffield", built on the summit of Pavonis Mons volcano (see Red Mars). The cable is supposed to be 10m thick, which means here that Sheffield city is very big here, at a large level of development. On the foreground, you can see colored urban lights. I imagine the main entry to the planet's surface would be like a rich and welcoming show for new settlers. I also imagine the tent' skin would be blue, to balance the red and grey landscape.”\(^{[59]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881d8/5c73127ce79c704c50c881db/1537230346111/SheffieldAndTheSpaceElevator%5B1%5D.jpg Articles - Spaceship Comets and Highways Through Space Artist’s impression of a space elevator connecting to the domed over city, Sheifeild, located on Pvonic Mons in Kim Robinson’s Mars trilogy. Images retrieved from: http://davinci-marsdesign.blogspot.com/2012/04/sheffield-and-space-elevator.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c73127ce79c704c50c881e8/1536896886414/jhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh.jpg Articles - Spaceship Comets and Highways Through Space “This artist's concept puts solar system distances in perspective. The scale bar is in astronomical units, with each set distance beyond 1 AU representing 10 times the previous distance. One AU is the distance from the Sun to the Earth, which is about 93 million miles or 150 million kilometers. Neptune, the most distant planet from the Sun, is about 30 AU.”\(^{[4]}\) Image Credit: NASA/JPL-Caltech https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c73127ce79c704c50c881fc/1538678002285/1449-enz.jpg Articles - Spaceship Comets and Highways Through Space The map above shows the migration patterns and timeline of the Polynesians who traveled from Asia to America by hopping from one tiny archipelago to another. Our descendants who travel from the Earth to the exoplanet Proxima B might adopt an analogous strategy by hopping from one comet to another until they reach their final destination. Image retrieved from: https://teara.govt.nz/en/map/1449/map-of-pacific-migrations https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881b4/5c73127ce79c704c50c881b5/1536856111055/alphacentfix2%5B1%5Dkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk.jpg Articles - Spaceship Comets and Highways Through Space - Copy of Trip to Alpha Centauri using a Starshot Probe SCMP Graphic: Dennis Wong, Dang Elland Sources: Universe Today, SIMBAD Dacabase, SCMP research https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c73127ce79c704c50c881b8/1536857488613/alphacentfix2%5B1%5Dkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk.jpg Articles - Spaceship Comets and Highways Through Space Image Source: https://i4is.org/wp-content/uploads/2018/05/Principium21.pdf https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c73127ce79c704c50c881fe/1538678306195/photosynthesis-process-2.jpg Articles - Spaceship Comets and Highways Through Space The infographic above shows how plants, via the process of photosynethesis, use light (sunlight or artificial light), carbon dioxide and water to produce breathable oxygen. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881a0/5c73127ce79c704c50c881a3/1536853352265/lunaring.png Articles - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881a0/5c73127ce79c704c50c881a1/1536853340541/lunar-ring_2748879k.jpg Articles - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881a0/5c73127ce79c704c50c881a5/1536853356980/Untitled.png Articles - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881c2/5c73127ce79c704c50c881c3/1536859913266/evolvingaste%5B1%5D.jpg Articles - Spaceship Comets and Highways Through Space Credit: Nils Faber & Angelo Vermeulen https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881f8/5c73127ce79c704c50c881f9/1538604155467/1_hHjG69bPm3VrMyUG2idPKg.jpeg Articles - Spaceship Comets and Highways Through Space “Conceptual model of a growing and evolving asteroid starship. The image of comet 67P by ESA is used as a placeholder for a large asteroid.”\(^{[6]}\) Composite image by Francisco Muñoz and Anton Dobrevski https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881be/5c73127ce79c704c50c881bf/1536861860343/d00fccc571b621e809cb4ef1b9b98ee7_full.jpg Articles - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c73127ce79c704c50c881b2/1537411163921/alphacentfix2%5B1%5D.jpg Articles - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881cc/5c73127ce79c704c50c881cd/1536717071163/jeremy-jozwik-ia-kuiperbeltterrain-comp2-0084.jpg Articles - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c73127ce79c704c50c881ea/1537041005162/energy-from-space-1.jpg Articles - Spaceship Comets and Highways Through Space Using a nuclear reactor to fuse together deuterium and helium-3 would generate a lot of energy; that energy would be transferred to a shock absorber on the rear of a spaceship which would give the spaceship thrust thereby causing it to accelerate. Image retrieved from: https://science.howstuffworks.com/environmental/green-science/energy-from-space.htm https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881ec/5c73127ce79c704c50c881ef/1536898850377/jhm27etrwqj7fgpuxvuj%5B1%5D.jpg Articles - Spaceship Comets and Highways Through Space Asteroid settlement concept. Credit and Copyright: Bryan Versteeg / DSI. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881ec/5c73127ce79c704c50c881ed/1536898837446/liian1htqo3l6hvx4kkj%5B1%5D.jpg Articles - Spaceship Comets and Highways Through Space Concept art for DSI's "Harvestor" craft. Credit and Copyright: Bryan Versteeg / DSI. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c88196/5c73127ce79c704c50c88197/1537229057732/maxresdefault.jpg Articles - Spaceship Comets and Highways Through Space - Copy of Starshot Probe Depiction of a Starshot probe being accellerated by Earth-based lasers. Credit: Breakthrough Starshot https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881d0/5c73127ce79c704c50c881d1/1536896535625/colony19%5B1%5D.jpg Articles - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881ae/5c73127ce79c704c50c881af/1536889609120/jakub-grygier-026-interstellar-travel-ad.jpg Articles - Spaceship Comets and Highways Through Space - Copy of Interstellar Spaceship Artist’s depiction of an interstellar spaceship accellerated by laser beams. Artwork by Jakub Grygier from Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c73127ce79c704c50c881ca/1546401363659/swe12_10836_coverbackgroundshadowport_mattbradbury%5B1%5D.jpg Articles - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c88190/5c73127ce79c704c50c88191/1551042796892/space-travel-1200x675%5B1%5D.jpg Articles - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c73127ce79c704c50c88194/1536288589788/Skylab-73-HC-440HR%5B1%5D.jpg Articles - Spaceship Comets and Highways Through Space Image of the Saturn V rocket launching to space. Image courtesy of NASA. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c73127ce79c704c50c8819a/1536985604633/41WSCf9QqtL._SX333_BO1%2C204%2C203%2C200_.jpg Articles - Spaceship Comets and Highways Through Space Robert Zubrin’s book, Entering Space, covers topics ranging from colonizing Mars and the solar system and explores the feasibility of interstellar travel with known physics.\(^{[1]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881de/5c73127ce79c704c50c881e5/1541980302277/ksr-04.png Articles - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881de/5c73127ce79c704c50c881e3/1537243316507/kkkk.png Articles - Spaceship Comets and Highways Through Space Infographics represent a visual explanation of the so-called terrariums discussed in Kim Stanley Robinsons, 2312. Also, there is a slight error in the last infographic: the asteroid does not spin, rather a cylinder inside of the hollowed out asteroid is the thing which is actually spinning. Infographics created by Pablo Defendini. Infographics retrieved from: http://www.defendini.com/2312.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881de/5c73127ce79c704c50c881df/1537243146946/livinginasteroidd.png Articles - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c73127ce79c704c50c881de/5c73127ce79c704c50c881e1/1537243162729/hhhhh.png Articles - Spaceship Comets and Highways Through Space https://www.gregschool.org/new-blog/utopia-life-in-the-year-2100-4e9ga monthly 0.5 2019-03-22 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c952727419202e734058a06/5c952727419202e734058a07/1544066498793/524246%5B1%5D.jpg Articles - Utopia: Life in the Year 2100 Image retrieved from: https://wall.alphacoders.com/big.php?i=524246 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c952728419202e734058a2e/1546303365164/42276747_2080497328640659_4459771513339379712_o%5B1%5D.jpg Articles - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c952727419202e734058a02/1553277163807/Neolithic-revolution-ancient-farmers.jpg Articles - Utopia: Life in the Year 2100 The Neolithic Revolution (which began, independently, in multiple different civilization 10 to 12 thousand years ago) occurred when, for the first time, we humans began to domesticate plants and animals. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c952728419202e734058a18/1544156143514/central+dome+super+computer.jpg Articles - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c952727419202e734058a0e/5c952727419202e734058a13/1546461550188/The-Venus-Project-Design-889x500%5B1%5D.jpg Articles - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c952727419202e734058a0e/5c952728419202e734058a15/1546461550632/The-Venus-Project-Restaurant-889x544%5B1%5D.jpg Articles - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c952727419202e734058a0e/5c952727419202e734058a0f/1546461550216/The-Venus-Project-Architecture-1-889x500%5B1%5D.jpg Articles - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c952727419202e734058a0e/5c952727419202e734058a11/1546461554396/The-Venus-Project-Buildings-889x493%5B1%5D.jpg Articles - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c952728419202e734058a1e/5c952728419202e734058a21/1544408785580/benjamin-parker-fleetovermiranda-render-wip.jpg Articles - Utopia: Life in the Year 2100 “Civilians watch a small fleet orbit around Uranus' moon Miranda.” Credit: https://www.artstation.com/artwork/mqZVx9 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c952728419202e734058a1e/5c952728419202e734058a1f/1544408724395/benjamin-parker-fleetovermiranda-render-k.jpg Articles - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c952728419202e734058a1a/1546233660364/11908915_472363736276164_3837059669263559235_o%5B1%5D.jpg Articles - Utopia: Life in the Year 2100 Image (click to enlarge) of lab-grown meat. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c952727419202e7340589f8/5c952727419202e7340589f9/1546230084517/1*ekxLnZoSewL3p7pVUrMEhQ.jpeg Articles - Utopia: Life in the Year 2100 Robert McCall, “The Prologue and the Promise” https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c952727419202e734058a0a/5c952727419202e734058a0b/1544066745624/neil-blevins-inc-the-robot-14-textured-poses1%5B1%5D.jpg Articles - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c952728419202e734058a1c/1546234016988/large_-085MyVwIWu7CejYdKdZJ_6R-zaYCURcCPnuQyPhrbA.jpg Articles - Utopia: Life in the Year 2100 ”Flipping good ... the Japanese cuisine machine hasn't dropped a pancake yet.”\(^{[3]}\) Image: Huis Ten Bosch/Facebook https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c952727419202e734058a04/1544143467767/8a6f20acd6bb4d346443d8872dec9649.jpg Articles - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c952728419202e734058a24/5c952728419202e734058a25/1544408466566/WANDERERS_verona_rupes_03%5B1%5D.jpg Articles - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c952728419202e734058a24/5c952728419202e734058a29/1553278214216/WANDERERS_verona_rupes_01%5B1%5D.jpg Articles - Utopia: Life in the Year 2100 “Base jumping off the tallest cliff in the Solar System, located on Uranus' moon Miranda. Uranus itself, along with a few other moons (from the top left to bottom right: Ariel (here on the far side of Uranus), Belinda, Puck and Portia) are seen in the background of the last shot. On Uranus´small moon Miranda lies a monumental cliff wall believed to be the tallest in the Solar System. It is called Verona Rupes. Observations are limited but it is certain that the cliffs rise at least 5 kilometers above the ground below. Maybe even twice as much. This extreme height combined with Miranda´s low gravity (0,018g) would make for a spectacular base-jump. After taking the leap from the top edge you could fall for at least 12 minutes and, with the help of a small rocket to brake your fall toward the bottom, end up landing safely on your feet. Miranda´s close orbit around giant Uranus also makes a magnificent huge cyan ball in the sky. The scene is built mostly in CG, except for the people who are shot live action and composited into the environment, and the foreground cliffs in the first shot which are made from several photos of a place in Norway known as "The Pulpit Rock". For building the landscape I used (amongst others) this satellite photo of Verona Rupes, taken by NASAs Voyager 2 during the flyby of Uranus in 1986. For the color and texture of Uranus I used this photo as reference. Also by Voyager 2, NASA.”\({[4]}\) Source: http://www.erikwernquist.com/wanderers/gallery_verona_rupes.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c952728419202e734058a24/5c952728419202e734058a27/1544408463612/WANDERERS_verona_rupes_02%5B1%5D.jpg Articles - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c952728419202e734058a2c/1544073254525/26166483_911930292319504_5468126342370460385_n%5B1%5D.jpg Articles - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c952727419202e734058a00/1553148746362/goddardtsiolkovsky%5B1%5D.jpg Articles - Utopia: Life in the Year 2100 Photographs of the two pioneers of rocketry science, Konstantin Tsiolkovsky (left) and Robert Goddard (right). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c952727419202e7340589fc/1546230422424/2483808_landscape.jpg Articles - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c952727419202e7340589fe/1553148030627/Diorama%2C_cavemen_-_National_Museum_of_Mongolian_History%5B1%5D.jpg Articles - Utopia: Life in the Year 2100 “A diorama showing Homo erectus, the earliest human species that is known to have controlled fire, from inside the National Museum of Mongolian History in Ulaanbaatar, Mongolia.”\(^{[1]}\) https://www.gregschool.org/new-blog/technological-revolutions-98ybg monthly 0.5 2019-03-22 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954a577817f7912a1c34a7/1546556065103/Maler_der_Grabkammer_des_Sennudem_001.jpg Articles - Technological Revolutions “Ploughing with a yoke of horned cattle in Ancient Egypt. Painting from the burial chamber of Sennedjem, c. 1200 BC.”\(^{[2]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954a577817f7912a1c34ab/1546556994722/Ending_Aging%5B1%5D.jpg Articles - Technological Revolutions Credit: https://en.wikipedia.org/wiki/File:Ending_Aging.jpg https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954a577817f7912a1c34b3/5c954a577817f7912a1c34b4/1546627071014/392448062_orig%5B1%5D.jpg Articles - Technological Revolutions Artist’s depiction of nanobots patroling the human bloodstream. Image retrieved from: https://www.cnet.com/news/nanobots-can-now-swarm-like-fish-to-perform-complex-medical-tasks/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954a577817f7912a1c34ad/5c954a577817f7912a1c34ae/1546626382657/Artificial-Intelligence-2%5B1%5D.jpg Articles - Technological Revolutions https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954a577817f7912a1c34b1/1546626649805/Moore%27s_Law_Transistor_Count_1971-2016%5B1%5D.png Articles - Technological Revolutions A plot of CPU transistor counts against dates of introduction. Source URL: https://commons.wikimedia.org/wiki/File:Moore%27s_Law_Transistor_Count_1971-2016.png https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954a577817f7912a1c34bf/1546631734569/Newcomens_Dampfmaschine_aus_Meyers_1890%5B1%5D.png Articles - Technological Revolutions “Newcomen's steam-powered atmospheric engine was the first practical piston steam engine. Subsequent steam engines were to power the Industrial Revolution.”\(^{[7]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954a577817f7912a1c34c1/5c954a577817f7912a1c34c2/1546632086035/Bane-Boon-1280x640%5B1%5D.jpg Articles - Technological Revolutions Image retrieved from: https://iconshots.com/concept/the-future-of-technology-should-we-be-worried/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954a577817f7912a1c34c5/1546635037806/superconductors.png Articles - Technological Revolutions The following graph reflects the empirical fact that as time has progressed, we have achieved superconductivity at higher and higher temperatures. Credit: Pia Jensen Ray https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954a577817f7912a1c34b7/1546628848879/shopping%5B2%5D.jpg Articles - Technological Revolutions In the book, Life 3.0, the cosmologist and AI researcher Max Tegmark explores the implications of AI and robotics. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954a587817f7912a1c34cd/1546553988948/stock-photo-the-train-moving-on-the-overpass-and-the-city-on-the-water-concept-of-modern-transport-futuristic-769589683%5B1%5D.jpg Articles - Technological Revolutions Arcologies on the surface of the sea could be connected by maglev transportation systems. As we discuss in the article, How to Colonize the Earth?, these sea-steading towers would extend within the depths of the oceans; the cities underneath the sea surface could also be connected by maglev monorail systems. Image Credit: https://www.shutterstock.com/image-illustration/train-moving-on-overpass-city-water-769589683?src=l4eCjvmchovnXUJuJH_WrQ-1-29 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954a577817f7912a1c34a9/1546556387544/Life-expectancy-GDP-capita.png Articles - Technological Revolutions This graph illustrates the increase in standards of living and life expectancy that occurred during the time of the first two industrial revolutions.\(^{[3]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954a577817f7912a1c34b9/1546630127945/ Articles - Technological Revolutions “The Principia states Newton's laws of motion, forming the foundation of classical mechanics; Newton's law of universal gravitation; and a derivation of Kepler's laws of planetary motion (which Kepler first obtained empirically). The Principia is considered one of the most important works in the history of science.”\(^{[5]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954a577817f7912a1c34bd/1546631010156/Joule%27s_Apparatus_%28Harper%27s_Scan%29%5B1%5D.png Articles - Technological Revolutions “Engraving of James Joule's apparatus for measuring the mechanical equivalent of heat, in which altitude potential energy from the weight on the right is converted into heat at the left, through stirring of water.”\(^{[7]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954a577817f7912a1c34c9/1546462732450/stock-photo-concept-of-magnetic-levitation-train-moving-on-the-sky-way-in-vacuum-tunnel-across-the-city-modern-755107045%5B1%5D.jpg Articles - Technological Revolutions The image above portrays how large buildings (which could be arcologies that people live in) could be connected by maglev trains operating within evacuated tunnels. Image Credit: https://www.shutterstock.com/image-illustration/concept-magnetic-levitation-train-moving-on-755107045 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954a587817f7912a1c34cb/1546462673761/furureofcities1%5B1%5D.jpg Articles - Technological Revolutions https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954a577817f7912a1c34bb/1546630451461/Newtons_laws_in_latin%5B1%5D.jpg Articles - Technological Revolutions “Newton's First and Second laws, in Latin, from the original 1687 Principia Mathematica”\(^{[6]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954a577817f7912a1c34a5/1546555589793/ Articles - Technological Revolutions “Smithsonian scientists and their Chinese colleagues found this and other handaxes in the same sediment layer with tektites, small rocks that formed during a meteor impact 803,000 years ago. Since the handaxes and tektites were in the same layer, both are the same age. Early humans must have moved into the area right after the impact. They may have made the handaxes from rocks that were exposed when forests burned.”\(^{[1]}\) Image Credit: James Di Loreto, & Donald H. Hurlbert, Smithsonian Institution https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954a577817f7912a1c34c7/1546635697448/Meissner_effect_p1390048%5B1%5D.jpg Articles - Technological Revolutions “A magnet levitating above a high-temperature superconductor, cooled with liquid nitrogen. Persistent electric current flows on the surface of the superconductor, acting to exclude the magnetic field of the magnet (Faraday's law of induction). This current effectively forms an electromagnet that repels the magnet.” Image source: https://en.wikipedia.org/wiki/Superconductivity#/media/File:Meissner_effect_p1390048.jpg https://www.gregschool.org/new-blog/2018/5/23/star-lifting-colonizing-the-stars-and-the-galaxies-5mjpt-9w4hc monthly 0.5 2019-03-19 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9015faee6eb0728acd220c/1552852554589/Local_Group_and_nearest_galaxies%5B1%5D.jpg Articles - Star Lifting: Colonizing the Stars and the Galaxies https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9015faee6eb0728acd2206/5c9015faee6eb0728acd2207/1536791569975/neil-blevins-megastructures-1-ringworld-color-sketch%5B1%5D.jpg Articles - Star Lifting: Colonizing the Stars and the Galaxies Artist’s depiction of a ring world. Artwork by Neil Blevins. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9015faee6eb0728acd2206/5c9015faee6eb0728acd2209/1536791569979/neil-blevins-megastructures-1-ringworld-design-packet%5B1%5D.jpg Articles - Star Lifting: Colonizing the Stars and the Galaxies https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9015faee6eb0728acd21ea/5c9015faee6eb0728acd21eb/1536791569963/Oneilcylinder1.jpg Articles - Star Lifting: Colonizing the Stars and the Galaxies https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9015faee6eb0728acd21fc/5c9015faee6eb0728acd21fd/1536791569970/megastructures_7_star_lifter_3%5B1%5D.jpg Articles - Star Lifting: Colonizing the Stars and the Galaxies Artist’s depiction of a star lifter. Artwork by Neil Blevins. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9015faee6eb0728acd2202/1536791569973/Physics_of_the_future_Kaku_2011%5B1%5D.jpg Articles - Star Lifting: Colonizing the Stars and the Galaxies "Physics of the Future: How Science Will Shape Human Destiny and Our Daily Lives by the Year 2100 is a 2011 book by theoretical physicist Michio Kaku, author of Hyperspace and Physics of the Impossible. In it Kaku speculates about possible future technological development over the next 100 years. He interviews notable scientists about their fields of research and lays out his vision of coming developments in medicine, computing, artificial intelligence, nanotechnology, and energy production. The book was on the New York Times Bestseller List for five weeks." https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9015faee6eb0728acd21f0/5c9015faee6eb0728acd21f1/1552943531025/1080p-Space-Desktop-Background-hd-desktop-wallpapers-cool-images-hd-apple-background-wallpapers-colourfull-free-display-lovely-wallpapers.jpg Articles - Star Lifting: Colonizing the Stars and the Galaxies Image retrieved from: https://thewallpaper.co/preview/?wallpaper=1080p-space-desktop-background-hd-desktop-wallpapers-cool-images-hd-apple-background-wallpapers-colourfull-free-display-lovely-wallpapers-1920x1080 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9015faee6eb0728acd21ee/1552861724343/neil-blevins-megastructures-9-gas-giant-refinery-5.jpg Articles - Star Lifting: Colonizing the Stars and the Galaxies Artist’s depiction of gas giant refineries used to extract materials such as helium-3 and deuterium from the atmosphere of one of the Jovian planets. Artwork by Neil Blevins at Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9015faee6eb0728acd21f4/5c9015faee6eb0728acd21f5/1552862368589/neil-blevins-megastructures-12-nicoll-dyson-laser-design-packet.jpg Articles - Star Lifting: Colonizing the Stars and the Galaxies Artist’s depiction of a Nicoll-Dyson Laser. Artwork by Neil Blevins at ArtStation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9015faee6eb0728acd21e6/5c9015faee6eb0728acd21e7/1552959611722/jeremy-jozwik-ia-kuiperbeltterrain-comp2-0084.jpg Articles - Star Lifting: Colonizing the Stars and the Galaxies - Kuiper Belt Laser Array Artist’s impression of an array of lasers built on a comet in the Kuiper Belt. These laser stations would also be built on comets within Oort clouds (not jude our own) and interstellar space to create an interstellar highway. Artwork by Jeremy Jozwik from Artstation who is also a member of the SFIA production team. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9015faee6eb0728acd2200/1528407608550/Star_lifting_1.svg%5B1%5D.png Articles - Star Lifting: Colonizing the Stars and the Galaxies Figure 1: A star lifter would consist of a ring of solar power stations and ion accelerators distributed around a star in the shape of a ring. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9015faee6eb0728acd2204/1528412559259/star+lifter.jpg Articles - Star Lifting: Colonizing the Stars and the Galaxies Figure 2 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9015faee6eb0728acd21e2/5c9015faee6eb0728acd21e3/1552959594319/neil-blevins-megastructures-7-star-lifter-3d-sketch.jpg Articles - Star Lifting: Colonizing the Stars and the Galaxies - Star Lifting “A star lifter removes mass from a star for either raw materials or to change the nature of the star itself. For example, you may remove mass from the star to collect hydrogen or other elements. Or you could remove mass in order to extend the life of the star, to make the star dimmer, or reduce the chances of a super nova.” Artwork by Neil Blevins from Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9015faee6eb0728acd21fa/1552864521733/Von-Neumann-Probe.jpg Articles - Star Lifting: Colonizing the Stars and the Galaxies Concept art by Mark Molnar https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9015faee6eb0728acd21f8/1552862976200/lzlsart9qi311%5B1%5D.jpg Articles - Star Lifting: Colonizing the Stars and the Galaxies Nicoll-Dyson Beam “Unleashing The Nicoll-Dyson Beam from Gigastructural Engineering & More. Inward Perfection has never been so easy when you can delete your enemies Capital systems with the press of a button. Edit: It also has multiple settings. Ranging from reducing all infrastructure to rubble to Solar System Deleter.” Image retrieved from: https://www.reddit.com/r/Stellaris/comments/8qgwe9/fear_me_for_i_am_your_apocalypse/ https://www.gregschool.org/new-blog/string-theory-and-colonizing-the-multiverse-mbzy6-94szd monthly 0.5 2019-03-21 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fac0c83025f04d004da3/1552974215990/universeismath.jpg Articles - String Theory and Colonizing the Multiverse https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c92fac0c83025f04d004d9f/5c92fac0c83025f04d004da0/1536805148903/gateway_hub_04_by_lorddoomhammer-d9u3226.png Articles - String Theory and Colonizing the Multiverse https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fac0c83025f04d004da5/1553057433719/four_forces%5B1%5D.jpg Articles - String Theory and Colonizing the Multiverse Image Credit: https://physicswithsampurkis.files.wordpress.com/2014/01/four_forces.jpg https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fac0c83025f04d004dab/1541982430321/shutterstock_84250684.jpg Articles - String Theory and Colonizing the Multiverse Our universe may be one of many, physicists say. Credit: Shutterstock/Victor Habbick https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fac0c83025f04d004daf/1553060137245/CERN_LHC%5B1%5D.jpg Articles - String Theory and Colonizing the Multiverse The image above shows a section of the LHC (Large Hadron Collider). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fac0c83025f04d004da9/1553058165874/crystal_to_string%5B1%5D.jpg Articles - String Theory and Colonizing the Multiverse The image above shows how various different small objects compare to each other in terms of size. Image retrieved from: http://www.particlecentral.com/strings_page.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fac0c83025f04d004db1/1553060486672/matrioshka+brainnnn.png Articles - String Theory and Colonizing the Multiverse “A matrioshka brain is a hypothetical megastructure proposed by Robert Bradbury, based on the Dyson sphere, of immense computational capacity. It is an example of a Class B stellar engine, employing the entire energy output of a star to drive computer systems.”\(^{[2]}\) Image from Steve Bowers https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fac0c83025f04d004dad/1553060002632/LeonardSusskindStanford2009_cropped%5B1%5D.jpg Articles - String Theory and Colonizing the Multiverse Leonard Susskind https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fac0c83025f04d004da7/1553057859737/calabi-yau7%5B1%5D.gif Articles - String Theory and Colonizing the Multiverse “String Theory predicts the existence of more than the 3 space dimensions and 1 time dimension we are all familiar with. According to string theory, there are additional dimensions that we are unfamiliar with because they are curled up into tiny complicated shapes that can only be seen on tiny scales. If we could shrink to this tiny, Planck-sized scale we could see that at every 3D point in space, we can also explore 6 additional dimensions. This animation shows an array of Calabi-Yau spaces which are projections of these higher dimensions into the more familiar dimensions we are aware of.”\(^{[1]}\) https://www.gregschool.org/classical-mechanics daily 0.75 2018-07-04 https://www.gregschool.org/classical-mechanics/2017/5/14/rotational-kinematics monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf83c59cc688076b7fdd1/1507588166242/gfnf.jpg Oscillatory and rotational motion - Rotational Kinematics https://www.gregschool.org/classical-mechanics/2017/5/14/torque monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf930c027d89dcc0d2228/1507588404050/gfnf.jpg Oscillatory and rotational motion - Torque https://www.gregschool.org/classical-mechanics/2017/5/14/introduction-to-rotational-kinetic-energy monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf8b9197aeaa9a58d0716/1507588284735/gfnf.jpg Oscillatory and rotational motion - Introduction to Rotational Kinetic Energy https://www.gregschool.org/classical-mechanics/2017/5/14/4ufuuy7fweohxl2tk6hryzmsq50amd monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf78990badec5d2319ab7/1507587980466/gfnf.jpg Oscillatory and rotational motion - Introduction to Mechanical Waves https://www.gregschool.org/classical-mechanics/category/Classical+Mechanics monthly 0.5 https://www.gregschool.org/electromagnetism daily 0.75 2017-09-06 https://www.gregschool.org/electromagnetism/2017/5/14/columns-law monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc434d32601e9d148bf0b6/1507607378489/electromagnetism+thumbnaillllll+imageeee.jpg Electromagnetism - Column's Law https://www.gregschool.org/electromagnetism/2017/5/14/electric-flux monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc3ee0914e6b12a393fde8/1507606244584/electromagnetism+thumbnaillllll+imageeee.jpg Electromagnetism - Electric Flux https://www.gregschool.org/electromagnetism/2017/6/20/derivation-of-guasss-law-from-columns-law monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc41027131a52388a3d5dc/1507606793199/electromagnetism+thumbnaillllll+imageeee.jpg Electromagnetism - Derivation of Guass's Law from Column's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5983b6ff1e5b6c1be89f919b/1504719682344/ Electromagnetism - Derivation of Guass's Law from Column's Law Figure 2 (click to enlarge) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5983af90ebbd1ab6e030c458/1504719682340/guass.jpg Electromagnetism - Derivation of Guass's Law from Column's Law Figure 1 (click to enlarge) https://www.gregschool.org/electromagnetism/2017/7/20/using-guasss-law-to-find-the-electric-field-produced-by-a-single-point-charge monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5983ba441e5b6c1be89fc0fe/1504719696428/ Electromagnetism - Using Guass's Law to find the Electric Field Produced by a Single Point Charge Figure 2 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5983c1f2f7e0ab6f61d65054/1504719696432/ Electromagnetism - Using Guass's Law to find the Electric Field Produced by a Single Point Charge Figure 3 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc41392994ca84b39c5432/1507606855719/electromagnetism+thumbnaillllll+imageeee.jpg Electromagnetism - Using Guass's Law to find the Electric Field Produced by a Single Point Charge https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5983b8899f745676d8a84980/1504719696421/guass.jpg Electromagnetism - Using Guass's Law to find the Electric Field Produced by a Single Point Charge Figure 1 https://www.gregschool.org/special-relativity daily 0.75 2017-09-06 https://www.gregschool.org/special-relativity/2017/5/14/introduction-to-special-relativity monthly 0.5 2017-11-09 https://www.gregschool.org/special-relativity/2017/5/14/8c5knwf9nztiio7uwnvvotz1pj86ht monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/598d0d3ea803bb1ee4694f07/1504673327843/ Special Relativity - Time Dilation Figure 1 https://www.gregschool.org/cosmology daily 0.75 2017-11-08 https://www.gregschool.org/cosmology/2017/5/14/dark-matter monthly 0.5 2017-11-11 https://www.gregschool.org/cosmology/2017/5/14/bentleys-and-olbers-paradoxes monthly 0.5 2017-11-10 https://www.gregschool.org/cosmology/2017/5/14/cosmic-microwave-background-radiation monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59193ff4893fc0567ac5bcf7/1504672850810/ Cosmology - Cosmic Microwave Background Radiation https://www.gregschool.org/cosmology/2017/5/14/surface-of-last-scattering monthly 0.5 2017-11-11 https://www.gregschool.org/cosmology/2017/5/14/dark-energy monthly 0.5 2017-11-11 https://www.gregschool.org/cosmology/2017/5/14/friedman-robertson-walker-frw-equation monthly 0.5 2017-11-11 https://www.gregschool.org/cosmology/2017/5/14/spectroscopy monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59194323be659485a8d5abe4/1504672500784/ Cosmology - Spectroscopy https://www.gregschool.org/cosmology/2017/5/14/xe30zrw2tke0y051q8xdpf9cxaff19 monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5919442515cf7d45e9761c26/1504672412824/ Cosmology - Scaling Factor, Hubble's Parameter, and the Age of the Universe https://www.gregschool.org/cosmology/2017/5/23/g76bh7ssk8up16r4w2ptuwsm37kpho monthly 0.5 2017-11-06 https://www.gregschool.org/cosmology/2017/5/14/solving-the-frw-equation-for-the-scaling-factor-in-different-scenarios-hdsrg-x7nsb monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a007a5c8165f5ff004353ad/1509937688558/AT_7e_Figure_27_01%5B2%5D.jpg Cosmology - Solving the FRW Equation for the Scaling Factor in different scenarios Figure 1: As you can see from the graph above, for the first roughly 10,000 years most of the energy density in the universe was due to the presence of radiation. During the time interval from when the universe was 10,000 years old to when it was several billion years old, the energy density of the universe was dominated by matter. In our present epoch, the energy density of the universe is dominated by dark energy (or vacuum energy). This graph has profound implications. As time progresses, dark energy will become more and more dominant and will remain the dominant source of energy in the universe; since dark energy causes everything in the universe to expand, the universe will continue to expand without ever stopping. This graph, essentially, implies the ultimate fate of the universe. The universe will continue to expand more and more until it becomes dark, empty, and lifeless. https://www.gregschool.org/cosmology/2017/5/14/genesis-of-the-elements-xz53h-yww35 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a032d3b24a69487b355d17d/1509985102690/ Cosmology - Genesis of the Elements Figure 3: The Alpha-Beta-Gamma paper demonstrated that after the first roughly three minutes of the universe since its initial Bang, hydrogen and helium nuclei were synthesized via nuclear fusion. After about three minutes, the universe cooled enough for fusion to stop; but the universe was still so hot that all of the matter comprising the universe was a plasma and plasma's are opaque to radiation. The matter comprising the universe was in a plasma state for the first roughly 300,000 years since the Big Bang; since plasma is opaque to radiation, for the first roughly 300,000 years light could not freely travel throughout the universe without constantly "bumping into stuff (atomic nuclei)." At sometime when the universe was about 300,000 to 400,000 years old, matter cooled enough for electrons to bind to atomic nuclei and for light to freely pass through the universe. Due to the expansion of space, Alpher and Herman estimated that wavelengths of this light should now be stretched into the microwave region. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a032d3b24a69487b355d17b/1509983399387/nuclear-fusion-stars%5B1%5D.png Cosmology - Genesis of the Elements Figure 2: All stars in the universe generate light and energy by fusing lighter elements into heavier elements. For stars up to the mass of about that of our Sun, light and energy is created by fusing hydrogen into helium. The image above illustrates the chain of nuclear reactions which occur in small to medium sized stars and very massive stars that allow them to generate light and energy. Stellar fusion accounts for where many of the light to medium-sized elements in the periodic table come from. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a032d3b24a69487b355d179/1509981827221/RutherfordGoilFoil+%281%29%5B1%5D.jpg Cosmology - Genesis of the Elements Figure 1: Rutherford's experiment involved putting a radioactive element known as radium inside of a lead box. The radium spontaneously emitted \(α\) particles in a narrow beam through a small hole in the box. These \(α\) particles were directed towards a gold foil. Most \(α\) particles passed straight through the gold foil but occasional one would get reflected back at an acute angle with the beam of \(α\) particles. This meant that atoms must have tiny, but very dense, nuclei. Image credit: http://m.teachastronomy.com/astropedia/article/The-Structure-of-the-Atom https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a032d3b24a69487b355d17f/1509987202844/ Cosmology - Genesis of the Elements Figure 4: As a star undergoes nuclear fusion in its core, it generates light. This light exerts an outward radiation pressure on the star which balances the inward gravitational forces that tend to pull the star's matter towards its center. But at the end of a star's life, nuclear fusion begins to slow down and eventually stop; this means that there is no outward radiation pressure to balance the gravitational forces exerted on the outward layers of the star and star eventually collapses. If the star is very massive, such a collapse will result in one of the most spectacular events in the universe: a supernova. The energy generated by a supernova explosion is so stupendous that it results in nuclear reactions which create the heavier elements in the period table. https://www.gregschool.org/quantum-mechanics daily 0.75 2017-11-08 https://www.gregschool.org/quantum-mechanics/2017/5/14/quantum-dynamics monthly 0.5 2017-11-11 https://www.gregschool.org/quantum-mechanics/2017/5/14/how-initial-states-of-definite-energy-change-with-time monthly 0.5 2017-11-11 https://www.gregschool.org/quantum-mechanics/2017/5/15/particle-in-one-dimensional-box monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/592479e7c534a50553d99559/1504671394203/sch.png Schrodinger's Equation - Time-Independant Schrodinger Equation: Free Particle and Particle in One-Dimensional Box Figure 2 (click to expand): The probability amplitude of measuring the particle at a position \(x\) in the presence of a potential \(V_0\) decreases exponentially with increasing \(V_0\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/591952af1b10e3f7ad2c98e2/1504671394205/ Schrodinger's Equation - Time-Independant Schrodinger Equation: Free Particle and Particle in One-Dimensional Box Figure 3 (click to expand): Illustration of a free particle moving in a one-dimensional box which is "pinned down" by a finite well. The probability amplitude of finding the particle outside of the box decreases exponentially as a function of distance. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/592354ce6b8f5b37844cd500/1504671394207/ Schrodinger's Equation - Time-Independant Schrodinger Equation: Free Particle and Particle in One-Dimensional Box Figure 4: Illustration shows the allowed energy levels of a particle trapped inside of a one-dimensional box. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/592351e99de4bb9c550b497d/1504671394201/kjkjnj.png Schrodinger's Equation - Time-Independant Schrodinger Equation: Free Particle and Particle in One-Dimensional Box Figure 1 (click to expand): Illustration of a free particle moving in a "one-dimensional box" which is trapped inside of an infinite potential well. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59234aac03596ed573bce9ab/1504671394198/ Schrodinger's Equation - Time-Independant Schrodinger Equation: Free Particle and Particle in One-Dimensional Box "A wave function that satisfies the nonrelativistic Schrödinger equation with V = 0. In other words, this corresponds to a particle traveling freely through empty space. The real part of the wave function is plotted here."\(^{[1]}\) https://www.gregschool.org/quantum-mechanics/2017/5/15/time-evolution-of-state-vectors monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a026d3bf9619a62ab661666/1510108644648/photon_double_slit2%5B1%5D.gif Schrodinger's Equation - Schrodinger's Time-Dependent Equation: Time-Evolution of State Vectors Figure 2: Schrodinger's equation is deterministic because the past or future quantum state \(|\psi(t)⟩\) of a quantum system can be determined with infinite precision. But, in general, a quantum system can be in a superposition of many different states where the measurement of any physical quantity is uncertain. For example, if anything the size of a small molecule or smaller passes through a double-slit in a double-slit experiment, where it hits the screen (which is to say, its final position) is uncertain (see illustration above). The quantum state of a quantum system is deterministic; but the eigenvalue that you'll measure after an experiment is done is the quantity which is not deterministic in quantum mechanics. Source: http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec13.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0267fc652dea4ceb34e37d/1510108644645/1_Lwu5UJMmcuFVJLZ1Ln4E0Q%5B1%5D.png Schrodinger's Equation - Schrodinger's Time-Dependent Equation: Time-Evolution of State Vectors Figure 1: The motion of a simple pendulum is an example of the time-reversibility of Newton's second law. Given the initial state of the pendulum, Newton's second law can be used to determine the past or future state of the system. For example, one could determine the velocity and position of the pendulum at any past or future time given its present state. https://www.gregschool.org/quantum-mechanics/2017/5/15/periodic-wavefunctions-that-is-ones-that-come-back-to-themselves-have-quantized-eigenvalues-of-momenta-and-angular-momenta-2k3el-yckar monthly 0.5 2017-11-09 https://www.gregschool.org/lagrangian-mechanics daily 0.75 2017-09-06 https://www.gregschool.org/lagrangian-mechanics/2017/5/18/v7t2klwmycopiblvbhzkhyw2duujqy monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf9d54c326dbd25b2fb3d/1507588569155/gfnf.jpg Lagrangian Mechanics - Introduction to Lagrangian Mechanics https://www.gregschool.org/lagrangian-mechanics/2017/5/18/derivation-of-the-euler-lagrange-equation monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf9ebbce176a8031ed1af/1507588588939/gfnf.jpg Lagrangian Mechanics - Derivation of the Euler-Lagrange Equation https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59207875a5790a9f652af8b8/1504719745581/ Lagrangian Mechanics - Derivation of the Euler-Lagrange Equation Figure 1 (click to expand) https://www.gregschool.org/lagrangian-mechanics/2017/5/18/finding-the-geodesic-on-a-cylinder monthly 0.5 2019-02-22 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbfa0046c3c48d677653bb/1507588614077/gfnf.jpg Lagrangian Mechanics - Finding the geodesic on a cylinder https://www.gregschool.org/lagrangian-mechanics/2017/5/18/brachistochrone-problem monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5920889cbe659438f080cba9/1504719809377/ Lagrangian Mechanics - Brachistochrone problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/592088d1cd0f6872c792b474/1504719809380/ Lagrangian Mechanics - Brachistochrone problem Credit\(^{[3]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5920887d6a49635fddd51175/1504719809373/ Lagrangian Mechanics - Brachistochrone problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbfa1751a58476eaac9b16/1507588635069/gfnf.jpg Lagrangian Mechanics - Brachistochrone problem https://www.gregschool.org/lagrangian-mechanics/2017/5/18/generalized-coordinates monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbfb558a02c75c23e526c9/1507588953954/gfnf.jpg Lagrangian Mechanics - Generalized coordinates https://www.gregschool.org/lagrangian-mechanics/2017/5/18/noethers-theorem monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbfb770abd045b7cc7c8ed/1507588997115/ Lagrangian Mechanics - Noether’s Theorem https://www.gregschool.org/schrodingers-equation-1 daily 0.75 2017-11-08 https://www.gregschool.org/schrodingers-equation-1/2017/5/23/math-interlude monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc4da33e00bed1b429eea3/1507610028408/electromagnetism+thumbnaillllll+imageeee.jpg Introduction to Matrix Mechanics - Quantum Mechanics: Math Interlude https://www.gregschool.org/schrodingers-equation-1/2017/5/23/pauli-matrices monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc4cd0f7e0ab3dbb237c96/1507609811147/electromagnetism+thumbnaillllll+imageeee.jpg Introduction to Matrix Mechanics - Pauli Matrices https://www.gregschool.org/schrodingers-equation-1/2017/5/23/measuring-the-spin-of-an-electron monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc4ca951a58476eab05ece/1507609773311/electromagnetism+thumbnaillllll+imageeee.jpg Introduction to Matrix Mechanics - Measuring the Spin of an Electron https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/592483b1be6594a48944dd65/1504671946323/ Introduction to Matrix Mechanics - Measuring the Spin of an Electron Figure 1 https://www.gregschool.org/schrodingers-equation-1/2017/5/23/the-eigenvalues-of-any-observable-hatl-must-be-real monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc4c37e5dd5b5a1b4d44f6/1507609663099/electromagnetism+thumbnaillllll+imageeee.jpg Introduction to Matrix Mechanics - The Eigenvalues of any Observable \(\hat{L}\) must be Real https://www.gregschool.org/schrodingers-equation-1/2017/5/23/fundamental-principles-and-postulates-of-quantum-mechanics monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc4c10d2b857fa05900fea/1507609620648/electromagnetism+thumbnaillllll+imageeee.jpg Introduction to Matrix Mechanics - Fundamental Principles and Postulates of Quantum Mechanics https://www.gregschool.org/schrodingers-equation-1/2017/5/23/calculating-the-wavefunction-collection-of-probability-amplitudes-associated-with-any-ket-vector-skh4m monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc4eb446c3c48d677a2328/1510112458035/electromagnetism+thumbnaillllll+imageeee.jpg Introduction to Matrix Mechanics - Calculating the Wavefunction Associated with any Ket Vector https://www.gregschool.org/schrodingers-equation-1/2017/5/23/the-eigenvectors-of-any-hermitian-operator-must-be-orthogonal-w2jps-sthp6 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a02748208522983b18ac7f8/1507610259512/electromagnetism+thumbnaillllll+imageeee.jpg Introduction to Matrix Mechanics - The Eigenvectors of any Hermitian Operator must be Orthogonal https://www.gregschool.org/cosmology2 daily 0.75 2017-09-06 https://www.gregschool.org/cosmology2/2017/5/27/origin-of-structure-and-clumpyness monthly 0.5 2017-11-11 https://www.gregschool.org/new-blog-2 daily 0.75 2019-03-23 https://www.gregschool.org/new-blog-2/2017/9/25/colonizing-and-terraforming-venus-59y59 monthly 0.5 2018-04-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac95be42b6a289d089bfdfd/1523144026480/Twitter+thumbnail_preview.jpg Articles Page 2 - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac95c22562fa799825cb6ef/1523146982511/share+b.jpg Articles Page 2 - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac95be42b6a289d089bfe01/1523144044465/email+thumbnail_preview.jpg Articles Page 2 - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac95be42b6a289d089bfe05/1508644545185/1.10-1024x768.jpg Articles Page 2 - Colonizing and Terraforming Venus Artist concept of lightning on Venus. Image credit: ESA https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac95be42b6a289d089bfe07/1507060053549/venus-cloud-city.jpg Articles Page 2 - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac95be42b6a289d089bfdff/1523144061656/google+share+thumbnail_preview.jpg Articles Page 2 - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac95be42b6a289d089bfdfb/1523144015110/facebook+thumbnail.jpg Articles Page 2 - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac95be42b6a289d089bfe09/1510882341344/TerraformedVenus%5B1%5D.jpg Articles Page 2 - Colonizing and Terraforming Venus "A conceptual picture I made of Venus if it were terraformed. (Credit: Daein Ballard) Notice the interesting cloud formations and that the planet has polar caps. I decided to show the planet this way after studying Venus' atmosphere. The two Hadley cells the planet has stop at 70 degrees north and south. So the polar regions are cut off from the warm air. Also the slow rotation of the planet causes the clouds to whip around the planet very fast, especially at the equator, to balance out the temperature difference between day and night sides of the planet."\(^{[5]}\) Image credit: Ittiz at the English language Wikipedia [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac95be42b6a289d089bfe03/1523144000964/space+colon+author+date.jpg Articles Page 2 - Colonizing and Terraforming Venus https://www.gregschool.org/new-blog-2/2017/11/2/gravitational-force-exerted-by-a-rod-zf4pf monthly 0.5 2018-04-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb886a8a922dc773e2f7e7/1523287857170/classical+mechanics+thumbnail.png Articles Page 2 - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb886a8a922dc773e2f7dd/1523288053202/sharee.png Articles Page 2 - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb886a8a922dc773e2f7df/1523287944108/facebook+thumbnail.jpg Articles Page 2 - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb886a8a922dc773e2f7e5/1523287964387/email+thumbnail.jpg Articles Page 2 - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb886a8a922dc773e2f7e9/1509666905146/rod.png Articles Page 2 - Gravitational Force Exerted by a Rod Figure 1: A rod of mass \(M\) and a particle of mass \(m\) are separated from each other by a distance of \(d\) along the \(x\)-axis. Each mass element \(dm\) comprising the rod is located at some position \(x\) along the \(x\)-axis and is separated from the particle \(m\) by some amount \(r\). By summing all the gravitational forces \(d\vec{F}_g\) exerted by each mass element \(dm\) comprising the rod, we can find the total gravitational force exerted on \(m\) by the entire rod. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb886a8a922dc773e2f7e3/1523287988805/google+share+thumbnail.jpg Articles Page 2 - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb886a8a922dc773e2f7e1/1523288004050/Twitter+thumbnail.jpg Articles Page 2 - Gravitational Force Exerted by a Rod https://www.gregschool.org/new-blog-2/2018/6/12/01kbzrqg971y7cr7mw0lgnob5i1y43 monthly 0.5 2018-07-19 https://www.gregschool.org/new-blog-2/2017/11/14/drakes-equation-d4hkm monthly 0.5 2018-07-19 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117cc1ae6cfef2ad2178b/1510779852179/75C0D4ADBC26486DAD4D19D3CBCEB9E1%5B1%5D.jpg Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way "Mr. Spock (Leonard Nimoy), communicating with the Horta through a Vulcan mind meld."\(^{[3]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117cc1ae6cfef2ad217a5/1511020696659/qiao-chen-ship9-3%5B1%5D.jpg Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way An artist's depiction of the starship proposed by Project Daedalus.\(^{[5]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117cc1ae6cfef2ad21785/1531967513017/email+img+thumbnail.jpg Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117cc1ae6cfef2ad21797/1531769943991/pular+planet.png Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way Artist's depiction of an exoplanet orbiting a pulsar. Due to the pulsar's radiation, the exoplanet glows. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b5117cc1ae6cfef2ad2178d/5b5117cc1ae6cfef2ad21792/1510878250166/20131102_cosmos-episode-2-hfs-herd-of-floaters%5B1%5D.jpg Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way A Lazy Herd of Floaters "An updated digital restoration by Adolf Schaller of detail in his original Hunters, Floaters, Sinkers mural which appeared on Cosmos, Episode 2, which speculates about life in the atmosphere of a gas-giant planet."\(^{[4]}\) Image by Adolf Schaller. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b5117cc1ae6cfef2ad2178d/5b5117cc1ae6cfef2ad2178e/1510878224307/20131102_cosmos-episode-2-jovian-life-full%5B1%5D.jpg Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way Hunters, Floaters, and Sinkers "This painting speculates about possible forms of life on a Jupiter-like gas giant. Airbrushed water-based acrylic."\(^{[4]}\) Image by Adolf Schaller. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b5117cc1ae6cfef2ad2178d/5b5117cc1ae6cfef2ad21794/1510878262303/20131102_cosmos-episode-2-hfs-a-hunter-close-up%5B1%5D.jpg Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way A Hunter "A speculative hunter animal evolved in the atmosphere of a gas-giant planet. Developed for Cosmos, Episode 2."\(^{[4]}\) Image by Adolf Schaller. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b5117cc1ae6cfef2ad2178d/5b5117cc1ae6cfef2ad21790/1510878236692/20131102_cosmos-episode-2-hfs-floater-close-up%5B1%5D.jpg Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way A "Floater" from Cosmos, Episode 2 "Part of the larger mural, "Hunters, Floaters, and Sinkers" painted for the series."\(^{[4]}\) Image by Adolf Schaller. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117cc1ae6cfef2ad2177f/1531967492944/facebook+img+thumbnail.jpg Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117cc1ae6cfef2ad21783/1531967526142/ Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117cc1ae6cfef2ad2179d/1510868724096/Heic0612b_H%5B1%5D.jpg Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way Artist's depiction of an exoplanet crossing our line of sight in front of its home-star. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117cc1ae6cfef2ad2177d/1531967467107/share+astronomy+and+cosmology+img.png Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117cc1ae6cfef2ad21799/1510874187182/Habitable-zone%5B1%5D.jpg Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way The habitable zone is a range of orbital distances (between an exoplanet and the star it orbits) where the planet is neither too hot nor too cold. This is also sometimes called the Goldilocks zone. In order for a planet to be truly "Earth-like," it must also have a mass 1-2 times that of the Earth, have an atmosphere, and orbit in a stable elliptical orbit that is not too essentric. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117cc1ae6cfef2ad21781/1531967540634/twiiter+img+thumbnail.jpg Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b5117cc1ae6cfef2ad2179f/5b5117cc1ae6cfef2ad217a2/1510875294374/HT-trappist-1-star-surface-3-jt-170221_4x3_992%5B1%5D.jpg Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way Imagine standing on the surface of the exoplanet TRAPPIST-1f. This artist's concept is one interpretation of what it could look like. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b5117cc1ae6cfef2ad2179f/5b5117cc1ae6cfef2ad217a0/1510875160635/proximasurface%5B1%5D.jpg Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way "This artist’s impression shows a view of the surface of the planet Proxima b orbiting the red dwarf star Proxima Centauri, the closest star to the solar system. The double star Alpha Centauri AB also appears in the image. Proxima b is a little more massive than the Earth and orbits in the habitable zone around Proxima Centauri, where the temperature is suitable for liquid water to exist on its surface."\(^{[1]}\) https://www.nasa.gov/feature/jpl/eso-discovers-earth-size-planet-in-habitable-zone-of-nearest-star Credits: ESO/M. Kornmesser https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117cc1ae6cfef2ad2179b/1510874927808/Kepler_spacecraft_artist_render_%28crop%29%5B1%5D.jpg Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way Artist's depiction of the Kepler space telescope. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117cc1ae6cfef2ad21787/1531967435336/astronomy+and+cosmology+thumbnail.png Articles Page 2 - Drake's Equation and Searching for Life in the Milky Way https://www.gregschool.org/new-blog-2/2017/9/24/introduction-to-double-integrals-1-9ekxy-2wbc7 monthly 0.5 2018-04-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac977bc88251b5348353fe6/1509398380899/riemann_boxes_m.jpg Articles Page 2 - Introduction to Double Integrals Figure 1: When we were deriving an expression for the definite integral in terms of the Riemann sum, we first approximated the area underneath \(f(x)\) by summing the areas of many very skinny rectangles as illustrated in (A). To define a double integral in terms of a Riemann sum, we first approximate the volume underneath a surface by summing the volumes of many very skinny columns as depicted in (C). The width and depth of each column is given by \(Δx\) and \(Δy\) and the height of each rectangle is given by the surface \(f(x,y)\) as shown in (B). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac977bc88251b5348353fe8/1507232588323/partial+der.jpg Articles Page 2 - Introduction to Double Integrals Figure 2: The volume underneath the surface \(f(x,y)\) can be approximated by summing the volumes of an \(nm\) number of columns underneath the surface. As these columns become infinitesimally skinny and as the number \(nm\) of them approaches infinity, this sum gives the exact volume underneath the surface \(f(x,y)\). https://www.gregschool.org/new-blog-2/2017/10/30/gravitational-force-exerted-by-a-sphere-rdyjt monthly 0.5 2018-09-14 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca5450f950b7425205c06e/1523208400289/google+share+thumbnail.jpg Articles Page 2 - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca5450f950b7425205c072/1523204866420/sphere+force.png Articles Page 2 - Gravitational Force Exerted by a Sphere Figure 1: A shell can be subdivided into many very skinny rings. Anyone of these rings can be represented by the ring \(QRR_1Q_1\) illustrated above. Image credit\(^{[1]}\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca5450f950b7425205c06a/1523208340227/Twitter+thumbnail.jpg Articles Page 2 - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca5450f950b7425205c070/1523208206453/classical+mechanics+thumbnail.png Articles Page 2 - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca5450f950b7425205c06c/1523208363916/email+thumbnail.jpg Articles Page 2 - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca5606575d1fd3933db43d/1523217470590/sharee.png Articles Page 2 - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca5450f950b7425205c068/1523208313862/facebook+thumbnail.jpg Articles Page 2 - Gravitational Force Exerted by a Sphere https://www.gregschool.org/new-blog-2/2017/9/30/proof-of-greens-theorem-4kbde monthly 0.5 2018-06-28 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b34709caa4a993c621b4aee/1530156044345/share+calculus+img.png Articles Page 2 - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b34709caa4a993c621b4afe/1530155160565/images.png Articles Page 2 - Proof of Green's Theorem Figure 3: We can break up the curve \(c\) into the two separate curves, \(c_1\) and \(c_2\). This also allows us to break up the function \(x(y)\) into the two separate functions, \(x(y_1)\) and \(x(y_2)\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b34709caa4a993c621b4af8/1530156011880/Calculus+thumbnail.png Articles Page 2 - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b34709caa4a993c621b4af2/1530162636743/twiiter+img+thumbnail.jpg Articles Page 2 - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b34709caa4a993c621b4afc/1530147999505/images.png Articles Page 2 - Proof of Green's Theorem Figure 2: We can split the curve \(c\) into two separate curves, \(c_1\) and \(c_2\). This also allows us to split the function \(y(x)\) into the two separate functions, \(y(x_1)\) and \(y(x_2)\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b34709caa4a993c621b4af0/1530156381931/facebook+img+thumbnail.jpg Articles Page 2 - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b34709caa4a993c621b4af4/1530156441620/google+img+thumbnail.jpg Articles Page 2 - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b34709caa4a993c621b4afa/1506810526998/429px-Green%27s-theorem-simple-region.svg.png Articles Page 2 - Proof of Green's Theorem Figure 1: The curve \(C=C_1+C_2+C_3+C_4\) is piece-wise smooth. It is "piece-wise" because it is split up into an \(n=4\) number of separate curves with an \(n=4\) number of "edges." It is "smooth" because each individual curve itself is smooth without any sharp edges or cusps. This curve is also positively-oriented because its direction goes counter-clockwise. Image by Cronholm 144. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b34709caa4a993c621b4af6/1530157315746/email+img+thumbnail.jpg Articles Page 2 - Proof of Green's Theorem https://www.gregschool.org/new-blog-2/2018/6/20/the-diversity-of-exoplanets-in-the-galaxy-me459 monthly 0.5 2018-07-19 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd225/1530138555487/maxresdefault.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy Image of auroras just above the Earth's surface obtained by the International Space Station. Image credit: NASA https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b51175f758d46a40f4dd213/5b51175f758d46a40f4dd214/1530133614272/image_4610_3e-Europa-Lander%5B1%5D.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b51175f758d46a40f4dd213/5b51175f758d46a40f4dd218/1530135817506/PIA19656-SaturnMoon-Enceladus-Ocean-ArtConcept-20150915%5B2%5D.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b51175f758d46a40f4dd213/5b51175f758d46a40f4dd216/1530135242345/PIA19058-SaturnMoon-Enceladus-PossibleHydrothermalActivity-ArtistConcept-20150311%5B2%5D.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy Artists impressions of subsurface oceans underneath thick ice sheets on Jupiter’s moon Europa and Saturn’s moon Enceladus. Top image by NASA. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd223/1530236766508/Graphite-and-diamond-with-scale%5B1%5D.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy Graphite (left) and diamond (right) are both, essentially, just made up of a bunch of carbon atoms. The difference between the two substances is how those carbon atoms are arranged. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd20d/1531966570270/email+img+thumbnail.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd227/1530042426129/aHR0cDovL3d3dy5zcGFjZS5jb20vaW1hZ2VzL2kvMDAwLzAzOC81ODAvb3JpZ2luYWwva2VwbGVyLTE4NmYtYXJ0LmpwZz8xMzk3Njg3MTkw%5B1%5D.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy Artist's impression of the Archipelago world, Kepler 186f. Credit: Danielle Futselaar https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd22f/1530743975575/trappist.png Articles Page 2 - The Diversity of Exoplanets in the Galaxy This artist's concept shows what the TRAPPIST-1 planetary system may look like, based on available data about the planets' diameters, masses and distances from the host star. Credits: NASA/JPL-Caltech View full image and caption https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd211/1531960026632/10629328_1041033252591158_1987130945153076812_o.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd22b/1530306062728/PIA21061-Pluto-DwarfPlanet-XRays-20160914%5B1%5D.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy X-ray image of Pluto obtained by Chandra X-Ray Observatory (blue spot on right) and up-close photograph of Pluto obtained by the spacecraft Deep Horizons as it flew by Pluto. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd206/1531966586224/facebook+img+thumbnail.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd221/1530305727092/aHR0cDovL3d3dy5zcGFjZS5jb20vaW1hZ2VzL2kvMDAwLzA1My8yNjkvb3JpZ2luYWwvc3VwZXItZWFydGgtY2FuY3JpLTU1LWUuanBn%5B1%5D.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy Artist's depiction of the exoplanet 55 Cancri E. Image credit: ESA/Hubble [CC BY 4.0 (https://creativecommons.org/licenses/by/4.0)], via Wikimedia Commons. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd20a/1531966612320/google+img+thumbnail.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd21f/1530132981476/Planets_everywhere_%28artist%E2%80%99s_impression%29%5B1%5D.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy "This artist's cartoon view gives an impression of how common planets are around the stars in the Milky Way. The planets, their orbits and their host stars are all vastly magnified compared to their real separations. A six-year search that surveyed millions of stars using the microlensing technique concluded that planets around stars are the rule rather than the exception. The average number of planets per star is greater than one."\(^{[1]}\) Image credit: by ESO/M. Kornmesser (http://www.eso.org/public/images/eso1204a/) [CC BY 4.0 (https://creativecommons.org/licenses/by/4.0)], via Wikimedia Commons https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd22d/1531960599987/2159_TRAPPIST-1e_1200_preview%5B1%5D.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy This poster imagines what a trip to TRAPPIST-1e might be like. Credits: NASA/JPL-Caltech View full image https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd204/1531966550594/share+astronomy+and+cosmology+img.png Articles Page 2 - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd229/1530047402295/1920px-Kepler186f-ComparisonGraphic-20140417%5B1%5D.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy Size comparison of Kepler-186f (artist's impression) with Earth along with their projected habitable zones. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd20f/1531966283722/astronomy+and+cosmology+thumbnail.png Articles Page 2 - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd208/1531966632845/twiiter+img+thumbnail.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd21d/1529888319405/aHR0cDovL3d3dy5zcGFjZS5jb20vaW1hZ2VzL2kvMDAwLzA2Mi8wODkvb3JpZ2luYWwvaG90LWp1cGl0ZXItY29uY2VwdGlvbi5qcGc%3D%5B1%5D.jpg Articles Page 2 - The Diversity of Exoplanets in the Galaxy Artist's depiction of a so-called hot Jupiter orbiting its planet star. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b51175f758d46a40f4dd21b/1531436786142/pular+planet.png Articles Page 2 - The Diversity of Exoplanets in the Galaxy Artist's conception of a planet orbiting a Pulsar. The Pulsar's radiation blasting the exoplanet would cause its surface to glow. https://www.gregschool.org/new-blog-2/2018/7/20/space-based-solar-power-3ptal-jreey-fh4ws monthly 0.5 2018-09-18 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf4ae/5b8b4e4b40ec9a2651daf4b1/1535827901771/hades__star___warp_lane_hub_by_gabriel_bs-db8y989.png Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System “Two hubs that can connect to create a temporary Warp Lane in your system The Warp Lane Hub can be connected to another Hub for one day, for a fixed Hydrogen cost. Once connected, ships can travel between the two end points instantly and without consuming Hydrogen.”\(^{[31]}\) Image credit: https://www.deviantart.com/gabrielbstiernstrom/art/Hades-Star-Warp-Lane-Hub-680163129 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf4ae/5b8b4e4b40ec9a2651daf4af/1535827892994/gateway_hub_04_by_lorddoomhammer-d9u3226.png Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s scifi depiction of a galactic empire using portals to travel across space.\(^{[30]}\) Image credit: https://www.deviantart.com/lorddoomhammer/art/Galactic-Network-594726702 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf40c/1535354571685/img_index_01.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "Since ancient times, people have always dreamed of going to space. Only astronauts have been able to go until now, but progress has been made on efforts to enable even private citizens to experience space, and space travel is finally about to become an industry. Shimizu foresaw the era of space travel early on, and has proposed a space hotel concept."\(^{[4]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf42c/1535568397254/13220830_239617033095862_8671672187626094751_n%5B1%5D.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf474/5b8b4e4b40ec9a2651daf475/1535356149316/espen-saetervik-rings.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of hoop worlds (also known as ring worlds). These megastructures can be built by building many adjacent orbital rings next to each other, side by side, and laying a surface down over those orbital rings. Image retrieved from https://www.iamag.co/espen-olsen-saetervik/espen-saetervik-rings/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf44a/5b8b4e4b40ec9a2651daf44b/1535827690138/earthring_1024.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of an orbital ring which appeared in Issue 7 of the magazine, All About Space. Image by Adrian Mann.\(^{[18]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf448/1535355196399/Kohlenstoffnanoroehre_Animation.gif Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Animation of a sheet of pure graphene rolled up into a carbon nanotube. Credit: https://commons.wikimedia.org/wiki/File:Kohlenstoffnanoroehre_Animation.gif https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf454/1535309881848/Nikola-Tesla.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Image above portrays Nikola Tesla, the famous inventor who first conceived of the notion of orbital rings in the 1870s shortly after recovering from malaria. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf470/1535738151212/Kepler_spacecraft_artist_render_%28crop%29%5B1%5D.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist's conception of the Kepler Space Telescope. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf456/5b8b4e4b40ec9a2651daf457/1535355930567/4304_1105960212_large_tiff.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf472/1535611314042/Oceanplanet_lucianomendez.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist's illustration of a hypothetical ocean planet with two natural satellites. Image credit: https://commons.wikimedia.org/wiki/File:Oceanplanet_lucianomendez.JPG https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf410/1535354657587/ Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Public Area "The public area would be assembled into a complex structure in the form of a truncated octahedron. It would have a great room consisting of a lobby, restaurant, entertainment room, and other spaces where people could enjoy a dining experience, sports, and a variety of amusements under low-gravity conditions."\(^{[4}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf412/5b8b4e4b40ec9a2651daf415/1535827243822/seattle_space_elevator_observatory_by_alterbr33d-d5j8j2p-750x375%402x%5B1%5D.png Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Space Elevator Depiction of a space elevator.\(^{[7]}\) Artwork retrieved from: http://prospective-tourisme.com/index.php/2017/08/10/entretien-laurent-queige-directeur-welcome-city-lab/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf412/5b8b4e4b40ec9a2651daf413/1535827236841/space-elevator%5B1%5D.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Space Elevator Depiction of a space elevator. Artwork by Glenn Clovis at Artstation.\(^{[6]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf450/1535309001976/Stanford_Torus_interior+highhd.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist's depiction of the interior of a Stanford torus. Painted by Donald E. Davis. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf490/5b8b4e4b40ec9a2651daf491/1535596948478/neil-blevins-megastructures-9-gas-giant-refinery-5%5B1%5D.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf430/1535609604928/c58d9cac14778ce30b60c5c6d63fee2a.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf478/1534192981008/shell+world.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "An engineer suggests building a roof over a small planet so that Earthlike conditions could be maintained."\(^{[26]}\) The Shell World could be used to maintain Earth-like conditions on the surface of an alien planet or moon; hanging cities could be suspended from the interior wall of the shell world; or the outer-surface of the Shell World could be engineered to closely resemble the Earth. Some combination of all of the above could be possible, albeit only to a certain extent. Credit: by Karl Tate, Infographics Artist https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf47a/1534192981013/cities+dangling+from+shell+world.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "Full cities could hang from the top of the shell that holds in the newly terraformed world's atmosphere."\(^{[27]}\) Image uploaded Oct. 7, 2013. Credit: Ken Roy/Tennessee Valley Interstellar Workshop https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf480/5b8b4e4b40ec9a2651daf485/1535351231677/ringworld.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Larry Niven's Ringworld. Image credit: https://bargainbin4u.wordpress.com/2008/07/14/ringworld-by-larry-niven/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf480/5b8b4e4b40ec9a2651daf481/1535350325687/ringworld_engineers_by_tomislavtikulin-db0bei8.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of a ring world. Image credit: https://www.deviantart.com/tomislavtikulin/art/Ringworld-Engineers-665659952 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf480/5b8b4e4b40ec9a2651daf483/1535350338882/halcyon_days_by_julian_faylona-d70cz32.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of a ring world. Image credit: https://www.deviantart.com/julian-faylona/art/Halcyon-Days-423868574 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf3f6/1535847641084/gggggggggggggggggggggggg.png Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf43e/5b8b4e4b40ec9a2651daf43f/1535488181201/Lunar_base_concept_drawing_s78_23252%5B1%5D.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Lunar Mass Driver Artist’s depiction of a lunar mass driver. The physicist Gerard K. O’Neil imagined using this device to electromagnetically launch lunar material into space for the purpose of being using to construct artificial space habitats for human residence and to move most industry off the Earth and into space. Image courtesy of NASA. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf43e/5b8b4e4b40ec9a2651daf441/1535488899287/moon+mass+drive-finished-jayproductspainting%5B1%5D.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Lunar Mass Driver Artist’s depiction of a Lunar mass driver. Artwork by Jay Wong. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf48c/5b8b4e4b40ec9a2651daf48d/1535483823007/jakub-grygier-005-matrioshka-brain-ab.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Matrioshka Brain Artist's impression of a Matrioshka Brain. Artwork by Jakub Grygier who is also a member of the SFIA production team. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf44e/1535355718877/med_bronx4.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "The inner and outer static orbital rings around Bronx are linked to a central geostationary ring by by carbon nanotube cables. The inner ring is only 265km above the clouds, while the outer ring is 75,600km from the planet's core."\(^{[19]}\) Image from Steve Bowers. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf418/1535328074668/405001%5B1%5D.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "The High Frontier: Human Colonies in Space is a 1976 book by Gerard K. O'Neill. It envisions large manned habitats in the Earth-Moon system, especially near stable Lagrangian points. Three designs are proposed: Island one (a modified Bernal sphere), Island two (a Stanford torus), and Island 3, two O'Neill cylinders. These would be constructed using raw materials from the lunar surface launched into space using a mass driver and from near-Earth asteroids. The habitats were to spin for simulated gravity and be illuminated and powered by the sun. Solar power satellites were proposed as a possible industry to support the habitats. The book won the 1977 Phi Beta Kappa Award in Science."\(^{[9]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf432/5b8b4e4b40ec9a2651daf439/1535329080141/neil-blevins-megastructures-7-star-lifter-1-b.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf432/5b8b4e4b40ec9a2651daf435/1535329245230/neil-blevins-megastructures-7-star-lifter-3d-sketch.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf432/5b8b4e4b40ec9a2651daf433/1535329173143/neil-blevins-megastructures-7-star-lifter-color-sketch.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf432/5b8b4e4b40ec9a2651daf437/1535329228095/neil-blevins-neil-blevins-megastructures-7-star-lifter-3.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf3f8/5b8b4e4b40ec9a2651daf3f9/1535343290369/sergio-botero-tflp-damocles-presentation-freight-cab-web.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf3f8/5b8b4e4b40ec9a2651daf3fd/1535343288243/sergio-botero-tflp-damocles-presentation-large-cab-dims.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf3f8/5b8b4e4b40ec9a2651daf403/1535343284499/sergio-botero-tflp-damocles-comp-1-v3-web.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf3f8/5b8b4e4b40ec9a2651daf405/1535343280086/sergio-botero-tflp-damocles-comp-5-web.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf3f8/5b8b4e4b40ec9a2651daf3ff/1535343280153/sergio-botero-tflp-damocles-comp-2-v1-web.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf3f8/5b8b4e4b40ec9a2651daf3fb/1535343280933/sergio-botero-tflp-damocles-presentation-large-cab-web.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf3f8/5b8b4e4b40ec9a2651daf407/1535343274958/sergio-botero-tflp-damocles-comp-3-web.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf3f8/5b8b4e4b40ec9a2651daf401/1535825798962/sergio-botero-tflp-damocles-comp-4-v1-web.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "Damocles is a large space port and elevator hub with stations fixed on [E]arth, located in an enormous, peaceful and very prosperous city, in a not-so-distant future.”\(^{[2]}\) In the year 2117 the most economical way to send people and cargo to outer space is using a space elevator. It’s not the quickest option but a very practical and effective one. Just like other similar Orbitowers placed on the Equator, the Damocles elevator hub provides this service. Space freight elevators are crucial to carry large components of interplanetary and the earlier interstellar vehicles into orbit, so they can be assembled in space instead of being launched by rockets. Autonomous trucks and cars arrive at the base’s ground to take passengers and cargo to the space elevator cabs. Flying vehicles land on the pads. The building itself is headquarters for many logistics companies, there are some offices and a hotel."\(^{[2]}\) Artwork by Sergio Botero at Artstation.\(^{[2]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf3f8/5b8b4e4b40ec9a2651daf409/1535343276062/sergio-botero-tflp-damocles-presentation-freight-cab-dims.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf424/1535327450524/glenn-clovis-spec-sheet-island-3-by-glennclovis-d5jj93n.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist's depiction of a Model 3 O'Neil cylinder which would be capable of supporting millions of a people, a complete biosphere, and all of the Earth's natural habitats. An O'Neil cylinder could also be used as an arc ship (sometimes also called a generation ship) to travel to other stars or galaxies. Image by Glenn Clovis from Artstation.\(^{[11]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf41a/5b8b4e4b40ec9a2651daf41f/1535827424197/Internal_view_of_the_O%27Neill_cylinder.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Solar eclipse inside an O'Neill cylinder\(^{[10]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf41a/5b8b4e4b40ec9a2651daf421/1535827420148/Spacecolony4.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Interior of an O'Neill cylinder\(^{[10]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf41a/5b8b4e4b40ec9a2651daf41b/1535827428335/Spacecolony3edit.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Interior of an O'Neill cylinder\(^{[10]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf41a/5b8b4e4b40ec9a2651daf41d/1535827414502/Spacecolony1.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System O'Neill cylinders\(^{[10]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf426/1535329695987/the-verge-lightfarm-studios.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf45e/1534192981005/ Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist's depiction of solar panels attached to a space elevator. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf444/5b8b4e4b40ec9a2651daf445/1535355566180/1492030052266.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of an orbital ring. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf4a8/5b8b4e4b40ec9a2651daf4a9/1535484695673/jeremy-jozwik-ia-coljupiter-comp2-raw-jpeg-0214.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Fusion Candles Artist's impression of Fusion Candles which could be used to move Jupiter and its moons across interstellar or even intergalactic space and away from our solar system. Spaceship Jupiter! Artwork by Jeremy Jozwik from Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf428/5b8b4e4b40ec9a2651daf429/1535827448497/space-colony-ix.png Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of an O’Neil cylinder. Artwork by Bruno Xavier.\(^{[12]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf460/1535610747216/med_venus2.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "Terraformed Venus is surrounded by a Dynamic Orbital Ring, mosty constructed from carbon extracted from its original atmosphere."\(^{[24]}\) Image by Steve Bowers. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf462/5b8b4e4b40ec9a2651daf46b/1535505977487/A2ljC-Qaok-kAJvzyNWu_Shimizu2%5B1%5D.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System The concept of the Ocean Spiral was first unveiled by Shimizu Corporation, in conjunction with Tokyo University and Japan Agency for Marine-Earth Science and Technology, in 2014. The company excepts it to take 5 years to build an Ocean Spiral. The company expects the project to cost ¥3 trillion (approximately £20 billion). The company claims it could be ready for human habitation by 2030. Learn more by reading the article, Ocean Spiral is a conceptual city proposed beneath the surface of the ocean. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf462/5b8b4e4b40ec9a2651daf467/1535505613347/P8_centre_shaft_sh_3115154k.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf462/5b8b4e4b40ec9a2651daf469/1535505602288/EeJcpqLjdfReW4kJ22xE_Shimizu3%5B1%5D.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf462/5b8b4e4b40ec9a2651daf463/1535505607498/1016944456%5B1%5D.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf462/5b8b4e4b40ec9a2651daf46d/1535505946498/tP0RZDSgdsNPw8Z245OD_Shimizu7%5B1%5D.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf462/5b8b4e4b40ec9a2651daf465/1535505936223/3N0rREtorxM8g6vSXCRG_Shimizu5%5B1%5D.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf40e/1535354651593/ Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Guest Room Module "A module with 104 individual rooms, including 64 guest rooms, would be arranged on a ring that is 140 meters in diameter. The ring would generate an artificial gravity field of 0.7 G by rotating around three times per minute, so people could relax almost in the same manner as on earth."\(^{[4]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf452/1535309406755/bigggstandfordtoruss.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Cut-away view of the interior of a Standford Torus. Image courtesy of NASA Ames Research Center. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf49c/5b8b4e4b40ec9a2651daf49f/1535352753554/med_suprajupiter.png Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System “A suprajovian ring suspended above the gas giant Mungo.” Image from Steve Bowers. Image can also be found at Orion’s Arm. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf49c/5b8b4e4b40ec9a2651daf4a3/1535487396885/alexey+shirokikh.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Designer Planet Artist’s depiction of a designer planet. Artwork by Alexey Shirokikh. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf49c/5b8b4e4b40ec9a2651daf49d/1535352742220/Athelan.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System “Athelan, a suprashell erected around the gas giant Uranus in the Old Solar System.” Image from Steve Bowers. Image can also be found on Orion’s Arm. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf49c/5b8b4e4b40ec9a2651daf4a1/1535487329539/Dreamsphere.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System “A Dreamsphere, a suprastellar shell completely surrounding a brown dwarf in the Stellar Umma region.” Image from Steve Bowers. Image can also be found on Orion’s Arm. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf494/5b8b4e4b40ec9a2651daf497/1535487301500/jeremy-jozwik-ia-neptune-comp2-0000.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artists depictions of gas giant refineries on two different gas giant planets. The gas giants depicted in these images are suspended by large blimps which hold a lifting gas. But it would also be possible, as we discuss in this article, to attach those gas giant refineries to the ceiling of a shell world or orbital ring. Artwork by Neil Blevins (top) and Jeremy Jozwik at Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf494/5b8b4e4b40ec9a2651daf495/1535487143670/neil-blevins-megastructures-9-gas-giant-refinery-color-sketch.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf494/5b8b4e4b40ec9a2651daf499/1535351657862/neil-blevins-megastructures-9-gas-giant-refinery-design-packet.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf43c/1535488475236/3001TheFinalOdyssey%5B1%5D.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "Arthur C. Clarke’s 3001: The Final Odyssey features an orbital ring held aloft by four enormous inhabitable towers (assumed successors to space elevators) at the Equator."\(^{[15]}\) For book summary, see: https://en.wikipedia.org/wiki/3001:_The_Final_Odyssey https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf488/5b8b4e4b40ec9a2651daf489/1535354345044/1pAZfg0WDtvCEBWpd997Kr9YV49FlqTHnQMz55sxqPc.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of a Matrioshka brain. Image retrieved from: https://www.reddit.com/r/Futurology/comments/zu399/this_day_will_come_the_matrioshka_brain/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf4ac/1535500914749/main-qimg-c723f245065082e7f3de09cd458d893e%5B1%5D.png Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System The infographic above shows the differences between a Type I (or K1), a Type II (or K2), and a Type III (or K3) civilization. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf3f2/5b8b4e4b40ec9a2651daf3f3/1535427182885/espen-saetervik-rings%5B2%5D.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf45a/5b8b4e4b40ec9a2651daf45b/1535611132816/SpaceX+crew+Big+Falcon+Rocket+%28BFR%29+launching+from+Earth.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Anywhere in the World in Under an Hour Elon Musk proposed using BFR rockets (see image above) as a planetary transportation system which could get you anywhere in the world in under one hour. Image courtesy of Space X. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf42e/1535609875282/final-frontier.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Final Frontier Voyager (2007), George Grie. Óleo sobre lienzo.\(^{[13]}\)Credit: https://commons.wikimedia.org/wiki/File:Final-Frontier.jpg https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4e4b40ec9a2651daf4a6/1535415737889/677_gas_interiors%5B1%5D.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Illustration showing the rocky, icy, metallic cores of the four Jovian planets. Credit: NASA/Lunar and Planetary Institute Retrieved from: https://solarsystem.nasa.gov/resources/677/gas-giant-interiors-2003/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4e4b40ec9a2651daf47c/5b8b4e4b40ec9a2651daf47d/1535351435005/shell_world_by_johnmalcolm1970.jpg Articles Page 2 - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of atlas towers connecting two separate shells in a shell world. Image credit: https://www.deviantart.com/johnmalcolm1970/art/Shell-World-114062545 https://www.gregschool.org/new-blog-2/2018/7/5/proof-of-the-theorem-fracsinxx1-t6c3x monthly 0.5 2018-07-19 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117238a922d1f46162120/1530817217237/squeezzeee.png Articles Page 2 - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) Figure 2: As you can see graphically, for values of \(ϴ\) in the range \(\frac{-π}{2}<ϴ<\frac{π}{2}\), the following inequalities are true \(1≥\frac{sinϴ}{ϴ}≥cosϴ\). Notice that as \(ϴ\) approaches zero from both the negative and positive directions, the function \(\frac{sinϴ}{ϴ}\) gets "squeezed" into the same point on the graph. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117238a922d1f46162112/1531965731847/share+calculus+img.png Articles Page 2 - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117238a922d1f4616211c/1531965646813/Calculus+thumbnail.png Articles Page 2 - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117238a922d1f46162116/1531965974433/ Articles Page 2 - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117238a922d1f46162114/1531966026247/facebook+img+thumbnail.jpg Articles Page 2 - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117238a922d1f4616211e/1531244510817/Limit_of_Sine_of_X_over_X-Proof_3.png Articles Page 2 - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) Figure 1: The wedge \(⪦OBA\) (colored blue) comprises a portion of the unit circle. The lengths \(AB\) and \(AC\) are the radius of the unit circle and are therefore equal to one. The heights of the triangles \(△OBA\) and \(△OCA\) can be found using basic trigonometry. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117238a922d1f46162118/1531965921845/twiiter+img+thumbnail.jpg Articles Page 2 - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5117238a922d1f4616211a/1531965935466/email+img+thumbnail.jpg Articles Page 2 - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://www.gregschool.org/new-blog-3 daily 0.75 2017-09-06 https://www.gregschool.org/new-blog-3/2017/6/20/76hgztk8ogz149g9acwmizq62okwe4 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbe128edaed80a4b2063ad/1507582256577/Untitled.jpg Kinematics - Position Vectors, Displacement, Velocity, and Acceleration https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/598367b32994ca1073c1770b/1504720181840/ Kinematics - Position Vectors, Displacement, Velocity, and Acceleration Figure 1 (click to enlarge) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5983789de3df28da0533f26f/1504720181845/ Kinematics - Position Vectors, Displacement, Velocity, and Acceleration Figure 2 https://www.gregschool.org/new-blog-3/2017/6/20/faxkbn1icm37pyljps0j38mgdt0t22 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbe18a2994ca84b3979c6d/1507582349713/Untitled.jpg Kinematics - Basic Equations of Kinematics https://www.gregschool.org/work-and-energy daily 0.75 2017-09-06 https://www.gregschool.org/work-and-energy/2017/6/21/the-dependency-of-theta-in-the-dot-product monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf476b7411c84d5126620/1507587195387/gfnf.jpg Work and Energy - The Dependency of theta in the dot product https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5983aa73b8a79b354104890d/1504719988092/ Work and Energy - The Dependency of theta in the dot product https://www.gregschool.org/work-and-energy/2017/8/26/work-measure-of-energy-transfer monthly 0.5 2018-01-07 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf53646c3c48d67761525/1507587384017/gfnf.jpg Work and Energy - Work: Measure of Energy Transfer https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ad885ebe42d663bf2e1c81/1504719976201/ff.png Work and Energy - Work: Measure of Energy Transfer Figure 1: Work done on a block by a constant force of \(-10\) newtons over a displacement of \(5\) meters. https://www.gregschool.org/work-and-energy/2017/8/26/work-done-by-earths-gravity monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ad84c2cf81e0f6ca8266f6/1504720009155/vv.png Work and Energy - Work done by Earth's Gravity Figure 1: As an object moves along the path \(\vec{R}(t)\) from an initial height of \(y_i\) to a final height of \(y_f\), the Earth's gravitational force \(-m\vec{g}\) does work on the object. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf6e6f9a61e6c50bc0856/1507587814899/gfnf.jpg Work and Energy - Work done by Earth's Gravity https://www.gregschool.org/work-and-energy/2017/8/27/work-done-by-force-moving-an-object-at-constant-height monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ac5f3ee6f2e1f1571bd04c/1504719999473/wet2.gif Work and Energy - Work-Kinetic Energy Theorem Figure 1: "Sunil Kumar Singh, Work - Kinetic Energy Theorem. February 2, 2013." http://cnx.org/content/m14095/latest/OpenStax CNX CC BY 3.0. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf6d151a58476eaac6e57/1507587794859/gfnf.jpg Work and Energy - Work-Kinetic Energy Theorem https://www.gregschool.org/quasars daily 0.75 2017-11-04 https://www.gregschool.org/new-blog-4 daily 0.75 2019-02-24 https://www.gregschool.org/new-blog-4/2017/6/28/colonizing-the-moon monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd20fb4c326d6f4eaa4f5e/1534379535900/space+travela+nd+colonization+thumbnail.jpg Outward Bound - Colonizing the Moon https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/598bef5915d5db7e604f616f/598bef5949fc2bdf477ecb94/1504670814209/LunarColonyRawlings650.jpg Outward Bound - Colonizing the Moon Domed lunar settlement illustration by Pat Rawlings, courtesy NASA. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/598bef5915d5db7e604f616f/598bef5c6a49636f7039c911/1504670814212/57c6c882c29938af2da30517ba011ce4--wallpaper-space-make-money.jpg Outward Bound - Colonizing the Moon Painting by Pat Rawlings courtesy NASA https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/598bef5915d5db7e604f616f/598bef5ebebafb811d543e0f/1504670814216/landscape-1436809198-1197px-inflatable-habitat-s89-20084.jpg Outward Bound - Colonizing the Moon Artist concept of a moon colony via NASA https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/598bef5915d5db7e604f616f/598bef60ebbd1a5963bcdcc4/1504670814220/3130B2CE00000578-3446968-The_colonisation_of_the_Moon_and_then_Mars_will_have_taken_place-a-4_1455490616552.jpg Outward Bound - Colonizing the Moon The Smart Things Future Living Report https://www.gregschool.org/new-blog-4/2017/6/28/colonizing-the-asteroids-and-comets-in-our-solar-system monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd2242914e6b94c00e16ea/1534379569084/space+travela+nd+colonization+thumbnail.jpg Outward Bound - Colonizing the Asteroids and Comets in our Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/598bf9fa6b8f5b57cf888b37/1504670946289/gjh.jpg Outward Bound - Colonizing the Asteroids and Comets in our Solar System Figure 1 (click to enlarge) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/598bfaa1c534a55657b23a6f/1504670946291/ Outward Bound - Colonizing the Asteroids and Comets in our Solar System Figure 2 - click to enlarge (Source) "This shot shows the inside of the asteroid from the previous scene. Just as I wrote about that scene, this is a highly speculative vision of an impressive piece of human engineering - a concept that science fiction author Kim Stanley Robinson calls a "terraruim" in his novel "2312". It is also not unlike what Arthur C. Clarke described in his novel "Rendezvous with Rama". What we see here is the inside of a hollowed out asteroid, pressurized and filled with a breathable atmosphere. Like I described in the previous scene, the whole structure is put into a revolving rotation, simulating the effect of gravity toward the inside "walls" of the cylinder shape we see. The structure in this scene has a diameter of about 7 kilometers and revolves with a speed of 1 rotation every 2 minutes, simulating the effect of 1g (the gravity pull we feel on Earth) at the surface of the inside. This place is also filled with water, creating lakes and seas wrapped along with the landscape. An artificial sun is running along a rail in the middle of the space, simulating a daylight cycle. This scene is of course built from scratch, but I used countless satellite photos of the Earth to texture the landscape. I actually used a slightly warped world map to create the outlines between land and water, as some may notice a couple of familiar shorelines."\(^{[3]}\) https://www.gregschool.org/new-blog-4/2017/6/28/terraforming-mars monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59545d4f197aeae989d892c0/1504671069022/ Outward Bound - Terraforming and Colonizing Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd22ee268b966b06470ce6/1534475777294/space+travela+nd+colonization+thumbnail.jpg Outward Bound - Terraforming and Colonizing Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/598b820737c581cb56c4ac02/1504671069020/ares2.jpg Outward Bound - Terraforming and Colonizing Mars Artist's depiction of the Ares spaceship from Kim Stanley Robinson's novel, Red Mars. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59545d7ce3df28275b0a516e/1504671069037/ Outward Bound - Terraforming and Colonizing Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/598b84109f745655815f327d/1504671069032/ Outward Bound - Terraforming and Colonizing Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/598b8142a5790a2392f5caa1/1504671069028/ Outward Bound - Terraforming and Colonizing Mars "This shot follows the cabin of a space elevator descending on a cable towards the northern parts of the Terra Cimmeria highlands on Mars. A large settlement, hinted as glowing lights in the dark, can be seen far below on the ground. One of Mars' two moons - Phobos - is seen above the cabin to the left of the cable in the beginning of the shot." This image was produced by Erik Wernquist. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/598b808915d5db8c6665223f/1504671069034/olympus.jpg Outward Bound - Terraforming and Colonizing Mars Poster by SpaceX https://www.gregschool.org/new-blog-4/2017/8/13/why-colonize-the-universe monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d3e300f5e231a4eced49e7/1507688500138/51i54HqlYHL._SY344_BO1%2C204%2C203%2C200_.jpg Outward Bound - Why Colonize the Universe? In Carl Sagan's book Pale Blue Dot, he argued that humans evolved a love for exploration as an essential part of our survival as a species. It was this evolutionary trait which compelled our hunter-gather ancestors to leave their home—Africa—when times were getting rough and to meander across the planet. As planetary catastrophes become increasingly likely as time rolls by, Sagan argues that this same "survival strategy" will perhaps compell humanity to colonize the solar system, and beyond. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd7f918fd4d260ef9b9a70/1507688500135/space+travela+nd+colonization+thumbnail.jpg Outward Bound - Why Colonize the Universe? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d3e5550abd046aead94cf7/1507688500140/factoriesins.jpg Outward Bound - Why Colonize the Universe? An O'Neil cylinder is a type of megastructure and artificial space habitat which was first proposed by the physicist Gerard O'Neil in 1976. An O'Neil cylinder would consist of two immense, rotating, cylindrical habitats (illustrated above) which would spin at a angular velocity that generated centrifugal forces along the interior surfaces of the cylinders which would emulate Earth-gravity. Each cylindrical habitat would be 5 miles in diameter and 20 miles long. https://www.gregschool.org/new-blog-4/2017/9/11/harvesting-resources-from-saturn-and-titan monthly 0.5 2018-04-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fbba62ec212defc9fec86f/1509918211623/facebook+img+thumbnail.jpg Outward Bound - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff83a2f9619a4291a4561b/1509918211631/space+travela+nd+colonization+thumbnail.png Outward Bound - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fbba7d085229ec68487ed1/1509918211627/google+img+thumbnail.jpg Outward Bound - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fbba908165f5e83ce1f7ee/1509918211625/twiiter+img+thumbnail.jpg Outward Bound - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fbbac00d9297e902c593aa/1509918211620/share+img+for+spacetrav+and+col+thumbnail.png Outward Bound - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fbba6cc830255c2b87cd6a/1509918211629/email+img+thumbnail.jpg Outward Bound - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b70924e45a7cbc861db975/1509918211633/WANDERERS_ligeia_mare_01.jpg Outward Bound - Harvesting Resources from Saturn and Titan "With an average temperature of -180 C all water here is frozen hard as rock. In fact, the surface landscape of Titan is indeed mostly made of frozen water ice. But Titan's atmosphere is rich in hydrocarbons such as methane and ethane, and the low temperature is perfect for these elements to occur naturally in three states; frozen, liquid and gas. So, just as on Earth where we have a water cycle (ice melts, becomes water, water evaporates into clouds, turning into liquid and becomes rain and so forth), Titan has a methane cycle. Methane evaporates and rises to form clouds, eventually turning into rain, falling over the surface. And this is the most amazing part; the rain in some places is enough to fill entire lakes. Lakes of methane! Titan is the only place in the Solar System, other than Earth, known to have large bodies of liquid on its surface. And they are really there, huge lakes, with shorelines, islands and small archipelagos. This scene takes place over a lake know as Ligeia Mare, the second largest on Titan, about 500 kilometers in diameter, located in the north polar region of the moon. The second fantastic feature I wanted to illustrate is the combination of Titan's very dense atmosphere and its relatively low gravity. As a human on Titan you would weigh about 14% of what you do on Earth, and in the dense atmosphere it would be enough to strap wings on your arms to make you able to fly like a bird. On Titan you could fly like a bird, over lakes of methane! (If you wore some really warm clothes of course.)" Image and image description credit: WANDERERS - a short film by EriK Wernquist https://www.gregschool.org/new-blog-4/2017/9/19/the-kardeshev-scale monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/59c1db0d6f4ca36e46f4b75b/59c1db0d1f318d7984d23891/1507687265519/dyson_sphere_second_1024.jpg Outward Bound - The Kardeshev Scale Dyson sphere. Credit: capnhack.com https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/59c1db0d6f4ca36e46f4b75b/59c1db131f318d7984d238db/1507750791352/17202572._SX540_.jpg Outward Bound - The Kardeshev Scale Artist's depiction of a ring world. Credit: http://richardfrazer.com/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d3df2ecf81e01fd0318dfe/1507687265518/1024px-Consommations_%C3%A9nerg%C3%A9tiques_des_trois_types_de_l%27%C3%A9chelle_de_Kardashev.svg.png Outward Bound - The Kardeshev Scale The Kardeshev scale ranks how advanced a technological civilization is based upon their total power consumption. A Type I civilization is capable of harnessing all of their home plant's power of \(~10^{16}W\); a Type II civilization has harnessed the power of their star ( \(~10^{26}W\)); and a Type III civilization has harnessed the power output of their entire galaxy ( \(~10^{36}W\)). There are even Type IV and Type V civilization which go beyond Kardeshev's original scale. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd6e1159cc68c004650b88/1507687265526/bubble-universes-computer-illustration-of-multiple-bubble-universes-G4C3H0.jpg Outward Bound - The Kardeshev Scale Artist's depiction of the multi-verse. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd7aff80bd5ee9087223bd/1507687265516/space+travela+nd+colonization+thumbnail.jpg Outward Bound - The Kardeshev Scale https://www.gregschool.org/new-blog-4/2017/9/25/colonizing-and-terraforming-venus-59y59-aty88 monthly 0.5 2018-04-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960e68a922dc773a0185b/1523144000964/space+colon+author+date.jpg Outward Bound - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960e68a922dc773a01851/1523145768016/share+b.jpg Outward Bound - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960e68a922dc773a01857/1523144061656/google+share+thumbnail_preview.jpg Outward Bound - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960e68a922dc773a01853/1523144015110/facebook+thumbnail.jpg Outward Bound - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960e68a922dc773a01859/1523144044465/email+thumbnail_preview.jpg Outward Bound - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960e68a922dc773a0185d/1508644545185/1.10-1024x768.jpg Outward Bound - Colonizing and Terraforming Venus Artist concept of lightning on Venus. Image credit: ESA https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960e68a922dc773a0185f/1507060053549/venus-cloud-city.jpg Outward Bound - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960e68a922dc773a01855/1523144026480/Twitter+thumbnail_preview.jpg Outward Bound - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960e68a922dc773a01861/1510882341344/TerraformedVenus%5B1%5D.jpg Outward Bound - Colonizing and Terraforming Venus "A conceptual picture I made of Venus if it were terraformed. (Credit: Daein Ballard) Notice the interesting cloud formations and that the planet has polar caps. I decided to show the planet this way after studying Venus' atmosphere. The two Hadley cells the planet has stop at 70 degrees north and south. So the polar regions are cut off from the warm air. Also the slow rotation of the planet causes the clouds to whip around the planet very fast, especially at the equator, to balance out the temperature difference between day and night sides of the planet."\(^{[5]}\) Image credit: Ittiz at the English language Wikipedia [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons https://www.gregschool.org/new-blog-4/2017/9/12/colonizing-the-kuiper-belt-and-oort-cloud-g53ff-smdal monthly 0.5 2018-04-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/59fce5b264265f1222b3f728/59fce5b264265f1222b3f72b/1507689697156/uranus-gas-zoom.jpg Outward Bound - Colonizing the Kuiper Belt and Oort Cloud Artist’s depiction of Neptune’s (above image) and Uranus’s (below image) atmosphere being harvested for resources such as nitrogen. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/59fce5b264265f1222b3f728/59fce5b264265f1222b3f729/1507689697153/george-dennis-the-fountains-of-neptune.jpg Outward Bound - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce5b264265f1222b3f71c/1509746045831/twiiter+img+thumbnail.jpg Outward Bound - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce5b264265f1222b3f72e/1507689697158/OortCloud_P-sys%28PNG-fin%291.png Outward Bound - Colonizing the Kuiper Belt and Oort Cloud Another size comparison of the solar system to the Oort Cloud. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce5b264265f1222b3f726/1507689697151/Ancient_Mars3_02.jpg Outward Bound - Colonizing the Kuiper Belt and Oort Cloud Artist's depiction of Fesenkov Crater on Mars filled with liquid water. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce5b264265f1222b3f722/1507689697148/space+travela+nd+colonization+thumbnail.jpg Outward Bound - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce5b264265f1222b3f71e/1509746082746/google+img+thumbnail.jpg Outward Bound - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce5b264265f1222b3f724/1507689697150/Kuiper_oort.jpg Outward Bound - Colonizing the Kuiper Belt and Oort Cloud A size comparison of the Kuiper belt and outer solar system to the Oort Cloud. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce5b264265f1222b3f718/1509745876713/share+technology++img.jpg Outward Bound - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce5b264265f1222b3f71a/1509746065358/facebook+img+thumbnail.jpg Outward Bound - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce5b264265f1222b3f720/1509745710543/email+img+thumbnail.jpg Outward Bound - Colonizing the Kuiper Belt and Oort Cloud https://www.gregschool.org/new-blog-4/2017/9/10/how-to-produce-water-and-oxygen-on-mars-njmkh-3ym9w monthly 0.5 2018-04-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960ff88251b53483274e2/1523144687004/google+share+thumbnail_preview.jpg Outward Bound - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960ff88251b53483274de/1523144639537/facebook+thumbnail.jpg Outward Bound - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960ff88251b53483274ea/1511021201272/mars3%5B1%5D.jpg Outward Bound - How to Produce Water and Oxygen on Mars The rover above is capable of releasing frozen water from regolith by heating it using microwaves. Credit: SUTD/Gilmour Space Corporation https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960ff88251b53483274e6/1523144599773/space+colon+author+date.jpg Outward Bound - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960ff88251b53483274e0/1523144648835/Twitter+thumbnail_preview.jpg Outward Bound - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960ff88251b53483274e4/1523144671889/email+thumbnail_preview.jpg Outward Bound - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960ff88251b53483274dc/1523145434173/share+b.jpg Outward Bound - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac960ff88251b53483274e8/1510888610952/extracting+water+from+Mars%27+regolith.jpg Outward Bound - How to Produce Water and Oxygen on Mars "Truck, oven, and slag pile system for extracting water from Martian soil."\(^{[2]}\) Artwork by Michael Carroll. https://www.gregschool.org/new-blog-4/2018/7/20/space-based-solar-power-3ptal-jreey-fh4ws-wk9fy monthly 0.5 2018-09-18 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0ba/5b8f60e140ec9ad5c875b0bb/1535488899287/moon+mass+drive-finished-jayproductspainting%5B1%5D.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Copy of Lunar Mass Driver Artist’s depiction of a Lunar mass driver. Artwork by Jay Wong. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0ba/5b8f60e140ec9ad5c875b0bd/1535488181201/Lunar_base_concept_drawing_s78_23252%5B1%5D.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Copy of Lunar Mass Driver Artist’s depiction of a lunar mass driver. The physicist Gerard K. O’Neil imagined using this device to electromagnetically launch lunar material into space for the purpose of being using to construct artificial space habitats for human residence and to move most industry off the Earth and into space. Image courtesy of NASA. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0ce/1535309406755/bigggstandfordtoruss.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Cut-away view of the interior of a Standford Torus. Image courtesy of NASA Ames Research Center. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b110/5b8f60e140ec9ad5c875b111/1535487301500/jeremy-jozwik-ia-neptune-comp2-0000.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artists depictions of gas giant refineries on two different gas giant planets. The gas giants depicted in these images are suspended by large blimps which hold a lifting gas. But it would also be possible, as we discuss in this article, to attach those gas giant refineries to the ceiling of a shell world or orbital ring. Artwork by Neil Blevins (top) and Jeremy Jozwik at Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b110/5b8f60e140ec9ad5c875b113/1535487143670/neil-blevins-megastructures-9-gas-giant-refinery-color-sketch.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b110/5b8f60e140ec9ad5c875b115/1535351657862/neil-blevins-megastructures-9-gas-giant-refinery-design-packet.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b072/1535847641084/gggggggggggggggggggggggg.png Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0ac/1535609604928/c58d9cac14778ce30b60c5c6d63fee2a.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0d6/5b8f60e140ec9ad5c875b0d7/1535611132816/SpaceX+crew+Big+Falcon+Rocket+%28BFR%29+launching+from+Earth.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Copy of Anywhere in the World in Under an Hour Elon Musk proposed using BFR rockets (see image above) as a planetary transportation system which could get you anywhere in the world in under one hour. Image courtesy of Space X. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b08e/5b8f60e140ec9ad5c875b08f/1535827243822/seattle_space_elevator_observatory_by_alterbr33d-d5j8j2p-750x375%402x%5B1%5D.png Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Copy of Space Elevator Depiction of a space elevator.\(^{[7]}\) Artwork retrieved from: http://prospective-tourisme.com/index.php/2017/08/10/entretien-laurent-queige-directeur-welcome-city-lab/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b08e/5b8f60e140ec9ad5c875b091/1535827236841/space-elevator%5B1%5D.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Copy of Space Elevator Depiction of a space elevator. Artwork by Glenn Clovis at Artstation.\(^{[6]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b128/1535500914749/main-qimg-c723f245065082e7f3de09cd458d893e%5B1%5D.png Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System The infographic above shows the differences between a Type I (or K1), a Type II (or K2), and a Type III (or K3) civilization. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b074/5b8f60e140ec9ad5c875b083/1535343290369/sergio-botero-tflp-damocles-presentation-freight-cab-web.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b074/5b8f60e140ec9ad5c875b085/1535343288243/sergio-botero-tflp-damocles-presentation-large-cab-dims.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b074/5b8f60e140ec9ad5c875b07b/1535343284499/sergio-botero-tflp-damocles-comp-1-v3-web.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b074/5b8f60e140ec9ad5c875b07d/1535343280086/sergio-botero-tflp-damocles-comp-5-web.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b074/5b8f60e140ec9ad5c875b081/1535343280153/sergio-botero-tflp-damocles-comp-2-v1-web.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b074/5b8f60e140ec9ad5c875b07f/1535343280933/sergio-botero-tflp-damocles-presentation-large-cab-web.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b074/5b8f60e140ec9ad5c875b077/1535343274958/sergio-botero-tflp-damocles-comp-3-web.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b074/5b8f60e140ec9ad5c875b079/1535825798962/sergio-botero-tflp-damocles-comp-4-v1-web.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "Damocles is a large space port and elevator hub with stations fixed on [E]arth, located in an enormous, peaceful and very prosperous city, in a not-so-distant future.”\(^{[2]}\) In the year 2117 the most economical way to send people and cargo to outer space is using a space elevator. It’s not the quickest option but a very practical and effective one. Just like other similar Orbitowers placed on the Equator, the Damocles elevator hub provides this service. Space freight elevators are crucial to carry large components of interplanetary and the earlier interstellar vehicles into orbit, so they can be assembled in space instead of being launched by rockets. Autonomous trucks and cars arrive at the base’s ground to take passengers and cargo to the space elevator cabs. Flying vehicles land on the pads. The building itself is headquarters for many logistics companies, there are some offices and a hotel."\(^{[2]}\) Artwork by Sergio Botero at Artstation.\(^{[2]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b074/5b8f60e140ec9ad5c875b075/1535343276062/sergio-botero-tflp-damocles-presentation-freight-cab-dims.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b094/1535328074668/405001%5B1%5D.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "The High Frontier: Human Colonies in Space is a 1976 book by Gerard K. O'Neill. It envisions large manned habitats in the Earth-Moon system, especially near stable Lagrangian points. Three designs are proposed: Island one (a modified Bernal sphere), Island two (a Stanford torus), and Island 3, two O'Neill cylinders. These would be constructed using raw materials from the lunar surface launched into space using a mass driver and from near-Earth asteroids. The habitats were to spin for simulated gravity and be illuminated and powered by the sun. Solar power satellites were proposed as a possible industry to support the habitats. The book won the 1977 Phi Beta Kappa Award in Science."\(^{[9]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0c4/1535355196399/Kohlenstoffnanoroehre_Animation.gif Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Animation of a sheet of pure graphene rolled up into a carbon nanotube. Credit: https://commons.wikimedia.org/wiki/File:Kohlenstoffnanoroehre_Animation.gif https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b104/5b8f60e140ec9ad5c875b105/1535354345044/1pAZfg0WDtvCEBWpd997Kr9YV49FlqTHnQMz55sxqPc.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of a Matrioshka brain. Image retrieved from: https://www.reddit.com/r/Futurology/comments/zu399/this_day_will_come_the_matrioshka_brain/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0a0/1535327450524/glenn-clovis-spec-sheet-island-3-by-glennclovis-d5jj93n.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist's depiction of a Model 3 O'Neil cylinder which would be capable of supporting millions of a people, a complete biosphere, and all of the Earth's natural habitats. An O'Neil cylinder could also be used as an arc ship (sometimes also called a generation ship) to travel to other stars or galaxies. Image by Glenn Clovis from Artstation.\(^{[11]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0a2/1535329695987/the-verge-lightfarm-studios.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0ae/5b8f60e140ec9ad5c875b0b1/1535329245230/neil-blevins-megastructures-7-star-lifter-3d-sketch.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0ae/5b8f60e140ec9ad5c875b0b3/1535329173143/neil-blevins-megastructures-7-star-lifter-color-sketch.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0ae/5b8f60e140ec9ad5c875b0b5/1535329080141/neil-blevins-megastructures-7-star-lifter-1-b.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0ae/5b8f60e140ec9ad5c875b0af/1535329228095/neil-blevins-neil-blevins-megastructures-7-star-lifter-3.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0d0/1535309881848/Nikola-Tesla.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Image above portrays Nikola Tesla, the famous inventor who first conceived of the notion of orbital rings in the 1870s shortly after recovering from malaria. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0da/1534192981005/ Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist's depiction of solar panels attached to a space elevator. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b08c/1535354657587/ Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Public Area "The public area would be assembled into a complex structure in the form of a truncated octahedron. It would have a great room consisting of a lobby, restaurant, entertainment room, and other spaces where people could enjoy a dining experience, sports, and a variety of amusements under low-gravity conditions."\(^{[4}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0ee/1535611314042/Oceanplanet_lucianomendez.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist's illustration of a hypothetical ocean planet with two natural satellites. Image credit: https://commons.wikimedia.org/wiki/File:Oceanplanet_lucianomendez.JPG https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b124/5b8f60e140ec9ad5c875b125/1535484695673/jeremy-jozwik-ia-coljupiter-comp2-raw-jpeg-0214.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Copy of Fusion Candles Artist's impression of Fusion Candles which could be used to move Jupiter and its moons across interstellar or even intergalactic space and away from our solar system. Spaceship Jupiter! Artwork by Jeremy Jozwik from Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0c6/5b8f60e140ec9ad5c875b0c7/1535827690138/earthring_1024.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of an orbital ring which appeared in Issue 7 of the magazine, All About Space. Image by Adrian Mann.\(^{[18]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0d2/5b8f60e140ec9ad5c875b0d3/1535355930567/4304_1105960212_large_tiff.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0dc/1535610747216/med_venus2.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "Terraformed Venus is surrounded by a Dynamic Orbital Ring, mosty constructed from carbon extracted from its original atmosphere."\(^{[24]}\) Image by Steve Bowers. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0a4/5b8f60e140ec9ad5c875b0a5/1535827448497/space-colony-ix.png Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of an O’Neil cylinder. Artwork by Bruno Xavier.\(^{[12]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b10c/5b8f60e140ec9ad5c875b10d/1535596948478/neil-blevins-megastructures-9-gas-giant-refinery-5%5B1%5D.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0de/5b8f60e140ec9ad5c875b0df/1535505607498/1016944456%5B1%5D.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0de/5b8f60e140ec9ad5c875b0e3/1535505977487/A2ljC-Qaok-kAJvzyNWu_Shimizu2%5B1%5D.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System The concept of the Ocean Spiral was first unveiled by Shimizu Corporation, in conjunction with Tokyo University and Japan Agency for Marine-Earth Science and Technology, in 2014. The company excepts it to take 5 years to build an Ocean Spiral. The company expects the project to cost ¥3 trillion (approximately £20 billion). The company claims it could be ready for human habitation by 2030. Learn more by reading the article, Ocean Spiral is a conceptual city proposed beneath the surface of the ocean. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0de/5b8f60e140ec9ad5c875b0e9/1535505613347/P8_centre_shaft_sh_3115154k.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0de/5b8f60e140ec9ad5c875b0e7/1535505936223/3N0rREtorxM8g6vSXCRG_Shimizu5%5B1%5D.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0de/5b8f60e140ec9ad5c875b0e1/1535505602288/EeJcpqLjdfReW4kJ22xE_Shimizu3%5B1%5D.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0de/5b8f60e140ec9ad5c875b0e5/1535505946498/tP0RZDSgdsNPw8Z245OD_Shimizu7%5B1%5D.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b096/5b8f60e140ec9ad5c875b099/1535827420148/Spacecolony4.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Interior of an O'Neill cylinder\(^{[10]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b096/5b8f60e140ec9ad5c875b09d/1535827414502/Spacecolony1.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System O'Neill cylinders\(^{[10]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b096/5b8f60e140ec9ad5c875b097/1535827424197/Internal_view_of_the_O%27Neill_cylinder.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Solar eclipse inside an O'Neill cylinder\(^{[10]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b096/5b8f60e140ec9ad5c875b09b/1535827428335/Spacecolony3edit.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Interior of an O'Neill cylinder\(^{[10]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0b8/1535488475236/3001TheFinalOdyssey%5B1%5D.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "Arthur C. Clarke’s 3001: The Final Odyssey features an orbital ring held aloft by four enormous inhabitable towers (assumed successors to space elevators) at the Equator."\(^{[15]}\) For book summary, see: https://en.wikipedia.org/wiki/3001:_The_Final_Odyssey https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0f4/1534192981008/shell+world.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "An engineer suggests building a roof over a small planet so that Earthlike conditions could be maintained."\(^{[26]}\) The Shell World could be used to maintain Earth-like conditions on the surface of an alien planet or moon; hanging cities could be suspended from the interior wall of the shell world; or the outer-surface of the Shell World could be engineered to closely resemble the Earth. Some combination of all of the above could be possible, albeit only to a certain extent. Credit: by Karl Tate, Infographics Artist https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b08a/1535354651593/ Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Guest Room Module "A module with 104 individual rooms, including 64 guest rooms, would be arranged on a ring that is 140 meters in diameter. The ring would generate an artificial gravity field of 0.7 G by rotating around three times per minute, so people could relax almost in the same manner as on earth."\(^{[4]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b118/5b8f60e140ec9ad5c875b119/1535487396885/alexey+shirokikh.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Copy of Designer Planet Artist’s depiction of a designer planet. Artwork by Alexey Shirokikh. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b118/5b8f60e140ec9ad5c875b11b/1535487329539/Dreamsphere.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System “A Dreamsphere, a suprastellar shell completely surrounding a brown dwarf in the Stellar Umma region.” Image from Steve Bowers. Image can also be found on Orion’s Arm. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b118/5b8f60e140ec9ad5c875b11d/1535352753554/med_suprajupiter.png Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System “A suprajovian ring suspended above the gas giant Mungo.” Image from Steve Bowers. Image can also be found at Orion’s Arm. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b118/5b8f60e140ec9ad5c875b11f/1535352742220/Athelan.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System “Athelan, a suprashell erected around the gas giant Uranus in the Old Solar System.” Image from Steve Bowers. Image can also be found on Orion’s Arm. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0f6/1534192981013/cities+dangling+from+shell+world.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "Full cities could hang from the top of the shell that holds in the newly terraformed world's atmosphere."\(^{[27]}\) Image uploaded Oct. 7, 2013. Credit: Ken Roy/Tennessee Valley Interstellar Workshop https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b108/5b8f60e140ec9ad5c875b109/1535483823007/jakub-grygier-005-matrioshka-brain-ab.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Copy of Copy of Matrioshka Brain Artist's impression of a Matrioshka Brain. Artwork by Jakub Grygier who is also a member of the SFIA production team. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0fc/5b8f60e140ec9ad5c875b101/1535351231677/ringworld.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Larry Niven's Ringworld. Image credit: https://bargainbin4u.wordpress.com/2008/07/14/ringworld-by-larry-niven/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0fc/5b8f60e140ec9ad5c875b0fd/1535350325687/ringworld_engineers_by_tomislavtikulin-db0bei8.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of a ring world. Image credit: https://www.deviantart.com/tomislavtikulin/art/Ringworld-Engineers-665659952 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0fc/5b8f60e140ec9ad5c875b0ff/1535350338882/halcyon_days_by_julian_faylona-d70cz32.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of a ring world. Image credit: https://www.deviantart.com/julian-faylona/art/Halcyon-Days-423868574 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0ca/1535355718877/med_bronx4.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "The inner and outer static orbital rings around Bronx are linked to a central geostationary ring by by carbon nanotube cables. The inner ring is only 265km above the clouds, while the outer ring is 75,600km from the planet's core."\(^{[19]}\) Image from Steve Bowers. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0f8/5b8f60e140ec9ad5c875b0f9/1535351435005/shell_world_by_johnmalcolm1970.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of atlas towers connecting two separate shells in a shell world. Image credit: https://www.deviantart.com/johnmalcolm1970/art/Shell-World-114062545 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0aa/1535609875282/final-frontier.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Final Frontier Voyager (2007), George Grie. Óleo sobre lienzo.\(^{[13]}\)Credit: https://commons.wikimedia.org/wiki/File:Final-Frontier.jpg https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b122/1535415737889/677_gas_interiors%5B1%5D.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Illustration showing the rocky, icy, metallic cores of the four Jovian planets. Credit: NASA/Lunar and Planetary Institute Retrieved from: https://solarsystem.nasa.gov/resources/677/gas-giant-interiors-2003/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0ec/1535738151212/Kepler_spacecraft_artist_render_%28crop%29%5B1%5D.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist's conception of the Kepler Space Telescope. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0f0/5b8f60e140ec9ad5c875b0f1/1535356149316/espen-saetervik-rings.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of hoop worlds (also known as ring worlds). These megastructures can be built by building many adjacent orbital rings next to each other, side by side, and laying a surface down over those orbital rings. Image retrieved from https://www.iamag.co/espen-olsen-saetervik/espen-saetervik-rings/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b088/1535354571685/img_index_01.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "Since ancient times, people have always dreamed of going to space. Only astronauts have been able to go until now, but progress has been made on efforts to enable even private citizens to experience space, and space travel is finally about to become an industry. Shimizu foresaw the era of space travel early on, and has proposed a space hotel concept."\(^{[4]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0a8/1535568397254/13220830_239617033095862_8671672187626094751_n%5B1%5D.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b06e/5b8f60e140ec9ad5c875b06f/1535427182885/espen-saetervik-rings%5B2%5D.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8f60e140ec9ad5c875b0cc/1535309001976/Stanford_Torus_interior+highhd.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist's depiction of the interior of a Stanford torus. Painted by Donald E. Davis. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b12a/5b8f60e140ec9ad5c875b12d/1535827892994/gateway_hub_04_by_lorddoomhammer-d9u3226.png Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s scifi depiction of a galactic empire using portals to travel across space.\(^{[30]}\) Image credit: https://www.deviantart.com/lorddoomhammer/art/Galactic-Network-594726702 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b12a/5b8f60e140ec9ad5c875b12b/1535827901771/hades__star___warp_lane_hub_by_gabriel_bs-db8y989.png Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System “Two hubs that can connect to create a temporary Warp Lane in your system The Warp Lane Hub can be connected to another Hub for one day, for a fixed Hydrogen cost. Once connected, ships can travel between the two end points instantly and without consuming Hydrogen.”\(^{[31]}\) Image credit: https://www.deviantart.com/gabrielbstiernstrom/art/Hades-Star-Warp-Lane-Hub-680163129 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8f60e140ec9ad5c875b0c0/5b8f60e140ec9ad5c875b0c1/1535355566180/1492030052266.jpg Outward Bound - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of an orbital ring. https://www.gregschool.org/space-transportation daily 0.75 2018-08-17 https://www.gregschool.org/space-transportation/2017/6/28/8fldcv2rgvjvjwb42w67qh0ude4ii0 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd396429f1872f5a463699/1534475664383/space+travela+nd+colonization+thumbnail.jpg Space Transportation - Alcubierre Warp Drive https://www.gregschool.org/space-transportation/2017/8/13/nuclear-fusion-engines monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd246fd55b41029c6b484a/1534475588401/space+travela+nd+colonization+thumbnail.jpg Space Transportation - Nuclear Fusion Engines https://www.gregschool.org/space-transportation/2017/9/21/shkadov-thruster monthly 0.5 2018-06-28 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f919608165f502329be917/1509497981395/facebook+img+thumbnail.jpg Space Transportation - Megastructures: Shkadov Thrusters https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f9195210952678f8a11958/1509497981402/email+img+thumbnail.jpg Space Transportation - Megastructures: Shkadov Thrusters https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ebd617268b9699fe3844c0/1509497981406/Shkadov_diagram.jpg Space Transportation - Megastructures: Shkadov Thrusters Figure 1: An arc mirror (dark orange arc) subtended by an angle \(2\phi\) reflects a star's radiation back towards itself. Photons collide against the portion of the star's surface which is subtended by the angle \(2\phi\). These collisions result in a net force \(\vec{F}\) exerted on the star causing the entire star to move in the direction of the arrow. The star's gravity pulls everything else in the star system along with it. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f91bdf4192021625efc477/1509497981404/space+travela+nd+colonization+thumbnail.png Space Transportation - Megastructures: Shkadov Thrusters https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ebccc47131a59c37b07cb4/1509497981409/neil-blevins-megastructures-5-shkadov-thruster-design-packet.jpg Space Transportation - Megastructures: Shkadov Thrusters Figure 2: Artist's depiction of a Shkadov thruster. Credit: https://www.artstation.com/artofsoulburn https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f91a6ce2c48325471de5a0/1509497981393/share+img+for+spacetrav+and+col+thumbnail.png Space Transportation - Megastructures: Shkadov Thrusters https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f91985ec212d39ca0ab20e/1509497981397/twiiter+img+thumbnail.jpg Space Transportation - Megastructures: Shkadov Thrusters https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f919716c3194e9a685663b/1509497981400/google+img+thumbnail.jpg Space Transportation - Megastructures: Shkadov Thrusters https://www.gregschool.org/space-transportation/2018/6/12/01kbzrqg971y7cr7mw0lgnob5i1y43-6kjrd monthly 0.5 2018-06-28 https://www.gregschool.org/black-holes-summary daily 0.75 2017-07-01 https://www.gregschool.org/new-blog-5 daily 0.75 2017-07-13 https://www.gregschool.org/new-blog-76 daily 0.75 2017-09-06 https://www.gregschool.org/new-blog-76/2017/8/10/introduction-to-einsteins-general-theory-of-relativity monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/598c16d46a49636f703b3191/1504673164151/Starshot.png General Relativity - Introduction to Einstein's General Theory of Relativity https://www.gregschool.org/new-blog-76/2017/8/10/einstein-equivalence-principle monthly 0.5 2017-11-09 https://www.gregschool.org/new-blog-31 daily 0.75 2018-07-19 https://www.gregschool.org/new-blog-31/2017/6/16/overview-of-calculus-hmtnx-fptl9 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a01f94053450a989d5a57f2/1497934508324/ Overview of calculus - Overview of Single-Variable Calculus Figure 2 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a01f93f53450a989d5a57ed/1507581121093/Untitled.jpg Overview of calculus - Overview of Single-Variable Calculus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a01f94053450a989d5a57f6/1497933573517/ Overview of calculus - Overview of Single-Variable Calculus Figure 4 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a01f94053450a989d5a57f8/1497933579348/ Overview of calculus - Overview of Single-Variable Calculus Figure 5 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a01f94053450a989d5a57f4/1497931192368/ Overview of calculus - Overview of Single-Variable Calculus Figure 3 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a01f94053450a989d5a57f0/1497934480889/ Overview of calculus - Overview of Single-Variable Calculus Figure 1 https://www.gregschool.org/new-blog-78 daily 0.75 2017-09-06 https://www.gregschool.org/new-blog-78/2017/8/10/introduction-to-linear-momentum monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf25d18b27de5f10403e9/1507586657951/gfnf.jpg Momentum - Introduction to Linear Momentum https://www.gregschool.org/new-blog-78/2017/8/10/derivation-on-momentum-conservation monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf3088a02c75c23e4b539/1507586829847/gfnf.jpg Momentum - Derivation of Momentum Conservation https://www.gregschool.org/new-blog-78/2017/8/10/inelastic-collisions monthly 0.5 2017-11-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf3af64b05fea9d3ca96c/1507586994321/gfnf.jpg Momentum - Inelastic Collisions https://www.gregschool.org/overview-of-physics daily 0.75 2017-09-06 https://www.gregschool.org/overview-of-physics/2017/5/14/introduction-to-newtonian-mechanics monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dac3f92278e744bbca7672/1507509247062/stock-vector-physics-and-science-icons-set-classical-mechanics-397461406.jpg Overview of Physics - Introduction to Physics and the Scientific Method https://www.gregschool.org/overview-of-physics/2017/5/18/what-do-we-mean-by-kinematics-dynamics-and-mechanics monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dac5f6edaed84653190072/1507509756584/classical+mechanics+thumbnail.jpg Overview of Physics - What do we mean by "kinematics," "dynamics," and "mechanics?" https://www.gregschool.org/overview-of-physics/2017/6/21/the-abstract-has-a-lot-to-say-about-the-physical-world monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dac64390bade192a01a33c/1507509840450/classical+mechanics+thumbnail.jpg Overview of Physics - The Abstract has a lot to say about the Physical World https://www.gregschool.org/new-blog-73 daily 0.75 2017-09-09 https://www.gregschool.org/new-blog-73/2017/6/12/p-series-convergence-and-divergence monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/593f64108419c276ef637188/1497326618764/ Series - P-Series Convergence and Divergence Figure 1 (click to enlarge) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbde8564b05fea9d3b6371/1507581577144/Untitled.jpg Series - P-Series Convergence and Divergence https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/593f63cfbf629a891ee6c94b/1497326554506/ Series - P-Series Convergence and Divergence Figure 2 (click to enlarge) https://www.gregschool.org/new-blog-73/2017/8/16/maclaurin-polynomial-and-series monthly 0.5 2018-07-06 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbdff14c0dbffb014aa46a/1507581942436/Untitled.jpg Series - Maclaurin/Taylor Polynomials and Series https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59add11437c581dc3568a902/1504985107253/Exp_series.gif Series - Maclaurin/Taylor Polynomials and Series Figure 1. Maclaurin polynomials of different order \(n\) (red curves) approximating the function \(e^x\) (blue curve). https://www.gregschool.org/astronomy daily 0.75 2018-07-19 https://www.gregschool.org/astronomy/2017/10/29/quasars monthly 0.5 2018-07-20 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe2251084665ad8a56cb82/1509827914262/share+technology++img.jpg Astronomy - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fded47e31d1945636849d4/1509827914278/PIA13033%5B1%5D.jpg Astronomy - Quasars Figure 1: "The 200-inch (5.1 m) Hale Telescope (f/3.3) was the world's largest effective telescope for 45 years (1948-1993). It is still a workhorse of modern astronomy. It is used nightly for a wide range of astronomical studies. On average the weather allows for at least some data collection about 290 nights a year."\(^{[1]}\) Image credit: Caltech/Palomar Observatory https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe2165e31d1945636e00b9/1509827914269/twiiter+img+thumbnail.jpg Astronomy - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe214a24a6943fd0cb7e59/1509827914266/facebook+img+thumbnail.jpg Astronomy - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe217364265f6a40130891/1509827914271/google+img+thumbnail.jpg Astronomy - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fdfee10852295261a453d8/1509827914285/Quasar%5B1%5D.png Astronomy - Quasars Figure 4: Illustration of the various different components of a quasar.\(^{[4]}\) Image credit: Futurism. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe211fe2c483f6d0418c71/1509827914276/astronomy+and+cosmology+thumbnail.png Astronomy - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fdf9c353450a448c6deb43/1509827914282/Best_image_of_bright_quasar_3C_273%5B1%5D.jpg Astronomy - Quasars Figure 3: "This image from Hubble’s Wide Field and Planetary Camera 2 (WFPC2) is likely the best of ancient and brilliant quasar 3C 273, which resides in a giant elliptical galaxy in the constellation of Virgo (The Virgin). Its light has taken some 2.5 billion years to reach us. Despite this great distance, it is still one of the closest quasars to our home. It was the first quasar ever to be identified, and was discovered in the early 1960s by astronomer Allan Sandage. The term quasar is an abbreviation of the phrase “quasi-stellar radio source”, as they appear to be star-like on the sky. In fact, quasars are the intensely powerful centres of distant, active galaxies, powered by a huge disc of particles surrounding a supermassive black hole. As material from this disc falls inwards, some quasars — including 3C 273 — have been observed to fire off super-fast jets into the surrounding space. In this picture, one of these jets appears as a cloudy streak, measuring some 200 000 light-years in length. Quasars are capable of emitting hundreds or even thousands of times the entire energy output of our galaxy, making them some of the most luminous and energetic objects in the entire Universe. Of these very bright objects, 3C 273 is the brightest in our skies. If it was located 30 light-years from our own planet — roughly seven times the distance between Earth and Proxima Centauri, the nearest star to us after the Sun — it would still appear as bright as the Sun in the sky. WFPC2 was installed on Hubble during shuttle mission STS-125. It is the size of a small piano and was capable of seeing images in the visible, near-ultraviolet, and near-infrared parts of the spectrum."\(^{[3]}\) Image Credit: ESA/Hubble [CC BY 4.0 (http://creativecommons.org/licenses/by/4.0)], via Wikimedia Commons https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe2131e31d1945636dfb00/1509827914273/email+img+thumbnail.jpg Astronomy - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fdf4d5e4966b0f25678cd5/1509827914280/3C273z%5B1%5D.gif Astronomy - Quasars Figure 2: "The spectrum of the quasar 3C 273. The strongest emission lines present are Balmer lines of hydrogen, as marked. In each case, the arrow is drawn from the rest wavelength to the observed wavelength of the line— shifted redward in each case by 15.8%. The other emission lines apparent in the spectrum are due to oxygen, helium, iron, and other elements. Credit: Michael A. Strauss, from data taken by the New Technology Telescope at La Silla, Chile; M. Türler et al. 2006, Astronomy and Astrophysics 451: L1– L4, http:// isdc.unige.ch/ 3c273/# emmi, http:// casswww.ucsd.edu/ archive/ public/ tutorial/ images/ 3C273z.gif Tyson, Neil deGrasse; Strauss, Michael A.; Gott, J. Richard. Welcome to the Universe: An Astrophysical Tour (p. 242). Princeton University Press. Kindle Edition."\(^{[2]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fdf333f9619a429181a1e6/1509827914286/orangepie%5B1%5D.jpg Astronomy - Quasars Figure 5: A 3-d map obtained by the Sloan Digital Survey of billions of light years of our local universe. Each dot is an entire galaxy and this survey shows millions of them. As you can see from this image, on the scale of billions of light-years the galaxies of congregated into a "web"-like structure of filaments and strands known as the cosmic web. Image Credit: M. Blanton and SDSS https://www.gregschool.org/astronomy/2018/6/20/the-diversity-of-exoplanets-in-the-galaxy-me459-3nb2d monthly 0.5 2018-07-20 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d77/1531966283722/astronomy+and+cosmology+thumbnail.png Astronomy - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d87/1530132981476/Planets_everywhere_%28artist%E2%80%99s_impression%29%5B1%5D.jpg Astronomy - The Diversity of Exoplanets in the Galaxy "This artist's cartoon view gives an impression of how common planets are around the stars in the Milky Way. The planets, their orbits and their host stars are all vastly magnified compared to their real separations. A six-year search that surveyed millions of stars using the microlensing technique concluded that planets around stars are the rule rather than the exception. The average number of planets per star is greater than one."\(^{[1]}\) Image credit: by ESO/M. Kornmesser (http://www.eso.org/public/images/eso1204a/) [CC BY 4.0 (https://creativecommons.org/licenses/by/4.0)], via Wikimedia Commons https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d8f/1530042426129/aHR0cDovL3d3dy5zcGFjZS5jb20vaW1hZ2VzL2kvMDAwLzAzOC81ODAvb3JpZ2luYWwva2VwbGVyLTE4NmYtYXJ0LmpwZz8xMzk3Njg3MTkw%5B1%5D.jpg Astronomy - The Diversity of Exoplanets in the Galaxy Artist's impression of the Archipelago world, Kepler 186f. Credit: Danielle Futselaar https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d6f/1531966586224/facebook+img+thumbnail.jpg Astronomy - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d79/1531960026632/10629328_1041033252591158_1987130945153076812_o.jpg Astronomy - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d93/1530306062728/PIA21061-Pluto-DwarfPlanet-XRays-20160914%5B1%5D.jpg Astronomy - The Diversity of Exoplanets in the Galaxy X-ray image of Pluto obtained by Chandra X-Ray Observatory (blue spot on right) and up-close photograph of Pluto obtained by the spacecraft Deep Horizons as it flew by Pluto. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d8d/1530138555487/maxresdefault.jpg Astronomy - The Diversity of Exoplanets in the Galaxy Image of auroras just above the Earth's surface obtained by the International Space Station. Image credit: NASA https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d89/1530305727092/aHR0cDovL3d3dy5zcGFjZS5jb20vaW1hZ2VzL2kvMDAwLzA1My8yNjkvb3JpZ2luYWwvc3VwZXItZWFydGgtY2FuY3JpLTU1LWUuanBn%5B1%5D.jpg Astronomy - The Diversity of Exoplanets in the Galaxy Artist's depiction of the exoplanet 55 Cancri E. Image credit: ESA/Hubble [CC BY 4.0 (https://creativecommons.org/licenses/by/4.0)], via Wikimedia Commons. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d97/1530743975575/trappist.png Astronomy - The Diversity of Exoplanets in the Galaxy This artist's concept shows what the TRAPPIST-1 planetary system may look like, based on available data about the planets' diameters, masses and distances from the host star. Credits: NASA/JPL-Caltech View full image and caption https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d91/1530047402295/1920px-Kepler186f-ComparisonGraphic-20140417%5B1%5D.jpg Astronomy - The Diversity of Exoplanets in the Galaxy Size comparison of Kepler-186f (artist's impression) with Earth along with their projected habitable zones. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d73/1531966612320/google+img+thumbnail.jpg Astronomy - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d6d/1531966550594/share+astronomy+and+cosmology+img.png Astronomy - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b5120def950b7b766e34d7b/5b5120def950b7b766e34d80/1530135817506/PIA19656-SaturnMoon-Enceladus-Ocean-ArtConcept-20150915%5B2%5D.jpg Astronomy - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b5120def950b7b766e34d7b/5b5120def950b7b766e34d7c/1530135242345/PIA19058-SaturnMoon-Enceladus-PossibleHydrothermalActivity-ArtistConcept-20150311%5B2%5D.jpg Astronomy - The Diversity of Exoplanets in the Galaxy Artists impressions of subsurface oceans underneath thick ice sheets on Jupiter’s moon Europa and Saturn’s moon Enceladus. Top image by NASA. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b5120def950b7b766e34d7b/5b5120def950b7b766e34d7e/1530133614272/image_4610_3e-Europa-Lander%5B1%5D.jpg Astronomy - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d8b/1530236766508/Graphite-and-diamond-with-scale%5B1%5D.jpg Astronomy - The Diversity of Exoplanets in the Galaxy Graphite (left) and diamond (right) are both, essentially, just made up of a bunch of carbon atoms. The difference between the two substances is how those carbon atoms are arranged. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d75/1531966570270/email+img+thumbnail.jpg Astronomy - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d85/1529888319405/aHR0cDovL3d3dy5zcGFjZS5jb20vaW1hZ2VzL2kvMDAwLzA2Mi8wODkvb3JpZ2luYWwvaG90LWp1cGl0ZXItY29uY2VwdGlvbi5qcGc%3D%5B1%5D.jpg Astronomy - The Diversity of Exoplanets in the Galaxy Artist's depiction of a so-called hot Jupiter orbiting its planet star. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d71/1531966632845/twiiter+img+thumbnail.jpg Astronomy - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d95/1531960599987/2159_TRAPPIST-1e_1200_preview%5B1%5D.jpg Astronomy - The Diversity of Exoplanets in the Galaxy This poster imagines what a trip to TRAPPIST-1e might be like. Credits: NASA/JPL-Caltech View full image https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5120def950b7b766e34d83/1531436786142/pular+planet.png Astronomy - The Diversity of Exoplanets in the Galaxy Artist's conception of a planet orbiting a Pulsar. The Pulsar's radiation blasting the exoplanet would cause its surface to glow. https://www.gregschool.org/astronomy/2017/6/16/formation-of-planets-and-stars-xa5hw-2rxlj monthly 0.5 2018-07-20 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ffc275652dea4f72000cb4/1498157418533/mwpan_aitoff_s.jpg Astronomy - A Brief Tour of our Milky Way Galaxy Picture of the Milky Way Galaxy as seen edge on. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ffc275652dea4f72000cb8/1498195183058/430453main_crabmosaic_hst_big_full.jpg Astronomy - A Brief Tour of our Milky Way Galaxy Image of Crab Nebula. (Image credit: NASA) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ffc275652dea4f72000cb2/1498195845727/ Astronomy - A Brief Tour of our Milky Way Galaxy Artist's depiction of the Milky Way Galaxy. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ffc275652dea4f72000cb6/1498193304895/ Astronomy - A Brief Tour of our Milky Way Galaxy Inferred image of the center of the Milky Way Galaxy. (Source) https://www.gregschool.org/astronomy/2017/11/14/drakes-equation-d4hkm-bs6gg monthly 0.5 2018-07-20 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121706d2a73943bc49b51/1531967526142/ Astronomy - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121706d2a73943bc49b69/1510874927808/Kepler_spacecraft_artist_render_%28crop%29%5B1%5D.jpg Astronomy - Drake's Equation and Searching for Life in the Milky Way Artist's depiction of the Kepler space telescope. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b5121706d2a73943bc49b6d/5b5121706d2a73943bc49b70/1510875294374/HT-trappist-1-star-surface-3-jt-170221_4x3_992%5B1%5D.jpg Astronomy - Drake's Equation and Searching for Life in the Milky Way Imagine standing on the surface of the exoplanet TRAPPIST-1f. This artist's concept is one interpretation of what it could look like. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b5121706d2a73943bc49b6d/5b5121706d2a73943bc49b6e/1510875160635/proximasurface%5B1%5D.jpg Astronomy - Drake's Equation and Searching for Life in the Milky Way "This artist’s impression shows a view of the surface of the planet Proxima b orbiting the red dwarf star Proxima Centauri, the closest star to the solar system. The double star Alpha Centauri AB also appears in the image. Proxima b is a little more massive than the Earth and orbits in the habitable zone around Proxima Centauri, where the temperature is suitable for liquid water to exist on its surface."\(^{[1]}\) https://www.nasa.gov/feature/jpl/eso-discovers-earth-size-planet-in-habitable-zone-of-nearest-star Credits: ESO/M. Kornmesser https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121706d2a73943bc49b59/1510779852179/75C0D4ADBC26486DAD4D19D3CBCEB9E1%5B1%5D.jpg Astronomy - Drake's Equation and Searching for Life in the Milky Way "Mr. Spock (Leonard Nimoy), communicating with the Horta through a Vulcan mind meld."\(^{[3]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121706d2a73943bc49b73/1511020696659/qiao-chen-ship9-3%5B1%5D.jpg Astronomy - Drake's Equation and Searching for Life in the Milky Way An artist's depiction of the starship proposed by Project Daedalus.\(^{[5]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121706d2a73943bc49b4b/1531967467107/share+astronomy+and+cosmology+img.png Astronomy - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121706d2a73943bc49b6b/1510868724096/Heic0612b_H%5B1%5D.jpg Astronomy - Drake's Equation and Searching for Life in the Milky Way Artist's depiction of an exoplanet crossing our line of sight in front of its home-star. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121706d2a73943bc49b55/1531967435336/astronomy+and+cosmology+thumbnail.png Astronomy - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b5121706d2a73943bc49b5b/5b5121706d2a73943bc49b5e/1510878262303/20131102_cosmos-episode-2-hfs-a-hunter-close-up%5B1%5D.jpg Astronomy - Drake's Equation and Searching for Life in the Milky Way A Hunter "A speculative hunter animal evolved in the atmosphere of a gas-giant planet. Developed for Cosmos, Episode 2."\(^{[4]}\) Image by Adolf Schaller. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b5121706d2a73943bc49b5b/5b5121706d2a73943bc49b5c/1510878250166/20131102_cosmos-episode-2-hfs-herd-of-floaters%5B1%5D.jpg Astronomy - Drake's Equation and Searching for Life in the Milky Way A Lazy Herd of Floaters "An updated digital restoration by Adolf Schaller of detail in his original Hunters, Floaters, Sinkers mural which appeared on Cosmos, Episode 2, which speculates about life in the atmosphere of a gas-giant planet."\(^{[4]}\) Image by Adolf Schaller. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b5121706d2a73943bc49b5b/5b5121706d2a73943bc49b62/1510878236692/20131102_cosmos-episode-2-hfs-floater-close-up%5B1%5D.jpg Astronomy - Drake's Equation and Searching for Life in the Milky Way A "Floater" from Cosmos, Episode 2 "Part of the larger mural, "Hunters, Floaters, and Sinkers" painted for the series."\(^{[4]}\) Image by Adolf Schaller. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b5121706d2a73943bc49b5b/5b5121706d2a73943bc49b60/1510878224307/20131102_cosmos-episode-2-jovian-life-full%5B1%5D.jpg Astronomy - Drake's Equation and Searching for Life in the Milky Way Hunters, Floaters, and Sinkers "This painting speculates about possible forms of life on a Jupiter-like gas giant. Airbrushed water-based acrylic."\(^{[4]}\) Image by Adolf Schaller. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121706d2a73943bc49b4d/1531967492944/facebook+img+thumbnail.jpg Astronomy - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121706d2a73943bc49b53/1531967513017/email+img+thumbnail.jpg Astronomy - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121706d2a73943bc49b4f/1531967540634/twiiter+img+thumbnail.jpg Astronomy - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121706d2a73943bc49b65/1531769943991/pular+planet.png Astronomy - Drake's Equation and Searching for Life in the Milky Way Artist's depiction of an exoplanet orbiting a pulsar. Due to the pulsar's radiation, the exoplanet glows. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121706d2a73943bc49b67/1510874187182/Habitable-zone%5B1%5D.jpg Astronomy - Drake's Equation and Searching for Life in the Milky Way The habitable zone is a range of orbital distances (between an exoplanet and the star it orbits) where the planet is neither too hot nor too cold. This is also sometimes called the Goldilocks zone. In order for a planet to be truly "Earth-like," it must also have a mass 1-2 times that of the Earth, have an atmosphere, and orbit in a stable elliptical orbit that is not too essentric. https://www.gregschool.org/articles-page-3 daily 0.75 2019-03-23 https://www.gregschool.org/articles-page-3/2017/5/4/chaos monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/591151f3ebbd1a1c7146dedc/1510175075112/ Articles page 3 - Chaos and Fractals Figure 3: After rolling the dice (and drawing a new point for each dice roll) billions of times, a fractal pattern known as the Siepinski triangle will eventually form. Remarkable! Image credit: by Beojan Stanislaus (Own work) [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7ab653450a448c8ebc47/1510175075100/twiiter+img+thumbnail.jpg Articles page 3 - Chaos and Fractals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7a6fe2c483f6d05e1621/1510175075104/email+img+thumbnail.jpg Articles page 3 - Chaos and Fractals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff3406084665ad8a6aeed1/1510175075108/Edward_lorenz%5B1%5D.jpg Articles page 3 - Chaos and Fractals Figure 1: "Edward Norton Lorenz (May 23, 1917 – April 16, 2008) was an American mathematician, meteorologist, and a pioneer of chaos theory, along with Mary Cartwright. He introduced the strange attractor notion and coined the term butterfly effect."\(^{[3]}\) This image is for educational purposes only. Image credit: https://history.aip.org/history/Thumbnails/lorenz_edward_a1.jpg https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7b35f9619a4291a33a08/1510175075096/share+chaos+theory+img.png Articles page 3 - Chaos and Fractals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7a9ef9619a4291a32659/1510175075102/google+img+thumbnail.jpg Articles page 3 - Chaos and Fractals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/591152916a49631ac1ea2b7e/1510175075114/ Articles page 3 - Chaos and Fractals Figure 4: An image of the Cantor set. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7a8bec212d4734b428bf/1510175075098/facebook+img+thumbnail.jpg Articles page 3 - Chaos and Fractals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7a5e71c10b5cf332538b/1510175075106/chaos+theory+thumbnail.png Articles page 3 - Chaos and Fractals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff4086652dea4f72f0058b/1510175075110/dice+game.jpg Articles page 3 - Chaos and Fractals Figure 2: The three points \((1,2)\), \((3,4)\), and \((5,6)\) form an equilateral triangle. Choose any arbitrary point \((x,y)\) anywhere on the plane either inside or outside the triangle. If you rolled a 1 or 2, then draw a new point \((x_0,y_0)\) whose distance is half way between the points \((x,y)\) and \((1,2)\). Repeat this many times. https://www.gregschool.org/articles-page-3/2017/8/21/our-future-as-cyborgs monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcd8f0e2c48368899b7590/1510175161926/technology+thumbnail.png Articles page 3 - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcd71fe4966b73fb5e06c5/1510175161916/share+technology++img.jpg Articles page 3 - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fc903c8165f523f3e7d89d/1510175161930/04-17-Asimo-Grand-Marshall-HIGPA%5B1%5D.jpg Articles page 3 - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcd6510d9297c985fd4996/1510175161919/facebook+img+thumbnail.jpg Articles page 3 - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcd646e4966b73fb5de391/1510175161925/email+img+thumbnail.jpg Articles page 3 - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcd6788e7b0f7a2846fc2e/1510175161921/twiiter+img+thumbnail.jpg Articles page 3 - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcd6628165f5c5830d6d7d/1510175161923/google+img+thumbnail.jpg Articles page 3 - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af503b893fc0f1e6fe9fb7/1510175161928/bionic_v2.png Articles page 3 - Our Future as Cyborgs https://www.gregschool.org/articles-page-3/2017/10/30/derivation-of-snells-law-a8sne monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f912aa6926705bd6810aae/1509495184204/email+img+thumbnail.jpg Articles page 3 - Derivation of Snell's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f912aa6926705bd6810aa6/1509495184185/share+img.jpg Articles page 3 - Derivation of Snell's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f912aa6926705bd6810aac/1509495184200/google+img+thumbnail.jpg Articles page 3 - Derivation of Snell's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f912aa6926705bd6810aa8/1509495184190/facebook+img+thumbnail.jpg Articles page 3 - Derivation of Snell's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f912aa6926705bd6810ab4/1509495184220/snells+law.jpg Articles page 3 - Derivation of Snell's Law Figure 2: As a light ray travels along the line \(QO\) through medium 1 and comes into contact with the interface between medium 1 and medium 2, it gets refracted—meaning, it passes through medium 2. Image credit: By Smedlib (Own work) [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f912aa6926705bd6810ab0/1509495184210/Calculus+thumbnail.png Articles page 3 - Derivation of Snell's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f912aa6926705bd6810ab2/1509495184214/snellslaw2.jpg Articles page 3 - Derivation of Snell's Law Figure 1: A light ray traveling along the line \(QO\) comes into contact with a surface at an \(θ_i\) (where \(θ_i\) is measured relative to the line perpendicular to the surface). Once this light ray comes into contact with this surface, it is reflected at an angle \(θ_r\) (\(θ_r\) is also measured relative to the perpendicular). According to the law of reflection, \(θ_i=θ_r\). Image credit: Download for free at http://cnx.org/contents/60b4727b-829e-4ea7-9238-9140b6a1b20c@4. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f912aa6926705bd6810aaa/1509495184195/twiiter+img+thumbnail.jpg Articles page 3 - Derivation of Snell's Law https://www.gregschool.org/articles-page-3/2017/9/21/shkadov-thruster-ljar4 monthly 0.5 2018-06-28 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f91d08085229220f420c05/1509497981397/twiiter+img+thumbnail.jpg Articles page 3 - Megastructures: Shkadov Thrusters https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f91d08085229220f420c0f/1509497981409/neil-blevins-megastructures-5-shkadov-thruster-design-packet.jpg Articles page 3 - Megastructures: Shkadov Thrusters Figure 2: Artist's depiction of a Shkadov thruster. Credit: https://www.artstation.com/artofsoulburn https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f91d08085229220f420c01/1509497981393/share+img+for+spacetrav+and+col+thumbnail.png Articles page 3 - Megastructures: Shkadov Thrusters https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f91d08085229220f420c09/1509497981402/email+img+thumbnail.jpg Articles page 3 - Megastructures: Shkadov Thrusters https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f91d08085229220f420c03/1509649775356/facebook+img+thumbnail.jpg Articles page 3 - Megastructures: Shkadov Thrusters https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f91d08085229220f420c07/1509497981400/google+img+thumbnail.jpg Articles page 3 - Megastructures: Shkadov Thrusters https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f91d08085229220f420c0b/1509497981404/space+travela+nd+colonization+thumbnail.png Articles page 3 - Megastructures: Shkadov Thrusters https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f91d08085229220f420c0d/1509497981406/Shkadov_diagram.jpg Articles page 3 - Megastructures: Shkadov Thrusters Figure 1: An arc mirror (dark orange arc) subtended by an angle \(2\phi\) reflects a star's radiation back towards itself. Photons collide against the portion of the star's surface which is subtended by the angle \(2\phi\). These collisions result in a net force \(\vec{F}\) exerted on the star causing the entire star to move in the direction of the arrow. The star's gravity pulls everything else in the star system along with it. https://www.gregschool.org/articles-page-3/2017/9/11/harvesting-resources-from-saturn-and-titan-l5msz monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff860324a6943fd0e9982e/1509669572916/share+img+for+spacetrav+and+col+thumbnail.png Articles page 3 - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff860324a6943fd0e99836/1509669490962/email+img+thumbnail.jpg Articles page 3 - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff860324a6943fd0e99830/1509917501164/facebook+img+thumbnail.jpg Articles page 3 - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff860324a6943fd0e9983a/1508646767750/WANDERERS_ligeia_mare_01.jpg Articles page 3 - Harvesting Resources from Saturn and Titan "With an average temperature of -180 C all water here is frozen hard as rock. In fact, the surface landscape of Titan is indeed mostly made of frozen water ice. But Titan's atmosphere is rich in hydrocarbons such as methane and ethane, and the low temperature is perfect for these elements to occur naturally in three states; frozen, liquid and gas. So, just as on Earth where we have a water cycle (ice melts, becomes water, water evaporates into clouds, turning into liquid and becomes rain and so forth), Titan has a methane cycle. Methane evaporates and rises to form clouds, eventually turning into rain, falling over the surface. And this is the most amazing part; the rain in some places is enough to fill entire lakes. Lakes of methane! Titan is the only place in the Solar System, other than Earth, known to have large bodies of liquid on its surface. And they are really there, huge lakes, with shorelines, islands and small archipelagos. This scene takes place over a lake know as Ligeia Mare, the second largest on Titan, about 500 kilometers in diameter, located in the north polar region of the moon. The second fantastic feature I wanted to illustrate is the combination of Titan's very dense atmosphere and its relatively low gravity. As a human on Titan you would weigh about 14% of what you do on Earth, and in the dense atmosphere it would be enough to strap wings on your arms to make you able to fly like a bird. On Titan you could fly like a bird, over lakes of methane! (If you wore some really warm clothes of course.)" Image and image description credit: WANDERERS - a short film by EriK Wernquist https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff860324a6943fd0e99834/1509669876565/google+img+thumbnail.jpg Articles page 3 - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff860324a6943fd0e99838/1509917604285/space+travela+nd+colonization+thumbnail.png Articles page 3 - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff860324a6943fd0e99832/1509669798150/twiiter+img+thumbnail.jpg Articles page 3 - Harvesting Resources from Saturn and Titan https://www.gregschool.org/articles-page-3/2017/10/27/gravitational-force-exerted-by-a-sphere-lm293 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2caf8165f531bc159e95/1509566648759/facebook+img+thumbnail.jpg Articles page 3 - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2caf8165f531bc159e9b/1509565382744/email+img+thumbnail.jpg Articles page 3 - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2caf8165f531bc159e99/1509566740045/google+img+thumbnail.jpg Articles page 3 - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2caf8165f531bc159e93/1509566039912/share+img+for+classical+mechanics+thumbnail.png Articles page 3 - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2caf8165f531bc159e9f/1509567101995/ring1.jpg Articles page 3 - Gravitational Force Exerted by a Disk Figure 1: A ring of mass \(M=\int{dm}\) exerts a gravitational force on a particle of mass \(m\) a horizontal distance \(h\) away from the center of the ring. The vertical component of force \(dF_y\) for every mass element \(dm\) in the ring is canceled out by the vertical component of force \(dF'_y\) for another mass element \(dm'\) located on the opposite side of the ring. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2caf8165f531bc159ea1/1509214998235/diskss.jpg Articles page 3 - Gravitational Force Exerted by a Disk Figure 2: A disk of mass \(M=\int{m_{ring}}\) exerts a gravitational force on a particle of mass \(m\) a distance \(h\) away from the center of the disk along the \(x\)-axis. By summing the gravitational force exerted on \(m\) by each ring of radius \(r\) from \(r=0\) to \(r=R\), we can find the total gravitational force exerted on \(m\) by the entire disk. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2caf8165f531bc159e97/1509566668834/twiiter+img+thumbnail.jpg Articles page 3 - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2caf8165f531bc159e9d/1509566564697/classical+mechanics+thumbnail.png Articles page 3 - Gravitational Force Exerted by a Disk https://www.gregschool.org/articles-page-3/2017/11/2/how-fast-does-water-rise-up-a-cone monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7d3a652dea4f72f761f8/1509916394698/Calculus+thumbnail.png Articles page 3 - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7d6a9140b72e2509c908/1509916394693/google+img+thumbnail.jpg Articles page 3 - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7d51084665ad8a739a9f/1509916394696/email+img+thumbnail.jpg Articles page 3 - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7d78c83025d8b000ea94/1509916394691/twiiter+img+thumbnail.jpg Articles page 3 - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff6673084665ad8a709b03/1509916394700/flow-rate-cone.gif Articles page 3 - How Fast Does Water Rise Up a Cone? Figure 1: Water being poured into a rectangular box with dimensions \(4ft×4ft×h\) at a rate of \(\frac{dV}{dt}=4\frac{ft^3}{min}\). The container at time \(t=0\) starts out empty. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7d594192021a543b80fb/1509916394689/facebook+img+thumbnail.jpg Articles page 3 - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7dcdc83025d8b000f538/1509916394688/share+calculus+img.png Articles page 3 - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff5855e31d1945638623da/1509916394702/flow-rate-cone.gif Articles page 3 - How Fast Does Water Rise Up a Cone? Figure 2: Water is poured into a cone of height \(h\) and radius \(r\) at a rate of \(\frac{dV}{dt}=4\frac{ft^3}{min}. The height of the water is given by \(y\). This image was modified under a Create Commons license. Image credit: https://www.mathalino.com/blog/romel-verterra/calculator-technique-solving-volume-flow-rate-problems-calculus https://www.gregschool.org/articles-page-3/2017/10/22/volume-of-an-oblate-spheroid-rl852 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd1d1553450a448c5f243c/1509759183401/temporary+shareeeeee.png Articles page 3 - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd1d1553450a448c5f2440/1509759470891/Twitter+thumbnail.jpg Articles page 3 - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd1d1553450a448c5f2448/1509754144604/oblate+spheroid+img1.png Articles page 3 - Volume of an Oblate Spheroid Figure 1: Graph of the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\) centered at the origin of the \(xy\)-plane. Also, I have drawn the \(i^{th}\) rectangle underneath the quarter-ellipse within the first quadrant. There are an \(n\) number of such rectangles underneath this quarter-ellipse along the interval \(Δx=3-0\).   https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd1d1553450a448c5f2446/1509758473080/Calculus+thumbnail.png Articles page 3 - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd1d1553450a448c5f2444/1509758531993/email+thumbnail.jpg Articles page 3 - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd1d1553450a448c5f243e/1509759571921/facebook+thumbnail.jpg Articles page 3 - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd1d1553450a448c5f2442/1509759611612/google+share+thumbnail.jpg Articles page 3 - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd1d1553450a448c5f244a/1509755409825/oblate+spheroid+img2.png Articles page 3 - Volume of an Oblate Spheroid Figure 2: A cylindrical shell is obtained by revolving the rectangle \(f(x_i)Δx\) about the \(y\)-axis. Doing this for all \(n\) rectangles, we get an \(n\) number of shells. By summing the volumes of these \(n\) number of cylindrical shells, we can obtain an estimate for total volume enclosed inside of the paraboloid obtained by rotating the quarter-ellipse (the one in the upper-right quadrant) about the \(x\)-axis. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd1d1553450a448c5f244c/1509393143387/oblate+sphereoid.jpg Articles page 3 - Volume of an Oblate Spheroid Figure 3: If \(a\) and \(c\) represents the semi-major and semi-minor axes of an ellipse, respectively, and if \(a=3\) and \(c=2\) then by rotating such an ellipse about an axis we can obtain an oblate spheroid. https://www.gregschool.org/articles-page-3/2017/10/29/quasars-3xbmj monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe254a24a6943fd0cbf03d/1509826851511/astronomy+and+cosmology+thumbnail.png Articles page 3 - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe254a24a6943fd0cbf039/1509827375093/google+img+thumbnail.jpg Articles page 3 - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe254a24a6943fd0cbf037/1509827352336/twiiter+img+thumbnail.jpg Articles page 3 - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe254a24a6943fd0cbf043/1509816781341/Best_image_of_bright_quasar_3C_273%5B1%5D.jpg Articles page 3 - Quasars Figure 3: "This image from Hubble’s Wide Field and Planetary Camera 2 (WFPC2) is likely the best of ancient and brilliant quasar 3C 273, which resides in a giant elliptical galaxy in the constellation of Virgo (The Virgin). Its light has taken some 2.5 billion years to reach us. Despite this great distance, it is still one of the closest quasars to our home. It was the first quasar ever to be identified, and was discovered in the early 1960s by astronomer Allan Sandage. The term quasar is an abbreviation of the phrase “quasi-stellar radio source”, as they appear to be star-like on the sky. In fact, quasars are the intensely powerful centres of distant, active galaxies, powered by a huge disc of particles surrounding a supermassive black hole. As material from this disc falls inwards, some quasars — including 3C 273 — have been observed to fire off super-fast jets into the surrounding space. In this picture, one of these jets appears as a cloudy streak, measuring some 200 000 light-years in length. Quasars are capable of emitting hundreds or even thousands of times the entire energy output of our galaxy, making them some of the most luminous and energetic objects in the entire Universe. Of these very bright objects, 3C 273 is the brightest in our skies. If it was located 30 light-years from our own planet — roughly seven times the distance between Earth and Proxima Centauri, the nearest star to us after the Sun — it would still appear as bright as the Sun in the sky. WFPC2 was installed on Hubble during shuttle mission STS-125. It is the size of a small piano and was capable of seeing images in the visible, near-ultraviolet, and near-infrared parts of the spectrum."\(^{[3]}\) Image Credit: ESA/Hubble [CC BY 4.0 (http://creativecommons.org/licenses/by/4.0)], via Wikimedia Commons https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe254a24a6943fd0cbf031/1509827157786/share+technology++img.jpg Articles page 3 - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe254a24a6943fd0cbf045/1509818196809/Quasar%5B1%5D.png Articles page 3 - Quasars Figure 4: Illustration of the various different components of a quasar.\(^{[4]}\) Image credit: Futurism. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe254a24a6943fd0cbf047/1509815102930/orangepie%5B1%5D.jpg Articles page 3 - Quasars Figure 5: A 3-d map obtained by the Sloan Digital Survey of billions of light years of our local universe. Each dot is an entire galaxy and this survey shows millions of them. As you can see from this image, on the scale of billions of light-years the galaxies of congregated into a "web"-like structure of filaments and strands known as the cosmic web. Image Credit: M. Blanton and SDSS https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe254a24a6943fd0cbf03f/1509813587682/PIA13033%5B1%5D.jpg Articles page 3 - Quasars Figure 1: "The 200-inch (5.1 m) Hale Telescope (f/3.3) was the world's largest effective telescope for 45 years (1948-1993). It is still a workhorse of modern astronomy. It is used nightly for a wide range of astronomical studies. On average the weather allows for at least some data collection about 290 nights a year."\(^{[1]}\) Image credit: Caltech/Palomar Observatory https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe254a24a6943fd0cbf041/1509815576468/3C273z%5B1%5D.gif Articles page 3 - Quasars Figure 2: "The spectrum of the quasar 3C 273. The strongest emission lines present are Balmer lines of hydrogen, as marked. In each case, the arrow is drawn from the rest wavelength to the observed wavelength of the line— shifted redward in each case by 15.8%. The other emission lines apparent in the spectrum are due to oxygen, helium, iron, and other elements. Credit: Michael A. Strauss, from data taken by the New Technology Telescope at La Silla, Chile; M. Türler et al. 2006, Astronomy and Astrophysics 451: L1– L4, http:// isdc.unige.ch/ 3c273/# emmi, http:// casswww.ucsd.edu/ archive/ public/ tutorial/ images/ 3C273z.gif Tyson, Neil deGrasse; Strauss, Michael A.; Gott, J. Richard. Welcome to the Universe: An Astrophysical Tour (p. 242). Princeton University Press. Kindle Edition."\(^{[2]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe254a24a6943fd0cbf035/1509827332035/facebook+img+thumbnail.jpg Articles page 3 - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe254a24a6943fd0cbf03b/1509826869477/email+img+thumbnail.jpg Articles page 3 - Quasars https://www.gregschool.org/articles-page-3/2017/10/22/partial-derivatives-6cjz9 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe287871c10b5cf3169bc4/1509828633114/facebook+img+thumbnail.jpg Articles page 3 - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe287871c10b5cf3169bce/1508723598292/MSP5083101ccb77dc1c84hg00003d8bb0b0083b496c.gif Articles page 3 - Introduction to Partial Derivatives Figure 1: Graph of the surface \(f(x,y)=x^2+y^2\). Image courtesy of Wolfram Alpha. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe287871c10b5cf3169bca/1509828286844/email+img+thumbnail.jpg Articles page 3 - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe287871c10b5cf3169bcc/1509828263016/Calculus+thumbnail.png Articles page 3 - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe287871c10b5cf3169bd0/1509324744015/partial+derivatives.jpg Articles page 3 - Introduction to Partial Derivatives Figure 2: The entire blue surface is given by the function \(f(x,y)=x^2+y^2\). By letting \(y=1\), we that \(y^2=1\) and \(f(x,1)=x^2+1\) giving us a parabola shifted up one unit along the \(z\)-axis. That is how we can analytically obtain the parabola \(f(x,y)\). We can also obtain \(f(x,1)\) by passing the plane \(y=1\) (illustrated as the black plane above) through the surface \(f(x,y)\). The points at which the two surfaces (the surface \(f(x,y)\) and the plane \(y=1\)) intersect form the red parabola drawn in the image above. Image credit: By IkamusumeFan (Own work) [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe287871c10b5cf3169bc2/1509828558864/share+calculus+img.png Articles page 3 - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe287871c10b5cf3169bc6/1509828608825/twiiter+img+thumbnail.jpg Articles page 3 - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe287871c10b5cf3169bc8/1509828652953/google+img+thumbnail.jpg Articles page 3 - Introduction to Partial Derivatives https://www.gregschool.org/articles-page-4 daily 0.75 2019-03-23 https://www.gregschool.org/articles-page-4/2017/9/27/introduction-to-line-integrals-bywel monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59daa50d2aeba571e4098dbe/1510175532388/sdf.jpg Articles page 4 - Introduction to Line Integrals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d9a6c0a803bb45f4162a6f/1507432031391/VIBrO.jpg Articles page 4 - Introduction to Line Integrals Figure 1: The width and height of each blue rectangle is given by the arc length \(ds\) and the function \(f(x,y)\), respectively. The line integral, \(\int_Cf(x,y)ds\), represents the infinite sum of the area of each blue rectangle along the curve \(C\) (the purple line on the \(xy\)-plane). This image is a derivative work. Original image: https://www.wikihow.com/User:Atheia https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d9a6c0a803bb45f4162a71/1507433707547/fhdhfdg.jpg Articles page 4 - Introduction to Line Integrals Figure 2: By the Pythagorean theorem, each infinitesimal arc length \(ds\) can be represented in terms of \(x\) and \(y\) as \(\sqrt{x+2+y^2}\). https://www.gregschool.org/articles-page-4/2017/9/30/solving-problems-using-line-integrals-z8s7t monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dabac5e5dd5b959940473e/1507491891563/156px-Circular_cylinder_rh.jpg Articles page 4 - Solving Problems using Line Integrals Figure 1: A cylinder with height \(h=2\) and radius \(r=1\). The "top" and "bottom" pieces of the cylinder are removed. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dabac5e5dd5b9599404740/1507147436235/Untitled.jpg Articles page 4 - Solving Problems using Line Integrals Figure 2: A proton \(P_2\) seperated by an initil seperation distance \(r_0\) from a station proton \(P_1\) moves along an arbitrary path until it reaches a seperation distance of \(r\). According to Column's law, the proton \(P_1\) will exert an electric force and, hence, also do work on the proton \(P_2\) as it moves from \(r_0\) to \(r\). The electric force forms a vector field and by calculuating the line integral along \(P_2\)'s path, we can calculate the amount of work done on \(P_2\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dabac5e5dd5b9599404742/1506906635307/main-qimg-ef54da6034b7e89fb771a40923f089ca.gif Articles page 4 - Solving Problems using Line Integrals Figure 3: A mass \(m\) is attached to the end of a rope of length \(L\). The mass falls and travels a distance \(s\) with a total angular displacement of \(θ\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dabac5e5dd5b959940473c/1507502227235/sdfsdfdsdfdfdf+october+8.jpg Articles page 4 - Solving Problems using Line Integrals https://www.gregschool.org/articles-page-4/2017/8/30/5g8xs8bx2yk4rez4xp70hkmry35965-k5dj3 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc39b4f6576e8869f79927/1507603176920/electromagnetism+thumbnaillllll+imageeee.jpg Articles page 4 - Calculating the amount of Electric Potential Energy Stored in a Capacitor https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc39b4f6576e8869f79929/1504719624283/kkk.png Articles page 4 - Calculating the amount of Electric Potential Energy Stored in a Capacitor Figure 1 https://www.gregschool.org/articles-page-4/2017/9/19/the-kardeshev-scale-ge4gb monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd7b6129f187ed8e5f80ff/1507687169817/space+travela+nd+colonization+thumbnail.jpg Articles page 4 - The Kardeshev Scale https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd7b6129f187ed8e5f8109/1507683863314/bubble-universes-computer-illustration-of-multiple-bubble-universes-G4C3H0.jpg Articles page 4 - The Kardeshev Scale Artist's depiction of the multi-verse. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd7b6129f187ed8e5f8101/1507057461266/1024px-Consommations_%C3%A9nerg%C3%A9tiques_des_trois_types_de_l%27%C3%A9chelle_de_Kardashev.svg.png Articles page 4 - The Kardeshev Scale The Kardeshev scale ranks how advanced a technological civilization is based upon their total power consumption. A Type I civilization is capable of harnessing all of their home plant's power of \(~10^{16}W\); a Type II civilization has harnessed the power of their star ( \(~10^{26}W\)); and a Type III civilization has harnessed the power output of their entire galaxy ( \(~10^{36}W\)). There are even Type IV and Type V civilization which go beyond Kardeshev's original scale. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/59dd7b6129f187ed8e5f8103/59dd7b6129f187ed8e5f8104/1507676111750/dyson_sphere_second_1024.jpg Articles page 4 - The Kardeshev Scale Dyson sphere. Credit: capnhack.com https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/59dd7b6129f187ed8e5f8103/59dd7b6129f187ed8e5f8106/1507750720730/17202572._SX540_.jpg Articles page 4 - The Kardeshev Scale Artist's depiction of a ring world. Credit: http://richardfrazer.com/ https://www.gregschool.org/articles-page-4/2017/10/6/calculating-the-arc-length-of-a-curve-hk54b monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd7e3d2994cac72c703af8/1507687678074/calculus+thumbnail.jpg Articles page 4 - Calculating the Arc Length of a Curve https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd7e3d2994cac72c703afa/1507341957781/arclengthimg1.jpg Articles page 4 - Calculating the Arc Length of a Curve Figure 1: The curve \(P_1P_n\) split up into an \(n\) number of chords \(P_iP_{i+1}\) where \(i=1,...,n\). By taking the sum of the lengths of each chord (represented by \(\sum_{i=1}^nL(P_iP_{i+1})\)) and then taking the limit as \(n→∞\), we obtain the exact arc length \(s\) of the entire curve. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd7e3d2994cac72c703afc/1507343004584/arclengthimg2.jpg Articles page 4 - Calculating the Arc Length of a Curve Figure 2: A close up view of the \(i^{th}\) chord subdividing the curve \(P_1P_n\). Since the chord \(P_iP_{i+1}\) forms a right triangle, by using the Pythagorean theorem we can express \(L(P_iP_{i+1})\) as \(\sqrt{(Δx_i)^2+(Δy_i)^2}\). https://www.gregschool.org/articles-page-4/2017/8/13/why-colonize-the-universe-z48ay monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd8034bebafb7a8ad973ef/1507059034215/factoriesins.jpg Articles page 4 - Why Colonize the Universe? An O'Neil cylinder is a type of megastructure and artificial space habitat which was first proposed by the physicist Gerard O'Neil in 1976. An O'Neil cylinder would consist of two immense, rotating, cylindrical habitats (illustrated above) which would spin at a angular velocity that generated centrifugal forces along the interior surfaces of the cylinders which would emulate Earth-gravity. Each cylindrical habitat would be 5 miles in diameter and 20 miles long. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd8034bebafb7a8ad973ed/1507058438785/51i54HqlYHL._SY344_BO1%2C204%2C203%2C200_.jpg Articles page 4 - Why Colonize the Universe? In Carl Sagan's book Pale Blue Dot, he argued that humans evolved a love for exploration as an essential part of our survival as a species. It was this evolutionary trait which compelled our hunter-gather ancestors to leave their home—Africa—when times were getting rough and to meander across the planet. As planetary catastrophes become increasingly likely as time rolls by, Sagan argues that this same "survival strategy" will perhaps compell humanity to colonize the solar system, and beyond. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd8034bebafb7a8ad973eb/1507688339362/space+travela+nd+colonization+thumbnail.jpg Articles page 4 - Why Colonize the Universe? https://www.gregschool.org/articles-page-4/2017/9/12/colonizing-the-kuiper-belt-and-oort-cloud-g53ff monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd84eea8b2b090a391a372/1507689697151/Ancient_Mars3_02.jpg Articles page 4 - Colonizing the Kuiper Belt and Oort Cloud Artist's depiction of Fesenkov Crater on Mars filled with liquid water. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce4d1e2c483b3c8a7dadb/1509746098354/share+technology++img.jpg Articles page 4 - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce423f9619ae4de04d0f5/1509746098355/facebook+img+thumbnail.jpg Articles page 4 - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/59dd84eea8b2b090a391a374/59dd84eea8b2b090a391a377/1507689697156/uranus-gas-zoom.jpg Articles page 4 - Colonizing the Kuiper Belt and Oort Cloud Artist’s depiction of Neptune’s (above image) and Uranus’s (below image) atmosphere being harvested for resources such as nitrogen. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/59dd84eea8b2b090a391a374/59dd84eea8b2b090a391a375/1507689697153/george-dennis-the-fountains-of-neptune.jpg Articles page 4 - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd84eea8b2b090a391a37a/1507689697158/OortCloud_P-sys%28PNG-fin%291.png Articles page 4 - Colonizing the Kuiper Belt and Oort Cloud Another size comparison of the solar system to the Oort Cloud. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce44f419202d6b98d22b3/1509746098357/twiiter+img+thumbnail.jpg Articles page 4 - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd84eea8b2b090a391a36e/1507689697148/space+travela+nd+colonization+thumbnail.jpg Articles page 4 - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce41a64265f1222b3c4c7/1509746098361/email+img+thumbnail.jpg Articles page 4 - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce4438165f503e34f6d8f/1509746098359/google+img+thumbnail.jpg Articles page 4 - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd84eea8b2b090a391a370/1507689697150/Kuiper_oort.jpg Articles page 4 - Colonizing the Kuiper Belt and Oort Cloud A size comparison of the Kuiper belt and outer solar system to the Oort Cloud. https://www.gregschool.org/articles-page-4/2017/10/14/optimizatio-z7f59 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911acf9619acf1651011e/1509295467142/Optimization+Problem.jpg Articles page 4 - Optimization Problem Figure 1: A graph of the circle \(x^2+y^2=4\) which is centered at the origin of the \(x\)-axis. If \((x,y)\) represents any point on the circle, if \(P\) is a point fixed at the coordinate point \((4,0)\), and if \(d\) represents the distance between those two points then, by using only calculus, we can find the point \((x,y)\) on the circle associated with the minimum distance \(d\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911acf9619acf16510114/1509493612642/facebook+img+thumbnail.jpg Articles page 4 - Optimization Problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911acf9619acf1651011a/1509492674642/email+img+thumbnail.jpg Articles page 4 - Optimization Problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911acf9619acf16510118/1509493672006/google+img+thumbnail.jpg Articles page 4 - Optimization Problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911acf9619acf16510112/1509492743734/share+img.jpg Articles page 4 - Optimization Problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911acf9619acf1651011c/1509492607607/Calculus+thumbnail.png Articles page 4 - Optimization Problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911acf9619acf16510116/1509493629913/twiiter+img+thumbnail.jpg Articles page 4 - Optimization Problem https://www.gregschool.org/articles-page-4/2017/10/14/maximizing-the-area-of-a-rectangle-stk62 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911bff9619acf165102a5/1509491428650/facebook+img+thumbnail.jpg Articles page 4 - Maximizing the Area of a Rectangle https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911bff9619acf165102a9/1509491415850/google+img+thumbnail.jpg Articles page 4 - Maximizing the Area of a Rectangle https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911bff9619acf165102ab/1509490808504/email+img+thumbnail.jpg Articles page 4 - Maximizing the Area of a Rectangle https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911bff9619acf165102af/1509297168705/Optimization+Problem+1.jpg Articles page 4 - Maximizing the Area of a Rectangle Figure 1: Given any rectangle \(xy\) where the perimeter \(2x+2y\) is the constant, we can use calculus to find that particular rectangle \(xy\) with the maximum area \(A\). The solution to this problem has practical applications. For example, suppose that someone had only 30 meters of fencing to enclose their backyard and they wanted to know what fencing layout would maximize the size and total area of their backyard. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911bff9619acf165102a3/1509490953440/share+img.jpg Articles page 4 - Maximizing the Area of a Rectangle https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911bff9619acf165102ad/1509490767138/Calculus+thumbnail.png Articles page 4 - Maximizing the Area of a Rectangle https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911bff9619acf165102a7/1509491391314/twiiter+img+thumbnail.jpg Articles page 4 - Maximizing the Area of a Rectangle https://www.gregschool.org/articles-page-4/2017/6/24/finding-the-minima-and-maxima-of-a-function-9g3gp monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911cac830259dbcf14c2b/1509495139370/share+img.jpg Articles page 4 - Finding the Minima and Maxima of a Function https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911cac830259dbcf14c2e/1509495139372/facebook+img+thumbnail.jpg Articles page 4 - Finding the Minima and Maxima of a Function https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911cac830259dbcf14c32/1509495139375/google+img+thumbnail.jpg Articles page 4 - Finding the Minima and Maxima of a Function https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911cac830259dbcf14c30/1509495139373/twiiter+img+thumbnail.jpg Articles page 4 - Finding the Minima and Maxima of a Function https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911cac830259dbcf14c34/1509495139377/email+img+thumbnail.jpg Articles page 4 - Finding the Minima and Maxima of a Function https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f911cac830259dbcf14c36/1509495139379/Calculus+thumbnail.jpg Articles page 4 - Finding the Minima and Maxima of a Function https://www.gregschool.org/newtons-laws daily 0.75 2018-09-14 https://www.gregschool.org/newtons-laws/2017/8/28/newtons-law-of-gravity monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbe349c027d89dcc0b93e5/1507582796854/Untitled.jpg Newton's Laws - Newton's Law of Gravity https://www.gregschool.org/newtons-laws/2017/8/29/newtons-three-laws-of-motion monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbe2a064b05fea9d3ba7ff/1507582628254/Untitled.jpg Newton's Laws - Newton's Three Laws of Motion https://www.gregschool.org/newtons-laws/2017/8/28/motion-of-objects-experiancing-air-friction monthly 0.5 2018-04-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf14cf9a61e6c50bbbcc8/1507586382008/gfnf.jpg Newton's Laws - Motion of objects experiancing air friction https://www.gregschool.org/newtons-laws/2017/11/2/gravitational-force-exerted-by-a-rod monthly 0.5 2018-04-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb87b1562fa79982a0128d/1523288170413/google+share+thumbnail.jpg Newton's Laws - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb879670a6adaedb5b874b/1523288170416/email+thumbnail.jpg Newton's Laws - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb87841ae6cf686afde0cf/1523288170409/facebook+thumbnail.jpg Newton's Laws - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fbb054e2c483cd2604f07c/1523288170419/rod.png Newton's Laws - Gravitational Force Exerted by a Rod Figure 1: A rod of mass \(M\) and a particle of mass \(m\) are separated from each other by a distance of \(d\) along the \(x\)-axis. Each mass element \(dm\) comprising the rod is located at some position \(x\) along the \(x\)-axis and is separated from the particle \(m\) by some amount \(r\). By summing all the gravitational forces \(d\vec{F}_g\) exerted by each mass element \(dm\) comprising the rod, we can find the total gravitational force exerted on \(m\) by the entire rod. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb87bf2b6a289d08df6b17/1523288170411/Twitter+thumbnail.jpg Newton's Laws - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb87ee70a6adaedb5b9ad5/1523288170407/sharee.png Newton's Laws - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb8729aa4a998f3f755542/1523288170418/classical+mechanics+thumbnail.png Newton's Laws - Gravitational Force Exerted by a Rod https://www.gregschool.org/newtons-laws/2017/10/27/gravitational-force-exerted-by-a-sphere-geml5 monthly 0.5 2018-04-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2d5a692670838629cc86/1509567663517/twiiter+img+thumbnail.jpg Newton's Laws - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2d5a692670838629cc88/1509567663519/google+img+thumbnail.jpg Newton's Laws - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2d5a692670838629cc90/1509567663526/diskss.jpg Newton's Laws - Gravitational Force Exerted by a Disk Figure 2: A disk of mass \(M=\int{m_{ring}}\) exerts a gravitational force on a particle of mass \(m\) a distance \(h\) away from the center of the disk along the \(x\)-axis. By summing the gravitational force exerted on \(m\) by each ring of radius \(r\) from \(r=0\) to \(r=R\), we can find the total gravitational force exerted on \(m\) by the entire disk. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2d5a692670838629cc82/1509567663512/share+img+for+classical+mechanics+thumbnail.png Newton's Laws - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2d5a692670838629cc8c/1509567663522/classical+mechanics+thumbnail.png Newton's Laws - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2d5a692670838629cc8e/1509567663524/ring1.jpg Newton's Laws - Gravitational Force Exerted by a Disk Figure 1: A ring of mass \(M=\int{dm}\) exerts a gravitational force on a particle of mass \(m\) a horizontal distance \(h\) away from the center of the ring. The vertical component of force \(dF_y\) for every mass element \(dm\) in the ring is canceled out by the vertical component of force \(dF'_y\) for another mass element \(dm'\) located on the opposite side of the ring. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2d5a692670838629cc8a/1509567663521/email+img+thumbnail.jpg Newton's Laws - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2d5a692670838629cc84/1509567663515/facebook+img+thumbnail.jpg Newton's Laws - Gravitational Force Exerted by a Disk https://www.gregschool.org/newtons-laws/2017/10/30/gravitational-force-exerted-by-a-sphere-rdyjt-btx7m monthly 0.5 2018-09-14 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca743e2b6a289d08b99219/1523208340227/Twitter+thumbnail.jpg Newton's Laws - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca743e2b6a289d08b99215/1523209738312/sharee.png Newton's Laws - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca743e2b6a289d08b99221/1523204866420/sphere+force.png Newton's Laws - Gravitational Force Exerted by a Sphere Figure 1: A shell can be subdivided into many very skinny rings. Anyone of these rings can be represented by the ring \(QRR_1Q_1\) illustrated above. Image credit\(^{[1]}\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca743e2b6a289d08b99217/1523208313862/facebook+thumbnail.jpg Newton's Laws - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca743e2b6a289d08b9921d/1523208400289/google+share+thumbnail.jpg Newton's Laws - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca743e2b6a289d08b9921b/1523208363916/email+thumbnail.jpg Newton's Laws - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca743e2b6a289d08b9921f/1523208206453/classical+mechanics+thumbnail.png Newton's Laws - Gravitational Force Exerted by a Sphere https://www.gregschool.org/new-blog-20 daily 0.75 2017-10-10 https://www.gregschool.org/new-blog-20/2017/8/30/5g8xs8bx2yk4rez4xp70hkmry35965 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ad98afcd39c3b55fa78ad2/1504719624283/kkk.png Capacitors - Calculating the amount of Electric Potential Energy Stored in a Capacitor Figure 1 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc32db6f4ca35190cf1592/1507604916120/electromagnetism+thumbnaillllll+imageeee.jpg Capacitors - Calculating the amount of Electric Potential Energy Stored in a Capacitor https://www.gregschool.org/new-blog-20/2017/8/30/capacitance monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc30356f4ca35190cef5c2/1507604869354/electromagnetism+thumbnaillllll+imageeee.jpg Capacitors - Capacitance https://www.gregschool.org/new-blog-20/2017/8/30/finding-the-electric-field-produced-by-a-parallel-plate-capacitor monthly 0.5 2017-10-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ad8bd2a803bb10bef9ec85/1504719611725/ddd.png Capacitors - Finding the Electric Field produced by a Parallel-Plate Capacitor https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ad953b4c0dbfd7d6d763d4/1504719611734/ddfdf.png Capacitors - Finding the Electric Field produced by a Parallel-Plate Capacitor https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc311bb1ffb66362919e6d/1507604895368/electromagnetism+thumbnaillllll+imageeee.jpg Capacitors - Finding the Electric Field produced by a Parallel-Plate Capacitor https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ad9111d55b41db66cc93d2/1504719611739/fff.png Capacitors - Finding the Electric Field produced by a Parallel-Plate Capacitor https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59adce43e5dd5b60a9d4efef/1504719611731/sf.png Capacitors - Finding the Electric Field produced by a Parallel-Plate Capacitor Figure 2 https://www.gregschool.org/new-blog-20/2017/8/30/finding-the-capacitance-of-a-parallel-plate-capacitor monthly 0.5 2017-11-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc30b3edaed80a4b246912/1507604675198/electromagnetism+thumbnaillllll+imageeee.jpg Capacitors - Finding the Capacitance of a Parallel-Plate Capacitor https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ac8b523e00bebf33d119f8/1504719599258/Fig1.jpg Capacitors - Finding the Capacitance of a Parallel-Plate Capacitor Figure 1: Parallel-plate capacitor. Each conductor is a flat plate with charges \(-Q\) and \(+Q\), areas of \(A\), and separated at a distance of \(d\). Courtesy of the Department of Physics and Astronomy, Michigan State University https://www.gregschool.org/integrals daily 0.75 2018-09-14 https://www.gregschool.org/integrals/2017/9/24/introduction-to-double-integrals-1 monthly 0.5 2018-04-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d2ee4218b27d3b0d81a37e/1523152770189/riemann_boxes_m.jpg Integrals - Introduction to Double Integrals Figure 1: When we were deriving an expression for the definite integral in terms of the Riemann sum, we first approximated the area underneath \(f(x)\) by summing the areas of many very skinny rectangles as illustrated in (A). To define a double integral in terms of a Riemann sum, we first approximate the volume underneath a surface by summing the volumes of many very skinny columns as depicted in (C). The width and depth of each column is given by \(Δx\) and \(Δy\) and the height of each rectangle is given by the surface \(f(x,y)\) as shown in (B). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d68b35a803bbe90ed071c1/1523152770191/partial+der.jpg Integrals - Introduction to Double Integrals Figure 2: The volume underneath the surface \(f(x,y)\) can be approximated by summing the volumes of an \(nm\) number of columns underneath the surface. As these columns become infinitesimally skinny and as the number \(nm\) of them approaches infinity, this sum gives the exact volume underneath the surface \(f(x,y)\). https://www.gregschool.org/integrals/2017/9/27/introduction-to-line-integrals monthly 0.5 2018-04-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d99659e9bfdf464d3e4f50/1507436224647/VIBrO.jpg Integrals - Introduction to Line Integrals Figure 1: The width and height of each blue rectangle is given by the arc length \(ds\) and the function \(f(x,y)\), respectively. The line integral, \(\int_Cf(x,y)ds\), represents the infinite sum of the area of each blue rectangle along the curve \(C\) (the purple line on the \(xy\)-plane). This image is a derivative work. Original image: https://www.wikihow.com/User:Atheia https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d99cb03e00beb58c4e7323/1507436224649/fhdhfdg.jpg Integrals - Introduction to Line Integrals Figure 2: By the Pythagorean theorem, each infinitesimal arc length \(ds\) can be represented in terms of \(x\) and \(y\) as \(\sqrt{x+2+y^2}\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59daa41a64b05f268bb33242/1507501085579/sdf.jpg Integrals - Introduction to Line Integrals https://www.gregschool.org/integrals/2017/9/30/solving-problems-using-line-integrals monthly 0.5 2018-04-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d53ea029f18722e25634f2/1507506885589/Untitled.jpg Integrals - Solving Problems using Line Integrals Figure 2: A proton \(P_2\) seperated by an initil seperation distance \(r_0\) from a station proton \(P_1\) moves along an arbitrary path until it reaches a seperation distance of \(r\). According to Column's law, the proton \(P_1\) will exert an electric force and, hence, also do work on the proton \(P_2\) as it moves from \(r_0\) to \(r\). The electric force forms a vector field and by calculuating the line integral along \(P_2\)'s path, we can calculate the amount of work done on \(P_2\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d188183e00be69b7c3517a/1507506885588/156px-Circular_cylinder_rh.jpg Integrals - Solving Problems using Line Integrals Figure 1: A cylinder with height \(h=2\) and radius \(r=1\). The "top" and "bottom" pieces of the cylinder are removed. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59daa883a803bb45f41dc507/1507506885586/sdfsdfdsdfdfdf+october+8.jpg Integrals - Solving Problems using Line Integrals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d19207017db22813f4a100/1507506885591/main-qimg-ef54da6034b7e89fb771a40923f089ca.gif Integrals - Solving Problems using Line Integrals Figure 3: A mass \(m\) is attached to the end of a rope of length \(L\). The mass falls and travels a distance \(s\) with a total angular displacement of \(θ\). https://www.gregschool.org/integrals/2017/10/27/gravitational-force-exerted-by-a-sphere monthly 0.5 2018-04-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa23fe0846657c0d448696/1509567663517/twiiter+img+thumbnail.jpg Integrals - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2ed053450ad9f171a760/1509568216076/Calculus+thumbnail.png Integrals - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa23de9140b71df4373eb4/1509567663519/google+img+thumbnail.jpg Integrals - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa23c0d6839ae2db9f574f/1509567663521/email+img+thumbnail.jpg Integrals - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f4bc8f71c10b247dd586fb/1509567663524/ring1.jpg Integrals - Gravitational Force Exerted by a Disk Figure 1: A ring of mass \(M=\int{dm}\) exerts a gravitational force on a particle of mass \(m\) a horizontal distance \(h\) away from the center of the ring. The vertical component of force \(dF_y\) for every mass element \(dm\) in the ring is canceled out by the vertical component of force \(dF'_y\) for another mass element \(dm'\) located on the opposite side of the ring. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f4c83071c10b247dd675cb/1509567663526/diskss.jpg Integrals - Gravitational Force Exerted by a Disk Figure 2: A disk of mass \(M=\int{m_{ring}}\) exerts a gravitational force on a particle of mass \(m\) a distance \(h\) away from the center of the disk along the \(x\)-axis. By summing the gravitational force exerted on \(m\) by each ring of radius \(r\) from \(r=0\) to \(r=R\), we can find the total gravitational force exerted on \(m\) by the entire disk. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa23cc08522944c7d66daf/1509567663515/facebook+img+thumbnail.jpg Integrals - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fa2656692670838628b567/1509567663512/share+img+for+classical+mechanics+thumbnail.png Integrals - Gravitational Force Exerted by a Disk https://www.gregschool.org/integrals/2017/8/29/finding-the-integral-of-kxm monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d96b287131a562e4837142/1507421210861/areaoftriangle.jpg Integrals - Finding the integral of \(kx^m\) Figure 1: The area underneath the function \(f(x)=2x\) is simply just the area of a triangle. The base of the triangle is \(x\) and its height is \(f(x)=2x\). Using the formula for the area of a triangle, we find that the area underneath \(f(x)=2x\) is \(x^2\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbda6fb7411c84d510d21e/1507580534039/Untitled.jpg Integrals - Finding the integral of \(kx^m\) https://www.gregschool.org/integrals/2017/8/29/introduction-to-integrals monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59addf52d7bdcecfe13491cf/1504735588352/Riemann_Integration_and_Darboux_Upper_Sums.gif Integrals - Introduction to Integrals Figure 2. The approximate area, \(\sum_{i=1}^nf(x_n)Δx\), underneath the curve \(y=x^2\) becomes closer and closer to the exact area underneath the curve as the number \(n\) of terms increases. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbd989914e6b12a38ed4a4/1507580301436/Untitled.jpg Integrals - Introduction to Integrals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59adde90e5dd5b60a9d5d03b/1504735588348/dfgd.png Integrals - Introduction to Integrals https://www.gregschool.org/integrals/2017/10/30/gravitational-force-exerted-by-a-sphere-jx7yd monthly 0.5 2018-09-14 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb8e01352f53a44f12f82f/1523209296661/email+thumbnail.jpg Integrals - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb8e01352f53a44f12f831/1523209296664/google+share+thumbnail.jpg Integrals - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb8e01352f53a44f12f829/1523209296655/sharee.png Integrals - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb8e01352f53a44f12f82b/1523209296657/facebook+thumbnail.jpg Integrals - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb8e01352f53a44f12f82d/1523209296659/Twitter+thumbnail.jpg Integrals - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb8e01352f53a44f12f833/1523209296666/classical+mechanics+thumbnail.png Integrals - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb8e01352f53a44f12f835/1523209296668/sphere+force.png Integrals - Gravitational Force Exerted by a Sphere Figure 1: A shell can be subdivided into many very skinny rings. Anyone of these rings can be represented by the ring \(QRR_1Q_1\) illustrated above. Image credit\(^{[1]}\). https://www.gregschool.org/integrals/2017/10/6/calculating-the-arc-length-of-a-curve-hk54b-xg8k6 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f54ea50852291b228d44b6/1507687678074/calculus+thumbnail.jpg Integrals - Calculating the Arc Length of a Curve https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f54ea50852291b228d44b8/1507341957781/arclengthimg1.jpg Integrals - Calculating the Arc Length of a Curve Figure 1: The curve \(P_1P_n\) split up into an \(n\) number of chords \(P_iP_{i+1}\) where \(i=1,...,n\). By taking the sum of the lengths of each chord (represented by \(\sum_{i=1}^nL(P_iP_{i+1})\)) and then taking the limit as \(n→∞\), we obtain the exact arc length \(s\) of the entire curve. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f54ea50852291b228d44ba/1507343004584/arclengthimg2.jpg Integrals - Calculating the Arc Length of a Curve Figure 2: A close up view of the \(i^{th}\) chord subdividing the curve \(P_1P_n\). Since the chord \(P_iP_{i+1}\) forms a right triangle, by using the Pythagorean theorem we can express \(L(P_iP_{i+1})\) as \(\sqrt{(Δx_i)^2+(Δy_i)^2}\). https://www.gregschool.org/integrals/2017/11/2/gravitational-force-exerted-by-a-rod-zf4pf-np6lw-pz3ga monthly 0.5 2018-04-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb8e1a88251b534876c39e/1523288053202/sharee.png Integrals - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb8e1a88251b534876c3a2/1523288004050/Twitter+thumbnail.jpg Integrals - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb8e1a88251b534876c3a8/1523287857170/classical+mechanics+thumbnail.png Integrals - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb8e1a88251b534876c3a6/1523287964387/email+thumbnail.jpg Integrals - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb8e1a88251b534876c3a0/1523287944108/facebook+thumbnail.jpg Integrals - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb8e1a88251b534876c3aa/1509666905146/rod.png Integrals - Gravitational Force Exerted by a Rod Figure 1: A rod of mass \(M\) and a particle of mass \(m\) are separated from each other by a distance of \(d\) along the \(x\)-axis. Each mass element \(dm\) comprising the rod is located at some position \(x\) along the \(x\)-axis and is separated from the particle \(m\) by some amount \(r\). By summing all the gravitational forces \(d\vec{F}_g\) exerted by each mass element \(dm\) comprising the rod, we can find the total gravitational force exerted on \(m\) by the entire rod. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb8e1a88251b534876c3a4/1523287988805/google+share+thumbnail.jpg Integrals - Gravitational Force Exerted by a Rod https://www.gregschool.org/integrals/2017/9/30/proof-of-greens-theorem-4kbde-fms6d monthly 0.5 2018-06-28 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3475f68a922d73de4c00ab/1530156381931/facebook+img+thumbnail.jpg Integrals - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3475f68a922d73de4c00af/1530156441620/google+img+thumbnail.jpg Integrals - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3475f68a922d73de4c00b3/1530156011880/Calculus+thumbnail.png Integrals - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3475f68a922d73de4c00ad/1530162636743/twiiter+img+thumbnail.jpg Integrals - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3475f68a922d73de4c00b7/1530147999505/images.png Integrals - Proof of Green's Theorem Figure 2: We can split the curve \(c\) into two separate curves, \(c_1\) and \(c_2\). This also allows us to split the function \(y(x)\) into the two separate functions, \(y(x_1)\) and \(y(x_2)\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3475f68a922d73de4c00a9/1530156044345/share+calculus+img.png Integrals - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3475f68a922d73de4c00b9/1530155160565/images.png Integrals - Proof of Green's Theorem Figure 3: We can break up the curve \(c\) into the two separate curves, \(c_1\) and \(c_2\). This also allows us to break up the function \(x(y)\) into the two separate functions, \(x(y_1)\) and \(x(y_2)\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3475f68a922d73de4c00b5/1506810526998/429px-Green%27s-theorem-simple-region.svg.png Integrals - Proof of Green's Theorem Figure 1: The curve \(C=C_1+C_2+C_3+C_4\) is piece-wise smooth. It is "piece-wise" because it is split up into an \(n=4\) number of separate curves with an \(n=4\) number of "edges." It is "smooth" because each individual curve itself is smooth without any sharp edges or cusps. This curve is also positively-oriented because its direction goes counter-clockwise. Image by Cronholm 144. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3475f68a922d73de4c00b1/1530157315746/email+img+thumbnail.jpg Integrals - Proof of Green's Theorem https://www.gregschool.org/articles-page-5 daily 0.75 2019-03-23 https://www.gregschool.org/articles-page-5/2017/8/13/nuclear-fusion-engines-g9fdd monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd24fc03596e7fc0b03459/1510177117202/space+travela+nd+colonization+thumbnail.jpg Articles page 5 - Nuclear Fusion Engines https://www.gregschool.org/articles-page-5/2017/6/28/terraforming-mars-gz3x8 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af755cf14aa16cb28c3ab5/1498701139592/ Articles page 5 - Terraforming and Colonizing Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af755cf14aa16cb28c3ab3/1502315090185/ares2.jpg Articles page 5 - Terraforming and Colonizing Mars Artist's depiction of the Ares spaceship from Kim Stanley Robinson's novel, Red Mars. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af755cf14aa16cb28c3ab9/1502431153897/ Articles page 5 - Terraforming and Colonizing Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af755cf14aa16cb28c3ab7/1502413444230/ Articles page 5 - Terraforming and Colonizing Mars "This shot follows the cabin of a space elevator descending on a cable towards the northern parts of the Terra Cimmeria highlands on Mars. A large settlement, hinted as glowing lights in the dark, can be seen far below on the ground. One of Mars' two moons - Phobos - is seen above the cabin to the left of the cable in the beginning of the shot." This image was produced by Erik Wernquist. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af755cf14aa16cb28c3abb/1502314679613/olympus.jpg Articles page 5 - Terraforming and Colonizing Mars Poster by SpaceX https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd23c08419c2764d7dbf1c/1510177067128/space+travela+nd+colonization+thumbnail.jpg Articles page 5 - Terraforming and Colonizing Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af755cf14aa16cb28c3abd/1498701189016/ Articles page 5 - Terraforming and Colonizing Mars https://www.gregschool.org/articles-page-5/2017/5/15/particle-in-one-dimensional-box-dwfnl monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af76a2d55b416b4ae15650/1495487701759/ Articles page 5 - Time-Independant Schrodinger Equation: Free Particle and Particle in One-Dimensional Box Figure 4: Illustration shows the allowed energy levels of a particle trapped inside of a one-dimensional box. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af76a2d55b416b4ae1564a/1495487069613/kjkjnj.png Articles page 5 - Time-Independant Schrodinger Equation: Free Particle and Particle in One-Dimensional Box Figure 1 (click to expand): Illustration of a free particle moving in a "one-dimensional box" which is trapped inside of an infinite potential well. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af76a2d55b416b4ae1564c/1495562943423/sch.png Articles page 5 - Time-Independant Schrodinger Equation: Free Particle and Particle in One-Dimensional Box Figure 2 (click to expand): The probability amplitude of measuring the particle at a position \(x\) in the presence of a potential \(V_0\) decreases exponentially with increasing \(V_0\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af76a2d55b416b4ae15648/1495485871466/ Articles page 5 - Time-Independant Schrodinger Equation: Free Particle and Particle in One-Dimensional Box "A wave function that satisfies the nonrelativistic Schrödinger equation with V = 0. In other words, this corresponds to a particle traveling freely through empty space. The real part of the wave function is plotted here."\(^{[1]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af76a2d55b416b4ae1564e/1494831797145/ Articles page 5 - Time-Independant Schrodinger Equation: Free Particle and Particle in One-Dimensional Box Figure 3 (click to expand): Illustration of a free particle moving in a one-dimensional box which is "pinned down" by a finite well. The probability amplitude of finding the particle outside of the box decreases exponentially as a function of distance. https://www.gregschool.org/articles-page-5/2017/5/14/friedman-robertson-walker-frw-equation-s6f2m monthly 0.5 2017-11-11 https://www.gregschool.org/articles-page-5/2017/5/14/solving-the-frw-equation-for-the-scaling-factor-in-different-scenarios-hdsrg monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ffd039ec212d4734becb0c/1509980764068/AT_7e_Figure_27_01%5B2%5D.jpg Articles page 5 - Solving the FRW Equation for the Scaling Factor in different scenarios Figure 1: As you can see from the graph above, for the first roughly 10,000 years most of the energy density in the universe was due to the presence of radiation. During the time interval from when the universe was 10,000 years old to when it was several billion years old, the energy density of the universe was dominated by matter. In our present epoch, the energy density of the universe is dominated by dark energy (or vacuum energy). This graph has profound implications. As time progresses, dark energy will become more and more dominant and will remain the dominant source of energy in the universe; since dark energy causes everything in the universe to expand, the universe will continue to expand without ever stopping. This graph, essentially, implies the ultimate fate of the universe. The universe will continue to expand more and more until it becomes dark, empty, and lifeless. https://www.gregschool.org/articles-page-5/2017/5/14/bentleys-and-olbers-paradoxes-e6hj4 monthly 0.5 2017-11-10 https://www.gregschool.org/articles-page-5/2017/5/14/8c5knwf9nztiio7uwnvvotz1pj86ht-thkb7 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af7e2fd55b416b4ae1a923/1502416195791/ Articles page 5 - Time Dilation Figure 1 https://www.gregschool.org/articles-page-5/2017/8/29/introduction-to-integrals-xl5rn monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b071649f7456145d0c076e/1504567134996/Riemann_Integration_and_Darboux_Upper_Sums.gif Articles page 5 - Introduction to Integrals Figure 2. The approximate area, \(\sum_{i=1}^nf(x_n)Δx\), underneath the curve \(y=x^2\) becomes closer and closer to the exact area underneath the curve as the number \(n\) of terms increases. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbd9d3c534a5f2363c4d29/1510176997141/Untitled.jpg Articles page 5 - Introduction to Integrals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b071649f7456145d0c076c/1504566939599/dfgd.png Articles page 5 - Introduction to Integrals https://www.gregschool.org/articles-page-5/2017/8/16/maclaurin-polynomial-and-series-9cll7 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbdfbbedaed80a4b204a38/1510176987588/Untitled.jpg Articles page 5 - Maclaurin/Taylor Polynomials and Series https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b44013d55b4168dbddb011/1504563483921/Exp_series.gif Articles page 5 - Maclaurin/Taylor Polynomials and Series Figure 1. Maclaurin polynomials of different order \(n\) (red curves) approximating the function \(e^x\) (blue curve). https://www.gregschool.org/articles-page-5/2017/10/6/calculating-the-volume-of-a-sphere-e6jde-bs7ml monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d95d69cd0f688947d834b5/1507412420221/moment-of-inertia-of-sphere.jpg Articles page 5 - Calculating the Volume of a Sphere Figure 4: By taking the infinite sum of the volumes, \(π(f(x))^2dx\), of every cylinder from \(x=0\) to \(x=R\), we can obtain the volume of half of the sphere depicted above. By multiplying our answer by two, we can obtain the volume of the whole sphere. Image credit: https://www.miniphysics.com/uy1-calculation-of-moment-of-inertia-of-solid-sphere.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59daa4b28a02c7abc31c7c36/1510175551473/sdf.jpg Articles page 5 - Calculating the Volume of a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d95d69cd0f688947d834b3/1507412420216/s9NuK.jpg Articles page 5 - Calculating the Volume of a Sphere Figure 3: By rotating the \(i^{th}\) rectangle about the \(x\)-axis, the cylinder depicted above is obtained. By doing this for each rectangle, an \(n\) number of cylinders are obtained. All of these cylinders fit inside of a hemisphere of radius \(r\) and the sum of the volumes of all of those cylinders approximate the volume of the hemisphere. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d95d69cd0f688947d834b1/1507412420213/volumeofsphereimg1.jpg Articles page 5 - Calculating the Volume of a Sphere Figure 2: A graph of the quarter circle \(x^2+y^2=r^2\) for \(x≥0\) and \(y≥0\). An \(n\) number of rectangles, \(f(x_i\)Δx\), are drawn underneath the curve. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d95d69cd0f688947d834af/1507412420207/320px-Rotationskoerper_animation.gif Articles page 5 - Calculating the Volume of a Sphere Figure 1: The "vase" shaped surface is obtained by revolving a curve about the vertical axis. The region of space that the surface encloses is called a solid of revolution. https://www.gregschool.org/articles-page-6 daily 0.75 2019-03-21 https://www.gregschool.org/articles-page-6/2017/5/14/dark-energy-exgdc monthly 0.5 2017-11-11 https://www.gregschool.org/articles-page-6/2017/5/14/cosmic-microwave-background-radiation-lfmal monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af7c52c027d8e9bfa7d30a/1494827005244/ Articles page 6 - Cosmic Microwave Background Radiation https://www.gregschool.org/articles-page-6/2017/5/14/dark-matter-yla9j monthly 0.5 2017-11-11 https://www.gregschool.org/articles-page-6/2017/8/30/finding-the-capacitance-of-a-parallel-plate-capacitor-ajby4 monthly 0.5 2017-11-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc3c75b1ffb66362922088/1510177451011/electromagnetism+thumbnaillllll+imageeee.jpg Articles page 6 - Finding the Capacitance of a Parallel-Plate Capacitor https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b032efc534a58c97cb0d19/1504480094587/Fig1.jpg Articles page 6 - Finding the Capacitance of a Parallel-Plate Capacitor Figure 1: Parallel-plate capacitor. Each conductor is a flat plate with charges \(-Q\) and \(+Q\), areas of \(A\), and separated at a distance of \(d\). Courtesy of the Department of Physics and Astronomy, Michigan State University https://www.gregschool.org/articles-page-6/2017/5/14/columns-law-7fdl2 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc43e5f43b55f79a348b9d/1510177552288/electromagnetism+thumbnaillllll+imageeee.jpg Articles page 6 - Column's Law https://www.gregschool.org/articles-page-6/2017/6/20/derivation-of-guasss-law-from-columns-law-mbxrn monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b03342d2b857ba2834b3fc/1501802501336/guass.jpg Articles page 6 - Derivation of Guass's Law from Column's Law Figure 1 (click to enlarge) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc41cc1f318db010fdb87c/1510177532479/electromagnetism+thumbnaillllll+imageeee.jpg Articles page 6 - Derivation of Guass's Law from Column's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b03342d2b857ba2834b3fe/1501804297766/ Articles page 6 - Derivation of Guass's Law from Column's Law Figure 2 (click to enlarge) https://www.gregschool.org/articles-page-6/2017/5/18/v7t2klwmycopiblvbhzkhyw2duujqy-bjxsk monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbfa88b07869b583659af8/1510177542782/gfnf.jpg Articles page 6 - Introduction to Lagrangian Mechanics https://www.gregschool.org/articles-page-6/2017/5/18/finding-the-geodesic-on-a-cylinder-mley2 monthly 0.5 2019-02-22 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbfa73cd39c33ffeae251e/1510177524654/gfnf.jpg Articles page 6 - Finding the geodesic on a cylinder https://www.gregschool.org/articles-page-6/2017/5/18/brachistochrone-problem-8bgmb monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbfa5ef5e2317170efd405/1510177508786/gfnf.jpg Articles page 6 - Brachistochrone problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b033c19f745650b3ec7ec7/1495304408606/ Articles page 6 - Brachistochrone problem Credit\(^{[3]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b033c19f745650b3ec7ec3/1495304339104/ Articles page 6 - Brachistochrone problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b033c19f745650b3ec7ec5/1495304353556/ Articles page 6 - Brachistochrone problem https://www.gregschool.org/articles-page-6/2017/5/18/generalized-coordinates-7r5bn monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbfb166f4ca35190cc6fb9/1510177516612/gfnf.jpg Articles page 6 - Generalized coordinates https://www.gregschool.org/articles-page-7 daily 0.75 2019-03-21 https://www.gregschool.org/articles-page-7/2017/5/14/electric-flux-enbx3 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc3f77b07869b58368dafd/1510177608894/electromagnetism+thumbnaillllll+imageeee.jpg Articles page 7 - Electric Flux https://www.gregschool.org/articles-page-7/2017/7/20/using-guasss-law-to-find-the-electric-field-produced-by-a-single-point-charge-8m3gx monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b033507131a5ba424f1743/1501805131555/ Articles page 7 - Using Guass's Law to find the Electric Field Produced by a Single Point Charge Figure 2 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b033507131a5ba424f1745/1501807096166/ Articles page 7 - Using Guass's Law to find the Electric Field Produced by a Single Point Charge Figure 3 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc41fe29f1876a45849d25/1510177599547/electromagnetism+thumbnaillllll+imageeee.jpg Articles page 7 - Using Guass's Law to find the Electric Field Produced by a Single Point Charge https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b033507131a5ba424f1741/1501804682969/guass.jpg Articles page 7 - Using Guass's Law to find the Electric Field Produced by a Single Point Charge Figure 1 https://www.gregschool.org/articles-page-7/2017/5/18/derivation-of-the-euler-lagrange-equation-s8wam monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbfaa93e00bed1b4262679/1510177576339/gfnf.jpg Articles page 7 - Derivation of the Euler-Lagrange Equation https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b033813e00be820cf34912/1495304730085/ Articles page 7 - Derivation of the Euler-Lagrange Equation Figure 1 (click to expand) https://www.gregschool.org/articles-page-7/2017/5/18/noethers-theorem-78d8y monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbfaf7c027d89dcc0d3a58/1510177619502/gfnf.jpg Articles page 7 - Noether’s Theorem https://www.gregschool.org/articles-page-7/2017/8/29/newtons-three-laws-of-motion-62d9d monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbe2d7e9bfdf322eccd41d/1510177711160/Untitled.jpg Articles page 7 - Newton's Three Laws of Motion https://www.gregschool.org/articles-page-7/2017/8/28/newtons-law-of-gravity-ybhff monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbe3a6f9a61e6c50baee2b/1510177685361/Untitled.jpg Articles page 7 - Newton's Law of Gravity https://www.gregschool.org/articles-page-7/2017/6/20/76hgztk8ogz149g9acwmizq62okwe4-cz2yr monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbe203197aeaa9a58bbb65/1510177702121/Untitled.jpg Articles page 7 - Position Vectors, Displacement, Velocity, and Acceleration https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b03535cd0f68dbd2291c17/1501784000999/ Articles page 7 - Position Vectors, Displacement, Velocity, and Acceleration Figure 1 (click to enlarge) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b03535cd0f68dbd2291c19/1501788322829/ Articles page 7 - Position Vectors, Displacement, Velocity, and Acceleration Figure 2 https://www.gregschool.org/articles-page-7/2017/6/20/faxkbn1icm37pyljps0j38mgdt0t22-ch2g2 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbe1d7b1ffb663628d9b87/1510177668944/Untitled.jpg Articles page 7 - Basic Equations of Kinematics https://www.gregschool.org/articles-page-7/2017/5/14/introduction-to-newtonian-mechanics-25a5e monthly 0.5 2017-11-09 https://www.gregschool.org/articles-page-7/2017/5/18/what-do-we-mean-by-kinematics-dynamics-and-mechanics-xr2cr monthly 0.5 2017-11-09 https://www.gregschool.org/articles-page-8 daily 0.75 2019-03-21 https://www.gregschool.org/articles-page-8/2017/5/14/xe30zrw2tke0y051q8xdpf9cxaff19-fyzrj monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af7a9cf7e0ab91b22cc150/1494828080386/ Articles page 8 - Scaling Factor, Hubble's Parameter, and the Age of the Universe https://www.gregschool.org/articles-page-8/2017/5/14/4ufuuy7fweohxl2tk6hryzmsq50amd-a67kn monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf7d37131a52388a06cd1/1510177823163/gfnf.jpg Articles page 8 - Introduction to Mechanical Waves https://www.gregschool.org/articles-page-8/2017/5/14/rotational-kinematics-5xef2 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf864b07869b583657f74/1510177833044/gfnf.jpg Articles page 8 - Rotational Kinematics https://www.gregschool.org/articles-page-8/2017/5/14/introduction-to-rotational-kinetic-energy-b8hy8 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf8dfbce176a8031ec46a/1510177841285/gfnf.jpg Articles page 8 - Introduction to Rotational Kinetic Energy https://www.gregschool.org/articles-page-8/2017/5/14/torque-6zmaw monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf963017db28a6c9509de/1510177858204/gfnf.jpg Articles page 8 - Torque https://www.gregschool.org/articles-page-8/2017/8/10/introduction-to-linear-momentum-mbs6h monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf285d7bdcefd90867d48/1510177736905/gfnf.jpg Articles page 8 - Introduction to Linear Momentum https://www.gregschool.org/articles-page-8/2017/8/10/derivation-on-momentum-conservation-bxjp5 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf33d46c3c48d6775f6cb/1510177725819/gfnf.jpg Articles page 8 - Derivation of Momentum Conservation https://www.gregschool.org/articles-page-8/2017/8/10/inelastic-collisions-mjsnh monthly 0.5 2017-11-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf3eff5e2317170ef7d55/1510177816337/gfnf.jpg Articles page 8 - Inelastic Collisions https://www.gregschool.org/articles-page-8/2017/8/28/motion-of-objects-experiancing-air-friction-wheys monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf1911f318db010f9f294/1510177749331/gfnf.jpg Articles page 8 - Motion of objects experiancing air friction https://www.gregschool.org/articles-page-8/2017/6/21/the-abstract-has-a-lot-to-say-about-the-physical-world-xk4tb monthly 0.5 2017-11-09 https://www.gregschool.org/solidsofrevolution daily 0.75 2017-11-04 https://www.gregschool.org/solidsofrevolution/2017/10/22/volume-of-an-oblate-spheroid monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd163ee2c483f6d02defca/1509760277356/email+thumbnail.jpg Solids of Revolution - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd16029140b72e25d930d6/1509760277357/Calculus+thumbnail.png Solids of Revolution - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd161464265f6a40ff563c/1509760277350/facebook+thumbnail.jpg Solids of Revolution - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd166c4192021a540ae4e6/1509760277354/google+share+thumbnail.jpg Solids of Revolution - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd18c7e31d1945635a85d8/1509760277348/temporary+shareeeeee.png Solids of Revolution - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd0a0053450a448c5d5d7a/1509760277361/oblate+spheroid+img2.png Solids of Revolution - Volume of an Oblate Spheroid Figure 2: A cylindrical shell is obtained by revolving the rectangle \(f(x_i)Δx\) about the \(y\)-axis. Doing this for all \(n\) rectangles, we get an \(n\) number of shells. By summing the volumes of these \(n\) number of cylindrical shells, we can obtain an estimate for total volume enclosed inside of the paraboloid obtained by rotating the quarter-ellipse (the one in the upper-right quadrant) about the \(x\)-axis. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f63ca00846653ab7a4fa4c/1509760277363/oblate+sphereoid.jpg Solids of Revolution - Volume of an Oblate Spheroid Figure 3: If \(a\) and \(c\) represents the semi-major and semi-minor axes of an ellipse, respectively, and if \(a=3\) and \(c=2\) then by rotating such an ellipse about an axis we can obtain an oblate spheroid. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd1697e4966b0f2558c951/1509760277352/Twitter+thumbnail.jpg Solids of Revolution - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcff39e2c483f6d02baa0a/1509760277359/oblate+spheroid+img1.png Solids of Revolution - Volume of an Oblate Spheroid Figure 1: Graph of the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\) centered at the origin of the \(xy\)-plane. Also, I have drawn the \(i^{th}\) rectangle underneath the quarter-ellipse within the first quadrant. There are an \(n\) number of such rectangles underneath this quarter-ellipse along the interval \(Δx=3-0\).   https://www.gregschool.org/solidsofrevolution/2017/10/6/calculating-the-volume-of-a-sphere-e6jde-mcsyn monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd1ae6e2c483f6d02e5cf9/1507412420221/moment-of-inertia-of-sphere.jpg Solids of Revolution - Calculating the Volume of a Sphere Figure 4: By taking the infinite sum of the volumes, \(π(f(x))^2dx\), of every cylinder from \(x=0\) to \(x=R\), we can obtain the volume of half of the sphere depicted above. By multiplying our answer by two, we can obtain the volume of the whole sphere. Image credit: https://www.miniphysics.com/uy1-calculation-of-moment-of-inertia-of-solid-sphere.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd1ae6e2c483f6d02e5cf1/1507501386946/sdf.jpg Solids of Revolution - Calculating the Volume of a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd1ae6e2c483f6d02e5cf3/1507412420207/320px-Rotationskoerper_animation.gif Solids of Revolution - Calculating the Volume of a Sphere Figure 1: The "vase" shaped surface is obtained by revolving a curve about the vertical axis. The region of space that the surface encloses is called a solid of revolution. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd1ae6e2c483f6d02e5cf5/1507412420213/volumeofsphereimg1.jpg Solids of Revolution - Calculating the Volume of a Sphere Figure 2: A graph of the quarter circle \(x^2+y^2=r^2\) for \(x≥0\) and \(y≥0\). An \(n\) number of rectangles, \(f(x_i\)Δx\), are drawn underneath the curve. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fd1ae6e2c483f6d02e5cf7/1507412420216/s9NuK.jpg Solids of Revolution - Calculating the Volume of a Sphere Figure 3: By rotating the \(i^{th}\) rectangle about the \(x\)-axis, the cylinder depicted above is obtained. By doing this for each rectangle, an \(n\) number of cylinders are obtained. All of these cylinders fit inside of a hemisphere of radius \(r\) and the sum of the volumes of all of those cylinders approximate the volume of the hemisphere. https://www.gregschool.org/arc-length daily 0.75 2017-10-10 https://www.gregschool.org/pulley-and-incline-problems daily 0.75 2017-10-07 https://www.gregschool.org/articles9blog daily 0.75 2019-03-21 https://www.gregschool.org/articles9blog/2017/2/13/introduction-to-einsteins-theory-of-general-relativity monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/58dac9e2be6594b226ab6aec/1510178006735/ articles page 9 - Introduction to Einstein's Theory of General Relativity https://www.gregschool.org/articles9blog/2017/4/27/colonizing-the-asteroids-and-comets-of-our-solar-system monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd21c880bd5e3fd03f894a/1510177997939/space+travela+nd+colonization+thumbnail.jpg articles page 9 - Colonizing the Asteroids and Comets of our Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5904f28029687f041ca549d9/1510177997941/ articles page 9 - Colonizing the Asteroids and Comets of our Solar System Figure 1 (click to enlarge) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/590283f76b8f5be39de0ffbf/1510177997943/WANDERERS_terrarium_01.jpg articles page 9 - Colonizing the Asteroids and Comets of our Solar System Figure 2 - click to enlarge (Source) "This shot shows the inside of the asteroid from the previous scene. Just as I wrote about that scene, this is a highly speculative vision of an impressive piece of human engineering - a concept that science fiction author Kim Stanley Robinson calls a "terraruim" in his novel "2312". It is also not unlike what Arthur C. Clarke described in his novel "Rendezvous with Rama". What we see here is the inside of a hollowed out asteroid, pressurized and filled with a breathable atmosphere. Like I described in the previous scene, the whole structure is put into a revolving rotation, simulating the effect of gravity toward the inside "walls" of the cylinder shape we see. The structure in this scene has a diameter of about 7 kilometers and revolves with a speed of 1 rotation every 2 minutes, simulating the effect of 1g (the gravity pull we feel on Earth) at the surface of the inside. This place is also filled with water, creating lakes and seas wrapped along with the landscape. An artificial sun is running along a rail in the middle of the space, simulating a daylight cycle. This scene is of course built from scratch, but I used countless satellite photos of the Earth to texture the landscape. I actually used a slightly warped world map to create the outlines between land and water, as some may notice a couple of familiar shorelines."\(^{[3]}\) https://www.gregschool.org/articles9blog/2017/5/4/colonizing-the-moon monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/590c101dbe659408c6859363/590d02ff2994cac296bf1023/1498698373172/.jpg articles page 9 - Colonizing the Moon The Smart Things Future Living Report https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/590c101dbe659408c6859363/590c105be6f2e13e8402dcac/1498698373171/landscape-1436809198-1197px-inflatable-habitat-s89-20084.jpg articles page 9 - Colonizing the Moon Artist concept of a moon colony via NASA https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/590c101dbe659408c6859363/590c103a893fc0ef1a3691de/1498698373169/LeapOfFaith.jpg articles page 9 - Colonizing the Moon Painting by Pat Rawlings courtesy NASA https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/590c101dbe659408c6859363/590c101d20099e8a5502e809/1498698373166/LunarColonyRawlings650.jpg articles page 9 - Colonizing the Moon Domed lunar settlement illustration by Pat Rawlings, courtesy NASA. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd2126be42d6ad78e8e1ef/1510177977619/space+travela+nd+colonization+thumbnail.jpg articles page 9 - Colonizing the Moon https://www.gregschool.org/articles9blog/2017/6/8/early-earth-history monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/593addbf725e25a4294e7e2a/1510177967240/Archean.png articles page 9 - Early Earth History Click to enlarge - (Source\(^{[2]}\)) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/593a328c6a4963644179b180/1510177967236/ articles page 9 - Early Earth History Click to enlarge - (Source\(^{[2]}\)) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/593dcb92579fb3fa4a7aee42/1510177967244/ articles page 9 - Early Earth History Modern stromatolites in Shark Bay, Western Australia. https://www.gregschool.org/articles9blog/2017/6/12/snowball-earth monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/593efd59440243f1b89935ac/1510177949269/ articles page 9 - Snowball Earth https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/593efc13e4fcb594910df733/1510177949267/ articles page 9 - Snowball Earth Picture of Earth 750 million years ago when the supercontinent Rodinia was getting torn apart. (Click to expand.) https://www.gregschool.org/articles9blog/2017/8/26/work-measure-of-energy-transfer-5kccp monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf5ab03596ed02a218901/1510177869133/gfnf.jpg articles page 9 - Work: Measure of Energy Transfer https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b03468d7bdce7d68cac713/1504544870969/ff.png articles page 9 - Work: Measure of Energy Transfer Figure 1: Work done on a block by a constant force of \(-10\) newtons over a displacement of \(5\) meters. https://www.gregschool.org/articles9blog/2017/5/14/genesis-of-the-elements-xz53h monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a009a5171c10bb0d5b68e8f/1509981827221/RutherfordGoilFoil+%281%29%5B1%5D.jpg articles page 9 - Genesis of the Elements Figure 1: Rutherford's experiment involved putting a radioactive element known as radium inside of a lead box. The radium spontaneously emitted \(α\) particles in a narrow beam through a small hole in the box. These \(α\) particles were directed towards a gold foil. Most \(α\) particles passed straight through the gold foil but occasional one would get reflected back at an acute angle with the beam of \(α\) particles. This meant that atoms must have tiny, but very dense, nuclei. Image credit: http://m.teachastronomy.com/astropedia/article/The-Structure-of-the-Atom https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a009a5171c10bb0d5b68e95/1509987202844/ articles page 9 - Genesis of the Elements Figure 4: As a star undergoes nuclear fusion in its core, it generates light. This light exerts an outward radiation pressure on the star which balances the inward gravitational forces that tend to pull the star's matter towards its center. But at the end of a star's life, nuclear fusion begins to slow down and eventually stop; this means that there is no outward radiation pressure to balance the gravitational forces exerted on the outward layers of the star and star eventually collapses. If the star is very massive, such a collapse will result in one of the most spectacular events in the universe: a supernova. The energy generated by a supernova explosion is so stupendous that it results in nuclear reactions which create the heavier elements in the period table. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a009a5171c10bb0d5b68e93/1509985102690/ articles page 9 - Genesis of the Elements Figure 3: The Alpha-Beta-Gamma paper demonstrated that after the first roughly three minutes of the universe since its initial Bang, hydrogen and helium nuclei were synthesized via nuclear fusion. After about three minutes, the universe cooled enough for fusion to stop; but the universe was still so hot that all of the matter comprising the universe was a plasma and plasma's are opaque to radiation. The matter comprising the universe was in a plasma state for the first roughly 300,000 years since the Big Bang; since plasma is opaque to radiation, for the first roughly 300,000 years light could not freely travel throughout the universe without constantly "bumping into stuff (atomic nuclei)." At sometime when the universe was about 300,000 to 400,000 years old, matter cooled enough for electrons to bind to atomic nuclei and for light to freely pass through the universe. Due to the expansion of space, Alpher and Herman estimated that wavelengths of this light should now be stretched into the microwave region. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a009a5171c10bb0d5b68e91/1509983399387/nuclear-fusion-stars%5B1%5D.png articles page 9 - Genesis of the Elements Figure 2: All stars in the universe generate light and energy by fusing lighter elements into heavier elements. For stars up to the mass of about that of our Sun, light and energy is created by fusing hydrogen into helium. The image above illustrates the chain of nuclear reactions which occur in small to medium sized stars and very massive stars that allow them to generate light and energy. Stellar fusion accounts for where many of the light to medium-sized elements in the periodic table come from. https://www.gregschool.org/articles9blog/2017/6/21/the-dependency-of-theta-in-the-dot-product-a6rdd monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b03474e9bfdfa96d5b4f08/1501801080881/ articles page 9 - The Dependency of theta in the dot product https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf4c0a9db09b4a1076070/1510177877901/gfnf.jpg articles page 9 - The Dependency of theta in the dot product https://www.gregschool.org/articles9blog/2017/8/27/work-done-by-force-moving-an-object-at-constant-height-dxkzp monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b0347f9f8dce50d397d42b/1504580497144/wet2.gif articles page 9 - Work-Kinetic Energy Theorem Figure 1: "Sunil Kumar Singh, Work - Kinetic Energy Theorem. February 2, 2013." http://cnx.org/content/m14095/latest/OpenStax CNX CC BY 3.0. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf66d9f8dceedaf2b6472/1510177903544/gfnf.jpg articles page 9 - Work-Kinetic Energy Theorem https://www.gregschool.org/articles9blog/2017/8/26/work-done-by-earths-gravity-nfmxr monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59b034896f4ca3de59072d5f/1504580902846/vv.png articles page 9 - Work done by Earth's Gravity Figure 1: As an object moves along the path \(\vec{R}(t)\) from an initial height of \(y_i\) to a final height of \(y_f\), the Earth's gravitational force \(-m\vec{g}\) does work on the object. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbf65129f1876a4581157d/1510177894624/gfnf.jpg articles page 9 - Work done by Earth's Gravity https://www.gregschool.org/optimization-problems daily 0.75 2017-11-02 https://www.gregschool.org/optimization-problems/2017/10/14/maximizing-the-area-of-a-rectangle monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f900fb692670c66b9ffbe7/1509495231581/share+img.jpg Optimization Problems - Maximizing the Area of a Rectangle https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f90060084665b98c384e67/1509495231583/facebook+img+thumbnail.jpg Optimization Problems - Maximizing the Area of a Rectangle https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f900858165f56e2e19d922/1509495231587/google+img+thumbnail.jpg Optimization Problems - Maximizing the Area of a Rectangle https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f60c036c3194053444a81e/1509495231593/Optimization+Problem+1.jpg Optimization Problems - Maximizing the Area of a Rectangle Figure 1: Given any rectangle \(xy\) where the perimeter \(2x+2y\) is the constant, we can use calculus to find that particular rectangle \(xy\) with the maximum area \(A\). The solution to this problem has practical applications. For example, suppose that someone had only 30 meters of fencing to enclose their backyard and they wanted to know what fencing layout would maximize the size and total area of their backyard. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f900a1e31d19ae5283d566/1509495231585/twiiter+img+thumbnail.jpg Optimization Problems - Maximizing the Area of a Rectangle https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f900498165f56e2e19d33b/1509495231591/Calculus+thumbnail.png Optimization Problems - Maximizing the Area of a Rectangle https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f9006f6c31945e330ed95e/1509495231589/email+img+thumbnail.jpg Optimization Problems - Maximizing the Area of a Rectangle https://www.gregschool.org/optimization-problems/2017/10/14/optimizatio monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f90775652dea2acb0dd9ea/1509495212815/Calculus+thumbnail.png Optimization Problems - Optimization Problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f907a1085229220f401ef2/1509495212804/facebook+img+thumbnail.jpg Optimization Problems - Optimization Problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f907bdc830259dbcf05f4f/1509495212813/email+img+thumbnail.jpg Optimization Problems - Optimization Problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f9080264265fe2cc7882c5/1509495212802/share+img.jpg Optimization Problems - Optimization Problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f6056453450a1e3bbe310a/1509495212818/Optimization+Problem.jpg Optimization Problems - Optimization Problem Figure 1: A graph of the circle \(x^2+y^2=4\) which is centered at the origin of the \(x\)-axis. If \((x,y)\) represents any point on the circle, if \(P\) is a point fixed at the coordinate point \((4,0)\), and if \(d\) represents the distance between those two points then, by using only calculus, we can find the point \((x,y)\) on the circle associated with the minimum distance \(d\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f907d0c830259dbcf061a6/1509495212807/twiiter+img+thumbnail.jpg Optimization Problems - Optimization Problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f907af24a69424ee475218/1509495212810/google+img+thumbnail.jpg Optimization Problems - Optimization Problem https://www.gregschool.org/optimization-problems/2017/10/30/derivation-of-snells-law monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f90a5908466550b1d2b758/1509495184210/Calculus+thumbnail.png Optimization Problems - Derivation of Snell's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f90acb0d92971863a0821a/1509495184185/share+img.jpg Optimization Problems - Derivation of Snell's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f90a8c652dea2acb0e2ae8/1509495184200/google+img+thumbnail.jpg Optimization Problems - Derivation of Snell's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f90a7e6c3194e9a68410a1/1509495184190/facebook+img+thumbnail.jpg Optimization Problems - Derivation of Snell's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f88cbf53450a66f3f4a05e/1509495184214/snellslaw2.jpg Optimization Problems - Derivation of Snell's Law Figure 1: A light ray traveling along the line \(QO\) comes into contact with a surface at an \(θ_i\) (where \(θ_i\) is measured relative to the line perpendicular to the surface). Once this light ray comes into contact with this surface, it is reflected at an angle \(θ_r\) (\(θ_r\) is also measured relative to the perpendicular). According to the law of reflection, \(θ_i=θ_r\). Image credit: Download for free at http://cnx.org/contents/60b4727b-829e-4ea7-9238-9140b6a1b20c@4. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f90a6f085229220f406b51/1509495184204/email+img+thumbnail.jpg Optimization Problems - Derivation of Snell's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f88981e2c48368e55888e3/1509495184220/snells+law.jpg Optimization Problems - Derivation of Snell's Law Figure 2: As a light ray travels along the line \(QO\) through medium 1 and comes into contact with the interface between medium 1 and medium 2, it gets refracted—meaning, it passes through medium 2. Image credit: By Smedlib (Own work) [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f90aa364265fe2cc78c2f8/1509495184195/twiiter+img+thumbnail.jpg Optimization Problems - Derivation of Snell's Law https://www.gregschool.org/optimization-problems/2017/6/24/finding-the-minima-and-maxima-of-a-function monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f8fd70e2c4839ccb95c670/1509495139370/share+img.jpg Optimization Problems - Finding the Minima and Maxima of a Function https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f8a85ec83025f48cb40da6/1509495139373/twiiter+img+thumbnail.jpg Optimization Problems - Finding the Minima and Maxima of a Function https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f8a8e60852296a947ad5ff/1509495139377/email+img+thumbnail.jpg Optimization Problems - Finding the Minima and Maxima of a Function https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f8a8b9e2c48368e55c6734/1509495139375/google+img+thumbnail.jpg Optimization Problems - Finding the Minima and Maxima of a Function https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f8a82d0852296a947abf53/1509495139372/facebook+img+thumbnail.jpg Optimization Problems - Finding the Minima and Maxima of a Function https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f8a4fd0846655cecee4a66/1509495139379/Calculus+thumbnail.jpg Optimization Problems - Finding the Minima and Maxima of a Function https://www.gregschool.org/articles-page-10 daily 0.75 2019-03-21 https://www.gregschool.org/articles-page-10/2017/1/23/superconductors-the-future-of-transportation-and-electric-transmission monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcdfacec212df7e4a987e7/1510178026387/facebook+img+thumbnail.jpg articles page 10 - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcdfba652dea0178315260/1510178026394/ articles page 10 - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcdf8ce2c483b3c8a72653/1510178026398/technology+thumbnail.png articles page 10 - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcdf9f085229fde9f96f45/1510178026396/email+img+thumbnail.jpg articles page 10 - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcdfca71c10b1aafb1a01b/1510178026390/twiiter+img+thumbnail.jpg articles page 10 - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce021419202d6b98c952b/1510178026383/ articles page 10 - Superconductors: the Future of Transportation and Electric Transmission https://www.gregschool.org/articles-page-10/2017/6/12/crispr-cas9-gene-editing monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/593f5ef815d5db7a1fd361db/1510178188878/ articles page 10 - CRISPR-CAS9 Gene Editing Figure 1 Source\(^{[1]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/593f60523a041171e036d6d3/1510178188884/rrr.png articles page 10 - CRISPR-CAS9 Gene Editing Figure 3 Source https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/593f5f6f59cc6882f35c19d2/1510178188881/ articles page 10 - CRISPR-CAS9 Gene Editing Figure 2 Source https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/593f609a8419c276ef634893/1510178188888/ articles page 10 - CRISPR-CAS9 Gene Editing Figure 4 (click to enlarge) https://www.gregschool.org/articles-page-10/2017/6/16/overview-of-calculus-hmtnx monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbdcbb29f1876a457f9167/1510078784067/Untitled.jpg articles page 10 - Overview of Single-Variable Calculus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59a39f767131a55eb412021e/1497934480889/ articles page 10 - Overview of Single-Variable Calculus Figure 1 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59a39f767131a55eb4120226/1497933579348/ articles page 10 - Overview of Single-Variable Calculus Figure 5 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59a39f767131a55eb4120220/1497934508324/ articles page 10 - Overview of Single-Variable Calculus Figure 2 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59a39f767131a55eb4120224/1497933573517/ articles page 10 - Overview of Single-Variable Calculus Figure 4 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59a39f767131a55eb4120222/1497931192368/ articles page 10 - Overview of Single-Variable Calculus Figure 3 https://www.gregschool.org/articles-page-10/2017/5/15/periodic-wavefunctions-that-is-ones-that-come-back-to-themselves-have-quantized-eigenvalues-of-momenta-and-angular-momenta-2k3el monthly 0.5 2017-11-09 https://www.gregschool.org/articles-page-10/2017/5/14/how-initial-states-of-definite-energy-change-with-time-5hyrx monthly 0.5 2017-11-11 https://www.gregschool.org/articles-page-10/2017/5/14/quantum-dynamics-2nhll monthly 0.5 2017-11-11 https://www.gregschool.org/articles-page-10/2017/5/23/the-eigenvectors-of-any-hermitian-operator-must-be-orthogonal-w2jps monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc4e8a1f318db010fe3230/1510110338040/electromagnetism+thumbnaillllll+imageeee.jpg articles page 10 - The Eigenvectors of any Hermitian Operator must be Orthogonal https://www.gregschool.org/articles-page-10/2017/5/27/origin-of-structure-and-clumpyness-dbe4t monthly 0.5 2017-11-11 https://www.gregschool.org/articles-page-10/2017/5/15/time-evolution-of-state-vectors-c6g7n monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a026de4652dea4ceb35eb78/1510108488383/photon_double_slit2%5B1%5D.gif articles page 10 - Schrodinger's Time-Dependent Equation: Time-Evolution of State Vectors Figure 2: Schrodinger's equation is deterministic because the past or future quantum state \(|\psi(t)⟩\) of a quantum system can be determined with infinite precision. But, in general, a quantum system can be in a superposition of many different states where the measurement of any physical quantity is uncertain. For example, if anything the size of a small molecule or smaller passes through a double-slit in a double-slit experiment, where it hits the screen (which is to say, its final position) is uncertain (see illustration above). The quantum state of a quantum system is deterministic; but the eigenvalue that you'll measure after an experiment is done is the quantity which is not deterministic in quantum mechanics. Source: http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec13.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a026de4652dea4ceb35eb76/1510107139616/1_Lwu5UJMmcuFVJLZ1Ln4E0Q%5B1%5D.png articles page 10 - Schrodinger's Time-Dependent Equation: Time-Evolution of State Vectors Figure 1: The motion of a simple pendulum is an example of the time-reversibility of Newton's second law. Given the initial state of the pendulum, Newton's second law can be used to determine the past or future state of the system. For example, one could determine the velocity and position of the pendulum at any past or future time given its present state. https://www.gregschool.org/articles-page-10/2017/5/23/calculating-the-wavefunction-collection-of-probability-amplitudes-associated-with-any-ket-vector-skh4m-ey7ag monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a027ccae2c48322bcc11559/1507610296214/electromagnetism+thumbnaillllll+imageeee.jpg articles page 10 - Calculating the Wavefunction Associated with any Ket Vector https://www.gregschool.org/chain-rule daily 0.75 2017-11-05 https://www.gregschool.org/chain-rule/2017/11/2/how-fast-does-water-rise-up-a-cone-tca7n monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7eeae4966b0f258977ea/1509916111643/share+calculus+img.png Chain rule - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7eeae4966b0f258977ee/1509916171756/twiiter+img+thumbnail.jpg Chain rule - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7eeae4966b0f258977f0/1509916335679/google+img+thumbnail.jpg Chain rule - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7eeae4966b0f258977f6/1509910135829/flow-rate-cone.gif Chain rule - How Fast Does Water Rise Up a Cone? Figure 1: Water being poured into a rectangular box with dimensions \(4ft×4ft×h\) at a rate of \(\frac{dV}{dt}=4\frac{ft^3}{min}\). The container at time \(t=0\) starts out empty. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7eeae4966b0f258977ec/1509916211322/facebook+img+thumbnail.jpg Chain rule - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7eeae4966b0f258977f2/1509915987988/email+img+thumbnail.jpg Chain rule - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7eeae4966b0f258977f4/1509915966119/Calculus+thumbnail.png Chain rule - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ff7eeae4966b0f258977f8/1509906523011/flow-rate-cone.gif Chain rule - How Fast Does Water Rise Up a Cone? Figure 2: Water is poured into a cone of height \(h\) and radius \(r\) at a rate of \(\frac{dV}{dt}=4\frac{ft^3}{min}. The height of the water is given by \(y\). This image was modified under a Create Commons license. Image credit: https://www.mathalino.com/blog/romel-verterra/calculator-technique-solving-volume-flow-rate-problems-calculus https://www.gregschool.org/gregschoollessons daily 0.75 2020-06-16 https://www.gregschool.org/gregschoollessons/2018/6/12/shkadov-thrusters monthly 0.5 2018-07-06 https://www.gregschool.org/gregschoollessons/2018/7/5/proof-of-the-theorem-fracsinxx1 monthly 0.5 2018-07-19 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff1de03ce6465a2fc5403/1532040995867/twiiter+img+thumbnail.jpg gregschool-lessons - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3e6ab92b6a28dc000daaa8/1532040995874/squeezzeee.png gregschool-lessons - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) Figure 2: As you can see graphically, for values of \(ϴ\) in the range \(\frac{-π}{2}<ϴ<\frac{π}{2}\), the following inequalities are true \(1≥\frac{sinϴ}{ϴ}≥cosϴ\). Notice that as \(ϴ\) approaches zero from both the negative and positive directions, the function \(\frac{sinϴ}{ϴ}\) gets "squeezed" into the same point on the graph. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff20f2b6a2853e2c0648b/1532040995865/ gregschool-lessons - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b44efc81ae6cff42b6ec0bf/1532040995872/Limit_of_Sine_of_X_over_X-Proof_3.png gregschool-lessons - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) Figure 1: The wedge \(⪦OBA\) (colored blue) comprises a portion of the unit circle. The lengths \(AB\) and \(AC\) are the radius of the unit circle and are therefore equal to one. The heights of the triangles \(△OBA\) and \(△OCA\) can be found using basic trigonometry. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff0c6758d46506ec951fa/1532040995871/Calculus+thumbnail.png gregschool-lessons - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff1eb8a922dd648cecacc/1532040995869/email+img+thumbnail.jpg gregschool-lessons - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff11f03ce6465a2fc38d3/1532040995860/share+calculus+img.png gregschool-lessons - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff247758d46506ec98957/1532040995863/facebook+img+thumbnail.jpg gregschool-lessons - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://www.gregschool.org/gregschoollessons/2019/2/7/leaving-the-solar-system monthly 0.5 2019-02-24 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c5c8ab5eb393140dc8136ed/5c5c8ab524a69477fa2fbf2a/1550429768532/every_thing_that_comes_to_end.jpg gregschool-lessons - Leaving the Solar System: Introduction to the Outward Bound Series https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c5c85c3c83025da56a8268a/1550429768526/maxresdefault.jpg gregschool-lessons - Leaving the Solar System: Introduction to the Outward Bound Series https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c5cb052f4e1fcec460236fb/1550429768522/WH-Phoebe-1024x599%5B1%5D.jpg gregschool-lessons - Leaving the Solar System: Introduction to the Outward Bound Series Image retrieved from: https://crossingzebras.com/wormhole-space-after-phoebe/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c5cb5311905f4e70cc1a7a9/1550429768542/grav_lens_telescope%5B1%5D%5B1%5D.jpg gregschool-lessons - Leaving the Solar System: Introduction to the Outward Bound Series A gravitational lens telescope, as envisioned by Claudio Maccone in his 2009 book Deep Space Flight and Communications. (Claudio Maccone) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c5ca0479140b77d1c908d28/1550429768537/wright_brothers%5B1%5D.jpg gregschool-lessons - Leaving the Solar System: Introduction to the Outward Bound Series The Wright brothers on the steps of their boyhood home at 7 Hawthorn St. in Dayton.\(^{[1]}\) Carillon Historical Park https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c5cb1e4e5e5f09c9b9ab007/5c5cb1e4e4966b3a9884e747/1550429768539/This-is-How-Earth-Moves-1.jpg gregschool-lessons - Leaving the Solar System: Introduction to the Outward Bound Series This image illustrates the fact that the Sun is actually moving through space relative to the Milky Way galaxy; from this frame of reference, the Earth is moving in a spiral-shaped path. Of course, we can actually alter this path as well as the Sun’s speed using a type of megastructure known as a Shkadov thruster; you could, in fact, give the Sun (and the Earth which goes around it) a radically different path which heads off-course away from the galaxy. Image retrieved from: https://wordlesstech.com/this-is-how-earth-moves/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c5c88186e9a7f7629ce39c3/5c5c881853450aa0aa44e214/1550429768528/034-035_AAS_024%5B1%5D.jpg gregschool-lessons - Leaving the Solar System: Introduction to the Outward Bound Series Infographic retrieved from: https://www.spaceanswers.com/issue-previews/5025/5025/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c5c84bd9b747a54aaaa7950/1550429768524/quote-the-moral-landscape-is-the-framework-i-use-for-thinking-about-questions-of-morality-sam-harris-12-51-41%5B1%5D.jpg gregschool-lessons - Leaving the Solar System: Introduction to the Outward Bound Series Quote by Sam Harris, author of the book, The Moral Landscape. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c5c833ab208fccb907b9a26/5c5c833b53450aa0aa449ec4/1550429768519/84v8X%5B1%5D.jpg gregschool-lessons - Leaving the Solar System: Introduction to the Outward Bound Series https://www.gregschool.org/gregschoollessons/2018/6/20/the-diversity-of-exoplanets-in-the-galaxy monthly 0.5 2019-04-01 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b47dee2758d462b097c5dbf/1532041055813/pular+planet.png gregschool-lessons - The Diversity of Exoplanets in the Galaxy Artist's conception of a planet orbiting a Pulsar. The Pulsar's radiation blasting the exoplanet would cause its surface to glow. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3d4c9e575d1fd7a47b9757/1532041055839/trappist.png gregschool-lessons - The Diversity of Exoplanets in the Galaxy This artist's concept shows what the TRAPPIST-1 planetary system may look like, based on available data about the planets' diameters, masses and distances from the host star. Credits: NASA/JPL-Caltech View full image and caption https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b33fb8770a6ad47c2974f19/5b33fb871ae6cf9caeda770d/1532041055805/image_4610_3e-Europa-Lander%5B1%5D.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b33fb8770a6ad47c2974f19/5b34019c2b6a2849de2b95a3/1532041055809/PIA19058-SaturnMoon-Enceladus-PossibleHydrothermalActivity-ArtistConcept-20150311%5B2%5D.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy Artists impressions of subsurface oceans underneath thick ice sheets on Jupiter’s moon Europa and Saturn’s moon Enceladus. Top image by NASA. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b33fb8770a6ad47c2974f19/5b3404cdf950b7fe67ec5fde/1532041055811/PIA19656-SaturnMoon-Enceladus-Ocean-ArtConcept-20150915%5B2%5D.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff4a41ae6cfa99e5a85ff/1532041055793/twiiter+img+thumbnail.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4fdacd70a6ad94de3560fe/1532041055803/10629328_1041033252591158_1987130945153076812_o.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b2dec5403ce6467a1a98419/1532041055822/aHR0cDovL3d3dy5zcGFjZS5jb20vaW1hZ2VzL2kvMDAwLzA1My8yNjkvb3JpZ2luYWwvc3VwZXItZWFydGgtY2FuY3JpLTU1LWUuanBn%5B1%5D.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy Artist's depiction of the exoplanet 55 Cancri E. Image credit: ESA/Hubble [CC BY 4.0 (https://creativecommons.org/licenses/by/4.0)], via Wikimedia Commons. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b303cc90e2e7265f3fdaf39/1532041055828/maxresdefault.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy Image of auroras just above the Earth's surface obtained by the International Space Station. Image credit: NASA https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3d4e83aa4a9983df717380/1532041055836/2159_TRAPPIST-1e_1200_preview%5B1%5D.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy This poster imagines what a trip to TRAPPIST-1e might be like. Credits: NASA/JPL-Caltech View full image https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b358f58758d46d1dc970da1/1532041055824/Graphite-and-diamond-with-scale%5B1%5D.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy Graphite (left) and diamond (right) are both, essentially, just made up of a bunch of carbon atoms. The difference between the two substances is how those carbon atoms are arranged. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff4658a922dd648cf2e46/1532041055798/email+img+thumbnail.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b32983070a6ad6e85177a32/1532041055829/aHR0cDovL3d3dy5zcGFjZS5jb20vaW1hZ2VzL2kvMDAwLzAzOC81ODAvb3JpZ2luYWwva2VwbGVyLTE4NmYtYXJ0LmpwZz8xMzk3Njg3MTkw%5B1%5D.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy Artist's impression of the Archipelago world, Kepler 186f. Credit: Danielle Futselaar https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff44f575d1fc08ba5ddc4/1532041055788/share+astronomy+and+cosmology+img.png gregschool-lessons - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b33f9d488251b744df1cd00/1532041055818/Planets_everywhere_%28artist%E2%80%99s_impression%29%5B1%5D.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy "This artist's cartoon view gives an impression of how common planets are around the stars in the Milky Way. The planets, their orbits and their host stars are all vastly magnified compared to their real separations. A six-year search that surveyed millions of stars using the microlensing technique concluded that planets around stars are the rule rather than the exception. The average number of planets per star is greater than one."\(^{[1]}\) Image credit: by ESO/M. Kornmesser (http://www.eso.org/public/images/eso1204a/) [CC BY 4.0 (https://creativecommons.org/licenses/by/4.0)], via Wikimedia Commons https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff34788251b6ef1518f01/1532041055801/astronomy+and+cosmology+thumbnail.png gregschool-lessons - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff476562fa778928b2493/1532041055790/facebook+img+thumbnail.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b369d6688251bb98f898239/1532041055834/PIA21061-Pluto-DwarfPlanet-XRays-20160914%5B1%5D.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy X-ray image of Pluto obtained by Chandra X-Ray Observatory (blue spot on right) and up-close photograph of Pluto obtained by the spacecraft Deep Horizons as it flew by Pluto. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b32ab9faa4a990534b0ec4b/1532041055832/1920px-Kepler186f-ComparisonGraphic-20140417%5B1%5D.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy Size comparison of Kepler-186f (artist's impression) with Earth along with their projected habitable zones. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff48f758d46506ec9e6c6/1532041055796/google+img+thumbnail.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b303e32758d46fa6607b4b4/1532041055816/aHR0cDovL3d3dy5zcGFjZS5jb20vaW1hZ2VzL2kvMDAwLzA2Mi8wODkvb3JpZ2luYWwvaG90LWp1cGl0ZXItY29uY2VwdGlvbi5qcGc%3D%5B1%5D.jpg gregschool-lessons - The Diversity of Exoplanets in the Galaxy Artist's depiction of a so-called hot Jupiter orbiting its planet star. https://www.gregschool.org/gregschoollessons/2017/9/11/harvesting-resources-from-saturn-and-titan-l5msz-te4fd monthly 0.5 2017-12-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03767d8165f5ed71a9742a/1513008775554/WANDERERS_ligeia_mare_01.jpg gregschool-lessons - Harvesting Resources from Saturn and Titan "With an average temperature of -180 C all water here is frozen hard as rock. In fact, the surface landscape of Titan is indeed mostly made of frozen water ice. But Titan's atmosphere is rich in hydrocarbons such as methane and ethane, and the low temperature is perfect for these elements to occur naturally in three states; frozen, liquid and gas. So, just as on Earth where we have a water cycle (ice melts, becomes water, water evaporates into clouds, turning into liquid and becomes rain and so forth), Titan has a methane cycle. Methane evaporates and rises to form clouds, eventually turning into rain, falling over the surface. And this is the most amazing part; the rain in some places is enough to fill entire lakes. Lakes of methane! Titan is the only place in the Solar System, other than Earth, known to have large bodies of liquid on its surface. And they are really there, huge lakes, with shorelines, islands and small archipelagos. This scene takes place over a lake know as Ligeia Mare, the second largest on Titan, about 500 kilometers in diameter, located in the north polar region of the moon. The second fantastic feature I wanted to illustrate is the combination of Titan's very dense atmosphere and its relatively low gravity. As a human on Titan you would weigh about 14% of what you do on Earth, and in the dense atmosphere it would be enough to strap wings on your arms to make you able to fly like a bird. On Titan you could fly like a bird, over lakes of methane! (If you wore some really warm clothes of course.)" Image and image description credit: WANDERERS - a short film by EriK Wernquist https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03767d8165f5ed71a97426/1510249027061/email+img+thumbnail.jpg gregschool-lessons - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03767d8165f5ed71a97420/1510250414295/facebook+img+thumbnail.jpg gregschool-lessons - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03767d8165f5ed71a9741e/1509669572916/share+img+for+spacetrav+and+col+thumbnail.png gregschool-lessons - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03767d8165f5ed71a97422/1510250397217/twiiter+img+thumbnail.jpg gregschool-lessons - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03767d8165f5ed71a97428/1509917604285/space+travela+nd+colonization+thumbnail.png gregschool-lessons - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03767d8165f5ed71a97424/1510250431177/google+img+thumbnail.jpg gregschool-lessons - Harvesting Resources from Saturn and Titan https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a2eae9553450a8ff1cc6d61/1513008820293/neil-blevins-megastructures-9-gas-giant-refinery-design-packet%5B1%5D.jpg gregschool-lessons - Harvesting Resources from Saturn and Titan Artist's depiction of aerostats harvesting resources from a gas giant's atmosphere. Credit: https://www.artstation.com/artofsoulburn https://www.gregschool.org/gregschoollessons/2017/11/2/how-fast-does-water-rise-up-a-cone-l22x2 monthly 0.5 2017-11-12 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03768a24a694f5e24e8706/1510250502786/facebook+img+thumbnail.jpg gregschool-lessons - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03768a24a694f5e24e870a/1510250517125/google+img+thumbnail.jpg gregschool-lessons - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03768a24a694f5e24e8710/1509916394700/flow-rate-cone.gif gregschool-lessons - How Fast Does Water Rise Up a Cone? Figure 1: Water being poured into a rectangular box with dimensions \(4ft×4ft×h\) at a rate of \(\frac{dV}{dt}=4\frac{ft^3}{min}\). The container at time \(t=0\) starts out empty. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03768a24a694f5e24e8712/1509916394702/flow-rate-cone.gif gregschool-lessons - How Fast Does Water Rise Up a Cone? Figure 2: Water is poured into a cone of height \(h\) and radius \(r\) at a rate of \(\frac{dV}{dt}=4\frac{ft^3}{min}. The height of the water is given by \(y\). This image was modified under a Create Commons license. Image credit: https://www.mathalino.com/blog/romel-verterra/calculator-technique-solving-volume-flow-rate-problems-calculus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03768a24a694f5e24e870c/1510249088202/email+img+thumbnail.jpg gregschool-lessons - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03768a24a694f5e24e8708/1510250486642/twiiter+img+thumbnail.jpg gregschool-lessons - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03768a24a694f5e24e8704/1509916394688/share+calculus+img.png gregschool-lessons - How Fast Does Water Rise Up a Cone? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03768a24a694f5e24e870e/1509916394698/Calculus+thumbnail.png gregschool-lessons - How Fast Does Water Rise Up a Cone? https://www.gregschool.org/gregschoollessons/2017/5/4/chaos-3gdk9 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037699ec212ddbe21808f6/1510175075096/share+chaos+theory+img.png gregschool-lessons - Chaos and Fractals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037699ec212ddbe2180904/1510175075110/dice+game.jpg gregschool-lessons - Chaos and Fractals Figure 2: The three points \((1,2)\), \((3,4)\), and \((5,6)\) form an equilateral triangle. Choose any arbitrary point \((x,y)\) anywhere on the plane either inside or outside the triangle. If you rolled a 1 or 2, then draw a new point \((x_0,y_0)\) whose distance is half way between the points \((x,y)\) and \((1,2)\). Repeat this many times. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037699ec212ddbe21808fa/1510250577481/twiiter+img+thumbnail.jpg gregschool-lessons - Chaos and Fractals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037699ec212ddbe2180902/1510175075108/Edward_lorenz%5B1%5D.jpg gregschool-lessons - Chaos and Fractals Figure 1: "Edward Norton Lorenz (May 23, 1917 – April 16, 2008) was an American mathematician, meteorologist, and a pioneer of chaos theory, along with Mary Cartwright. He introduced the strange attractor notion and coined the term butterfly effect."\(^{[3]}\) This image is for educational purposes only. Image credit: https://history.aip.org/history/Thumbnails/lorenz_edward_a1.jpg https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037699ec212ddbe21808fc/1510250614334/google+img+thumbnail.jpg gregschool-lessons - Chaos and Fractals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037699ec212ddbe2180906/1510175075112/ gregschool-lessons - Chaos and Fractals Figure 3: After rolling the dice (and drawing a new point for each dice roll) billions of times, a fractal pattern known as the Siepinski triangle will eventually form. Remarkable! Image credit: by Beojan Stanislaus (Own work) [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037699ec212ddbe2180908/1510175075114/ gregschool-lessons - Chaos and Fractals Figure 4: An image of the Cantor set. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037699ec212ddbe21808f8/1510250594593/facebook+img+thumbnail.jpg gregschool-lessons - Chaos and Fractals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037699ec212ddbe21808fe/1510249147234/email+img+thumbnail.jpg gregschool-lessons - Chaos and Fractals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037699ec212ddbe2180900/1510175075106/chaos+theory+thumbnail.png gregschool-lessons - Chaos and Fractals https://www.gregschool.org/gregschoollessons/2017/10/22/partial-derivatives-6cjz9-njhjd monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376a88165f5ed71a97d63/1510250685822/facebook+img+thumbnail.jpg gregschool-lessons - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376a88165f5ed71a97d6d/1508723598292/MSP5083101ccb77dc1c84hg00003d8bb0b0083b496c.gif gregschool-lessons - Introduction to Partial Derivatives Figure 1: Graph of the surface \(f(x,y)=x^2+y^2\). Image courtesy of Wolfram Alpha. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376a88165f5ed71a97d6b/1509828263016/Calculus+thumbnail.png gregschool-lessons - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376a88165f5ed71a97d6f/1509324744015/partial+derivatives.jpg gregschool-lessons - Introduction to Partial Derivatives Figure 2: The entire blue surface is given by the function \(f(x,y)=x^2+y^2\). By letting \(y=1\), we that \(y^2=1\) and \(f(x,1)=x^2+1\) giving us a parabola shifted up one unit along the \(z\)-axis. That is how we can analytically obtain the parabola \(f(x,y)\). We can also obtain \(f(x,1)\) by passing the plane \(y=1\) (illustrated as the black plane above) through the surface \(f(x,y)\). The points at which the two surfaces (the surface \(f(x,y)\) and the plane \(y=1\)) intersect form the red parabola drawn in the image above. Image credit: By IkamusumeFan (Own work) [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376a88165f5ed71a97d61/1509828558864/share+calculus+img.png gregschool-lessons - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376a88165f5ed71a97d69/1510249198901/email+img+thumbnail.jpg gregschool-lessons - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376a88165f5ed71a97d65/1510250668795/twiiter+img+thumbnail.jpg gregschool-lessons - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376a88165f5ed71a97d67/1510250704201/google+img+thumbnail.jpg gregschool-lessons - Introduction to Partial Derivatives https://www.gregschool.org/gregschoollessons/2017/10/29/quasars-3xbmj-geyeg monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376c6652deaa9dbe0e0b7/1510249237714/email+img+thumbnail.jpg gregschool-lessons - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376c6652deaa9dbe0e0c3/1509815102930/orangepie%5B1%5D.jpg gregschool-lessons - Quasars Figure 5: A 3-d map obtained by the Sloan Digital Survey of billions of light years of our local universe. Each dot is an entire galaxy and this survey shows millions of them. As you can see from this image, on the scale of billions of light-years the galaxies of congregated into a "web"-like structure of filaments and strands known as the cosmic web. Image Credit: M. Blanton and SDSS https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376c6652deaa9dbe0e0bd/1509815576468/3C273z%5B1%5D.gif gregschool-lessons - Quasars Figure 2: "The spectrum of the quasar 3C 273. The strongest emission lines present are Balmer lines of hydrogen, as marked. In each case, the arrow is drawn from the rest wavelength to the observed wavelength of the line— shifted redward in each case by 15.8%. The other emission lines apparent in the spectrum are due to oxygen, helium, iron, and other elements. Credit: Michael A. Strauss, from data taken by the New Technology Telescope at La Silla, Chile; M. Türler et al. 2006, Astronomy and Astrophysics 451: L1– L4, http:// isdc.unige.ch/ 3c273/# emmi, http:// casswww.ucsd.edu/ archive/ public/ tutorial/ images/ 3C273z.gif Tyson, Neil deGrasse; Strauss, Michael A.; Gott, J. Richard. Welcome to the Universe: An Astrophysical Tour (p. 242). Princeton University Press. Kindle Edition."\(^{[2]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376c6652deaa9dbe0e0af/1509827157786/share+technology++img.jpg gregschool-lessons - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376c6652deaa9dbe0e0b1/1510250758465/facebook+img+thumbnail.jpg gregschool-lessons - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376c6652deaa9dbe0e0bb/1509813587682/PIA13033%5B1%5D.jpg gregschool-lessons - Quasars Figure 1: "The 200-inch (5.1 m) Hale Telescope (f/3.3) was the world's largest effective telescope for 45 years (1948-1993). It is still a workhorse of modern astronomy. It is used nightly for a wide range of astronomical studies. On average the weather allows for at least some data collection about 290 nights a year."\(^{[1]}\) Image credit: Caltech/Palomar Observatory https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376c6652deaa9dbe0e0b9/1509826851511/astronomy+and+cosmology+thumbnail.png gregschool-lessons - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376c6652deaa9dbe0e0c1/1509818196809/Quasar%5B1%5D.png gregschool-lessons - Quasars Figure 4: Illustration of the various different components of a quasar.\(^{[4]}\) Image credit: Futurism. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376c6652deaa9dbe0e0b5/1510250775740/google+img+thumbnail.jpg gregschool-lessons - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376c6652deaa9dbe0e0b3/1510250744758/twiiter+img+thumbnail.jpg gregschool-lessons - Quasars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376c6652deaa9dbe0e0bf/1509816781341/Best_image_of_bright_quasar_3C_273%5B1%5D.jpg gregschool-lessons - Quasars Figure 3: "This image from Hubble’s Wide Field and Planetary Camera 2 (WFPC2) is likely the best of ancient and brilliant quasar 3C 273, which resides in a giant elliptical galaxy in the constellation of Virgo (The Virgin). Its light has taken some 2.5 billion years to reach us. Despite this great distance, it is still one of the closest quasars to our home. It was the first quasar ever to be identified, and was discovered in the early 1960s by astronomer Allan Sandage. The term quasar is an abbreviation of the phrase “quasi-stellar radio source”, as they appear to be star-like on the sky. In fact, quasars are the intensely powerful centres of distant, active galaxies, powered by a huge disc of particles surrounding a supermassive black hole. As material from this disc falls inwards, some quasars — including 3C 273 — have been observed to fire off super-fast jets into the surrounding space. In this picture, one of these jets appears as a cloudy streak, measuring some 200 000 light-years in length. Quasars are capable of emitting hundreds or even thousands of times the entire energy output of our galaxy, making them some of the most luminous and energetic objects in the entire Universe. Of these very bright objects, 3C 273 is the brightest in our skies. If it was located 30 light-years from our own planet — roughly seven times the distance between Earth and Proxima Centauri, the nearest star to us after the Sun — it would still appear as bright as the Sun in the sky. WFPC2 was installed on Hubble during shuttle mission STS-125. It is the size of a small piano and was capable of seeing images in the visible, near-ultraviolet, and near-infrared parts of the spectrum."\(^{[3]}\) Image Credit: ESA/Hubble [CC BY 4.0 (http://creativecommons.org/licenses/by/4.0)], via Wikimedia Commons https://www.gregschool.org/gregschoollessons/2017/10/22/volume-of-an-oblate-spheroid-rl852-8yer8 monthly 0.5 2017-11-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376d7ec212ddbe2181709/1510250892415/google+share+thumbnail.jpg gregschool-lessons - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376d7ec212ddbe2181711/1509755409825/oblate+spheroid+img2.png gregschool-lessons - Volume of an Oblate Spheroid Figure 2: A cylindrical shell is obtained by revolving the rectangle \(f(x_i)Δx\) about the \(y\)-axis. Doing this for all \(n\) rectangles, we get an \(n\) number of shells. By summing the volumes of these \(n\) number of cylindrical shells, we can obtain an estimate for total volume enclosed inside of the paraboloid obtained by rotating the quarter-ellipse (the one in the upper-right quadrant) about the \(x\)-axis. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376d7ec212ddbe2181713/1509393143387/oblate+sphereoid.jpg gregschool-lessons - Volume of an Oblate Spheroid Figure 3: If \(a\) and \(c\) represents the semi-major and semi-minor axes of an ellipse, respectively, and if \(a=3\) and \(c=2\) then by rotating such an ellipse about an axis we can obtain an oblate spheroid. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376d7ec212ddbe2181707/1510250842787/Twitter+thumbnail.jpg gregschool-lessons - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376d7ec212ddbe218170d/1509758473080/Calculus+thumbnail.png gregschool-lessons - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376d7ec212ddbe2181703/1509759183401/temporary+shareeeeee.png gregschool-lessons - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376d7ec212ddbe218170f/1510347563387/oblate+spheroid+img1.png gregschool-lessons - Volume of an Oblate Spheroid Figure 1: Graph of the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\) centered at the origin of the \(xy\)-plane. Also, I have drawn the \(i^{th}\) rectangle underneath the quarter-ellipse within the first quadrant. There are an \(n\) number of such rectangles underneath this quarter-ellipse along the interval \(Δx=3-0\).   https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376d7ec212ddbe2181705/1510250867979/facebook+thumbnail.jpg gregschool-lessons - Volume of an Oblate Spheroid https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376d7ec212ddbe218170b/1510249382296/email+thumbnail.jpg gregschool-lessons - Volume of an Oblate Spheroid https://www.gregschool.org/gregschoollessons/2017/8/21/our-future-as-cyborgs-lfz6p monthly 0.5 2019-03-23 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376e60d9297d83e401419/1510175161930/04-17-Asimo-Grand-Marshall-HIGPA%5B1%5D.jpg gregschool-lessons - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376e60d9297d83e401411/1510250972172/google+img+thumbnail.jpg gregschool-lessons - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376e60d9297d83e401413/1510249455185/email+img+thumbnail.jpg gregschool-lessons - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376e60d9297d83e40140b/1510175161916/share+technology++img.jpg gregschool-lessons - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376e60d9297d83e40140d/1510250950786/facebook+img+thumbnail.jpg gregschool-lessons - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376e60d9297d83e401417/1510175161928/bionic_v2.png gregschool-lessons - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376e60d9297d83e401415/1510175161926/technology+thumbnail.png gregschool-lessons - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376e60d9297d83e40140f/1510250935466/twiiter+img+thumbnail.jpg gregschool-lessons - Our Future as Cyborgs https://www.gregschool.org/gregschoollessons/2017/10/27/gravitational-force-exerted-by-a-sphere-lm293-p3sph monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376f9e4966b6eaa5b6a92/1510251067171/google+img+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376f9e4966b6eaa5b6a9a/1509214998235/diskss.jpg gregschool-lessons - Gravitational Force Exerted by a Disk Figure 2: A disk of mass \(M=\int{m_{ring}}\) exerts a gravitational force on a particle of mass \(m\) a distance \(h\) away from the center of the disk along the \(x\)-axis. By summing the gravitational force exerted on \(m\) by each ring of radius \(r\) from \(r=0\) to \(r=R\), we can find the total gravitational force exerted on \(m\) by the entire disk. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376f9e4966b6eaa5b6a8e/1510251051966/facebook+img+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376f9e4966b6eaa5b6a96/1509566564697/classical+mechanics+thumbnail.png gregschool-lessons - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376f9e4966b6eaa5b6a90/1510251037038/twiiter+img+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376f9e4966b6eaa5b6a94/1510249547836/email+img+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376f9e4966b6eaa5b6a8c/1509566039912/share+img+for+classical+mechanics+thumbnail.png gregschool-lessons - Gravitational Force Exerted by a Disk https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0376f9e4966b6eaa5b6a98/1509567101995/ring1.jpg gregschool-lessons - Gravitational Force Exerted by a Disk Figure 1: A ring of mass \(M=\int{dm}\) exerts a gravitational force on a particle of mass \(m\) a horizontal distance \(h\) away from the center of the ring. The vertical component of force \(dF_y\) for every mass element \(dm\) in the ring is canceled out by the vertical component of force \(dF'_y\) for another mass element \(dm'\) located on the opposite side of the ring. https://www.gregschool.org/gregschoollessons/2017/9/21/shkadov-thruster-ljar4-xp8c5 monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037716f9619acb4fed3c84/1510421524549/google+img+thumbnail.jpg gregschool-lessons - Shkadov thruster https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037716f9619acb4fed3c7d/1509497981393/share+img+for+spacetrav+and+col+thumbnail.png gregschool-lessons - Shkadov thruster https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037716f9619acb4fed3c88/1509497981404/space+travela+nd+colonization+thumbnail.png gregschool-lessons - Shkadov thruster https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037716f9619acb4fed3c7f/1510421566742/facebook+img+thumbnail.jpg gregschool-lessons - Shkadov thruster https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037716f9619acb4fed3c86/1510421582019/email+img+thumbnail.jpg gregschool-lessons - Shkadov thruster https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037716f9619acb4fed3c8c/1509497981409/neil-blevins-megastructures-5-shkadov-thruster-design-packet.jpg gregschool-lessons - Shkadov thruster Figure 2: Artist's depiction of a Shkadov thruster. Credit: https://www.artstation.com/artofsoulburn https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037716f9619acb4fed3c8a/1509497981406/Shkadov_diagram.jpg gregschool-lessons - Shkadov thruster Figure 1: An arc mirror (dark orange arc) subtended by an angle \(2\phi\) reflects a star's radiation back towards itself. Photons collide against the portion of the star's surface which is subtended by the angle \(2\phi\). These collisions result in a net force \(\vec{F}\) exerted on the star causing the entire star to move in the direction of the arrow. The star's gravity pulls everything else in the star system along with it. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037716f9619acb4fed3c81/1510421490617/twiiter+img+thumbnail.jpg gregschool-lessons - Shkadov thruster https://www.gregschool.org/gregschoollessons/2017/10/30/derivation-of-snells-law-a8sne-a8e5w monthly 0.5 2017-11-12 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037722f9619acb4fed3f54/1509495184200/google+img+thumbnail.jpg gregschool-lessons - Derivation of Snell's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037722f9619acb4fed3f52/1509495184195/twiiter+img+thumbnail.jpg gregschool-lessons - Derivation of Snell's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037722f9619acb4fed3f58/1509495184210/Calculus+thumbnail.png gregschool-lessons - Derivation of Snell's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037722f9619acb4fed3f5a/1509495184214/snellslaw2.jpg gregschool-lessons - Derivation of Snell's Law Figure 1: A light ray traveling along the line \(QO\) comes into contact with a surface at an \(θ_i\) (where \(θ_i\) is measured relative to the line perpendicular to the surface). Once this light ray comes into contact with this surface, it is reflected at an angle \(θ_r\) (\(θ_r\) is also measured relative to the perpendicular). According to the law of reflection, \(θ_i=θ_r\). Image credit: Download for free at http://cnx.org/contents/60b4727b-829e-4ea7-9238-9140b6a1b20c@4. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037722f9619acb4fed3f4d/1509495184185/share+img.jpg gregschool-lessons - Derivation of Snell's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037722f9619acb4fed3f68/1509495184220/snells+law.jpg gregschool-lessons - Derivation of Snell's Law Figure 2: As a light ray travels along the line \(QO\) through medium 1 and comes into contact with the interface between medium 1 and medium 2, it gets refracted—meaning, it passes through medium 2. Image credit: By Smedlib (Own work) [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037722f9619acb4fed3f50/1509495184190/facebook+img+thumbnail.jpg gregschool-lessons - Derivation of Snell's Law https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037722f9619acb4fed3f56/1510249639872/email+img+thumbnail.jpg gregschool-lessons - Derivation of Snell's Law https://www.gregschool.org/gregschoollessons/2017/10/14/optimizatio-z7f59-3jc23 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03783153450ac45add7552/1509493612642/facebook+img+thumbnail.jpg gregschool-lessons - Optimization Problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03783153450ac45add7556/1509493672006/google+img+thumbnail.jpg gregschool-lessons - Optimization Problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03783153450ac45add755d/1509295467142/Optimization+Problem.jpg gregschool-lessons - Optimization Problem Figure 1: A graph of the circle \(x^2+y^2=4\) which is centered at the origin of the \(x\)-axis. If \((x,y)\) represents any point on the circle, if \(P\) is a point fixed at the coordinate point \((4,0)\), and if \(d\) represents the distance between those two points then, by using only calculus, we can find the point \((x,y)\) on the circle associated with the minimum distance \(d\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03783153450ac45add7554/1509493629913/twiiter+img+thumbnail.jpg gregschool-lessons - Optimization Problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03783153450ac45add755b/1509492607607/Calculus+thumbnail.png gregschool-lessons - Optimization Problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03783153450ac45add7550/1509492743734/share+img.jpg gregschool-lessons - Optimization Problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03783153450ac45add7558/1509492674642/email+img+thumbnail.jpg gregschool-lessons - Optimization Problem https://www.gregschool.org/gregschoollessons/2017/10/14/maximizing-the-area-of-a-rectangle-stk62-kh39r monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03784ac830253dadebc1ad/1509490767138/Calculus+thumbnail.png gregschool-lessons - Maximizing the Area of a Rectangle https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03784ac830253dadebc1a3/1509491428650/facebook+img+thumbnail.jpg gregschool-lessons - Maximizing the Area of a Rectangle https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03784ac830253dadebc1a9/1509491415850/google+img+thumbnail.jpg gregschool-lessons - Maximizing the Area of a Rectangle https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03784ac830253dadebc1ab/1509490808504/email+img+thumbnail.jpg gregschool-lessons - Maximizing the Area of a Rectangle https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03784ac830253dadebc1af/1509297168705/Optimization+Problem+1.jpg gregschool-lessons - Maximizing the Area of a Rectangle Figure 1: Given any rectangle \(xy\) where the perimeter \(2x+2y\) is the constant, we can use calculus to find that particular rectangle \(xy\) with the maximum area \(A\). The solution to this problem has practical applications. For example, suppose that someone had only 30 meters of fencing to enclose their backyard and they wanted to know what fencing layout would maximize the size and total area of their backyard. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03784ac830253dadebc1a7/1509491391314/twiiter+img+thumbnail.jpg gregschool-lessons - Maximizing the Area of a Rectangle https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03784ac830253dadebc1a1/1509490953440/share+img.jpg gregschool-lessons - Maximizing the Area of a Rectangle https://www.gregschool.org/gregschoollessons/2017/6/24/finding-the-minima-and-maxima-of-a-function-9g3gp-jzmsa monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037854c830253dadebc51b/1509495139379/Calculus+thumbnail.jpg gregschool-lessons - Finding the Minima and Maxima of a Function https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037854c830253dadebc517/1509495139375/google+img+thumbnail.jpg gregschool-lessons - Finding the Minima and Maxima of a Function https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037854c830253dadebc515/1509495139373/twiiter+img+thumbnail.jpg gregschool-lessons - Finding the Minima and Maxima of a Function https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037854c830253dadebc510/1509495139370/share+img.jpg gregschool-lessons - Finding the Minima and Maxima of a Function https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037854c830253dadebc513/1509495139372/facebook+img+thumbnail.jpg gregschool-lessons - Finding the Minima and Maxima of a Function https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037854c830253dadebc519/1509495139377/email+img+thumbnail.jpg gregschool-lessons - Finding the Minima and Maxima of a Function https://www.gregschool.org/gregschoollessons/2017/9/12/colonizing-the-kuiper-belt-and-oort-cloud-g53ff-66yzf monthly 0.5 2017-12-12 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03785f8165f5ed71a9eacb/1509746098354/share+technology++img.jpg gregschool-lessons - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03785f8165f5ed71a9ead9/1507689697151/Ancient_Mars3_02.jpg gregschool-lessons - Colonizing the Kuiper Belt and Oort Cloud Artist's depiction of Fesenkov Crater on Mars filled with liquid water. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03785f8165f5ed71a9ead5/1507689697148/space+travela+nd+colonization+thumbnail.jpg gregschool-lessons - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03785f8165f5ed71a9eae1/1507689697158/OortCloud_P-sys%28PNG-fin%291.png gregschool-lessons - Colonizing the Kuiper Belt and Oort Cloud Another size comparison of the solar system to the Oort Cloud. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03785f8165f5ed71a9eacf/1509746098357/twiiter+img+thumbnail.jpg gregschool-lessons - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5a03785f8165f5ed71a9eadb/5a03785f8165f5ed71a9eadc/1507689697153/george-dennis-the-fountains-of-neptune.jpg gregschool-lessons - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5a03785f8165f5ed71a9eadb/5a03785f8165f5ed71a9eade/1507689697156/uranus-gas-zoom.jpg gregschool-lessons - Colonizing the Kuiper Belt and Oort Cloud Artist’s depiction of Neptune’s (above image) and Uranus’s (below image) atmosphere being harvested for resources such as nitrogen. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03785f8165f5ed71a9eacd/1509746098355/facebook+img+thumbnail.jpg gregschool-lessons - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03785f8165f5ed71a9ead1/1509746098359/google+img+thumbnail.jpg gregschool-lessons - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03785f8165f5ed71a9ead3/1509746098361/email+img+thumbnail.jpg gregschool-lessons - Colonizing the Kuiper Belt and Oort Cloud https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03785f8165f5ed71a9ead7/1507689697150/Kuiper_oort.jpg gregschool-lessons - Colonizing the Kuiper Belt and Oort Cloud A size comparison of the Kuiper belt and outer solar system to the Oort Cloud. https://www.gregschool.org/gregschoollessons/2017/8/13/why-colonize-the-universe-z48ay-f5rbb monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03786bc830253dadebcb42/1507058438785/51i54HqlYHL._SY344_BO1%2C204%2C203%2C200_.jpg gregschool-lessons - Why Colonize the Universe? In Carl Sagan's book Pale Blue Dot, he argued that humans evolved a love for exploration as an essential part of our survival as a species. It was this evolutionary trait which compelled our hunter-gather ancestors to leave their home—Africa—when times were getting rough and to meander across the planet. As planetary catastrophes become increasingly likely as time rolls by, Sagan argues that this same "survival strategy" will perhaps compell humanity to colonize the solar system, and beyond. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03786bc830253dadebcb40/1507688339362/space+travela+nd+colonization+thumbnail.jpg gregschool-lessons - Why Colonize the Universe? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03786bc830253dadebcb44/1507059034215/factoriesins.jpg gregschool-lessons - Why Colonize the Universe? An O'Neil cylinder is a type of megastructure and artificial space habitat which was first proposed by the physicist Gerard O'Neil in 1976. An O'Neil cylinder would consist of two immense, rotating, cylindrical habitats (illustrated above) which would spin at a angular velocity that generated centrifugal forces along the interior surfaces of the cylinders which would emulate Earth-gravity. Each cylindrical habitat would be 5 miles in diameter and 20 miles long. https://www.gregschool.org/gregschoollessons/2017/10/6/calculating-the-arc-length-of-a-curve-hk54b-l6tsz monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03787fe2c483a1fc725184/1507687678074/calculus+thumbnail.jpg gregschool-lessons - Calculating the Arc Length of a Curve https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03787fe2c483a1fc725186/1507341957781/arclengthimg1.jpg gregschool-lessons - Calculating the Arc Length of a Curve Figure 1: The curve \(P_1P_n\) split up into an \(n\) number of chords \(P_iP_{i+1}\) where \(i=1,...,n\). By taking the sum of the lengths of each chord (represented by \(\sum_{i=1}^nL(P_iP_{i+1})\)) and then taking the limit as \(n→∞\), we obtain the exact arc length \(s\) of the entire curve. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03787fe2c483a1fc725188/1507343004584/arclengthimg2.jpg gregschool-lessons - Calculating the Arc Length of a Curve Figure 2: A close up view of the \(i^{th}\) chord subdividing the curve \(P_1P_n\). Since the chord \(P_iP_{i+1}\) forms a right triangle, by using the Pythagorean theorem we can express \(L(P_iP_{i+1})\) as \(\sqrt{(Δx_i)^2+(Δy_i)^2}\). https://www.gregschool.org/gregschoollessons/2017/9/19/the-kardeshev-scale-ge4gb-3zfyp monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037896085229fe4473034d/1507683863314/bubble-universes-computer-illustration-of-multiple-bubble-universes-G4C3H0.jpg gregschool-lessons - The Kardeshev Scale Artist's depiction of the multi-verse. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037896085229fe44730343/1507687169817/space+travela+nd+colonization+thumbnail.jpg gregschool-lessons - The Kardeshev Scale https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037896085229fe44730345/1507057461266/1024px-Consommations_%C3%A9nerg%C3%A9tiques_des_trois_types_de_l%27%C3%A9chelle_de_Kardashev.svg.png gregschool-lessons - The Kardeshev Scale The Kardeshev scale ranks how advanced a technological civilization is based upon their total power consumption. A Type I civilization is capable of harnessing all of their home plant's power of \(~10^{16}W\); a Type II civilization has harnessed the power of their star ( \(~10^{26}W\)); and a Type III civilization has harnessed the power output of their entire galaxy ( \(~10^{36}W\)). There are even Type IV and Type V civilization which go beyond Kardeshev's original scale. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5a037896085229fe44730347/5a037896085229fe4473034a/1507750720730/17202572._SX540_.jpg gregschool-lessons - The Kardeshev Scale Artist's depiction of a ring world. Credit: http://richardfrazer.com/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5a037896085229fe44730347/5a037896085229fe44730348/1507676111750/dyson_sphere_second_1024.jpg gregschool-lessons - The Kardeshev Scale Dyson sphere. Credit: capnhack.com https://www.gregschool.org/gregschoollessons/2017/9/30/solving-problems-using-line-integrals-z8s7t-e2kk8 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378a00d9297d83e408b34/1507491891563/156px-Circular_cylinder_rh.jpg gregschool-lessons - Solving Problems using Line Integrals Figure 1: A cylinder with height \(h=2\) and radius \(r=1\). The "top" and "bottom" pieces of the cylinder are removed. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378a00d9297d83e408b36/1507147436235/Untitled.jpg gregschool-lessons - Solving Problems using Line Integrals Figure 2: A proton \(P_2\) seperated by an initil seperation distance \(r_0\) from a station proton \(P_1\) moves along an arbitrary path until it reaches a seperation distance of \(r\). According to Column's law, the proton \(P_1\) will exert an electric force and, hence, also do work on the proton \(P_2\) as it moves from \(r_0\) to \(r\). The electric force forms a vector field and by calculuating the line integral along \(P_2\)'s path, we can calculate the amount of work done on \(P_2\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378a00d9297d83e408b32/1507502227235/sdfsdfdsdfdfdf+october+8.jpg gregschool-lessons - Solving Problems using Line Integrals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378a00d9297d83e408b38/1506906635307/main-qimg-ef54da6034b7e89fb771a40923f089ca.gif gregschool-lessons - Solving Problems using Line Integrals Figure 3: A mass \(m\) is attached to the end of a rope of length \(L\). The mass falls and travels a distance \(s\) with a total angular displacement of \(θ\). https://www.gregschool.org/gregschoollessons/2017/9/27/introduction-to-line-integrals-bywel-5asgd monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378aa085229fe447309d4/1507433707547/fhdhfdg.jpg gregschool-lessons - Introduction to Line Integrals Figure 2: By the Pythagorean theorem, each infinitesimal arc length \(ds\) can be represented in terms of \(x\) and \(y\) as \(\sqrt{x+2+y^2}\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378aa085229fe447309d0/1510175532388/sdf.jpg gregschool-lessons - Introduction to Line Integrals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378aa085229fe447309d2/1507432031391/VIBrO.jpg gregschool-lessons - Introduction to Line Integrals Figure 1: The width and height of each blue rectangle is given by the arc length \(ds\) and the function \(f(x,y)\), respectively. The line integral, \(\int_Cf(x,y)ds\), represents the infinite sum of the area of each blue rectangle along the curve \(C\) (the purple line on the \(xy\)-plane). This image is a derivative work. Original image: https://www.wikihow.com/User:Atheia https://www.gregschool.org/gregschoollessons/2017/10/6/calculating-the-volume-of-a-sphere-e6jde-bs7ml-nl5p5 monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378b824a694f5e24f19d6/1507412420221/moment-of-inertia-of-sphere.jpg gregschool-lessons - Calculating the Volume of a Sphere Figure 4: By taking the infinite sum of the volumes, \(π(f(x))^2dx\), of every cylinder from \(x=0\) to \(x=R\), we can obtain the volume of half of the sphere depicted above. By multiplying our answer by two, we can obtain the volume of the whole sphere. Image credit: https://www.miniphysics.com/uy1-calculation-of-moment-of-inertia-of-solid-sphere.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378b824a694f5e24f19d0/1507412420207/320px-Rotationskoerper_animation.gif gregschool-lessons - Calculating the Volume of a Sphere Figure 1: The "vase" shaped surface is obtained by revolving a curve about the vertical axis. The region of space that the surface encloses is called a solid of revolution. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378b824a694f5e24f19d4/1507412420216/s9NuK.jpg gregschool-lessons - Calculating the Volume of a Sphere Figure 3: By rotating the \(i^{th}\) rectangle about the \(x\)-axis, the cylinder depicted above is obtained. By doing this for each rectangle, an \(n\) number of cylinders are obtained. All of these cylinders fit inside of a hemisphere of radius \(r\) and the sum of the volumes of all of those cylinders approximate the volume of the hemisphere. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378b824a694f5e24f19ce/1510175551473/sdf.jpg gregschool-lessons - Calculating the Volume of a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378b824a694f5e24f19d2/1507412420213/volumeofsphereimg1.jpg gregschool-lessons - Calculating the Volume of a Sphere Figure 2: A graph of the quarter circle \(x^2+y^2=r^2\) for \(x≥0\) and \(y≥0\). An \(n\) number of rectangles, \(f(x_i\)Δx\), are drawn underneath the curve. https://www.gregschool.org/gregschoollessons/2017/8/16/maclaurin-polynomial-and-series-9cll7-my4k9 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378db9140b70c95b2253f/1504563483921/Exp_series.gif gregschool-lessons - Maclaurin/Taylor Polynomials and Series Figure 1. Maclaurin polynomials of different order \(n\) (red curves) approximating the function \(e^x\) (blue curve). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378db9140b70c95b2253d/1507581887299/Untitled.jpg gregschool-lessons - Maclaurin/Taylor Polynomials and Series https://www.gregschool.org/gregschoollessons/2017/8/29/introduction-to-integrals-xl5rn-y4ls9 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378eb9140b70c95b2292a/1504566939599/dfgd.png gregschool-lessons - Introduction to Integrals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378eb9140b70c95b22926/1510176997141/Untitled.jpg gregschool-lessons - Introduction to Integrals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378eb9140b70c95b22930/1504567134996/Riemann_Integration_and_Darboux_Upper_Sums.gif gregschool-lessons - Introduction to Integrals Figure 2. The approximate area, \(\sum_{i=1}^nf(x_n)Δx\), underneath the curve \(y=x^2\) becomes closer and closer to the exact area underneath the curve as the number \(n\) of terms increases. https://www.gregschool.org/gregschoollessons/2017/6/28/8fldcv2rgvjvjwb42w67qh0ude4ii0-3yepp-2p2s7 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0378f50d9297d83e40a2d1/1507670521347/space+travela+nd+colonization+thumbnail.jpg gregschool-lessons - Alcubierre Warp Drive https://www.gregschool.org/gregschoollessons/2017/6/28/terraforming-mars-gz3x8-s9hg4 monthly 0.5 2019-03-19 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03792b0d9297d83e40af22/1502413444230/ gregschool-lessons - Terraforming and Colonizing Mars "This shot follows the cabin of a space elevator descending on a cable towards the northern parts of the Terra Cimmeria highlands on Mars. A large settlement, hinted as glowing lights in the dark, can be seen far below on the ground. One of Mars' two moons - Phobos - is seen above the cabin to the left of the cable in the beginning of the shot." This image was produced by Erik Wernquist. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03792b0d9297d83e40af28/1498701189016/ gregschool-lessons - Terraforming and Colonizing Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03792b0d9297d83e40af20/1498701139592/ gregschool-lessons - Terraforming and Colonizing Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03792b0d9297d83e40af1e/1502315090185/ares2.jpg gregschool-lessons - Terraforming and Colonizing Mars Artist's depiction of the Ares spaceship from Kim Stanley Robinson's novel, Red Mars. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c90777eee6eb06073b7a7f1/5c90777e15fcc09c62fa950d/1552971654919/marsssssssssssssssssssssss.jpg gregschool-lessons - Terraforming and Colonizing Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c907dfa9140b7ad40265fd1/5c907eb4ee6eb06073b7dca0/1552973573193/iceteroiddd.jpg gregschool-lessons - Terraforming and Colonizing Mars - Absolute Zero Artist’s depiction of iceteroids located within a nebula. Image Credit: https://store.steampowered.com/news/?appids=310380&enddate=1498892400&appgroupname=Fractured+Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c907d0ae79c709a0f3604d4/5c907d0a9b747a6c2b91b21c/1552973117109/dn10573-1_800%5B1%5D.jpg gregschool-lessons - Terraforming and Colonizing Mars An orbiting array of reflective balloons focuses sunlight onto the surface of Mars, providing extra heat and solar power for human colonists (Illustration: Rigel Woida) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c907d0ae79c709a0f3604d4/5c907d0c0852294993ed240b/1552973137671/dn10573-2_700%5B1%5D.jpg gregschool-lessons - Terraforming and Colonizing Mars The lake of water ice seen here could be melted to provide liquid water for future Mars astronauts (Image: ESA/DLR/F U Berlin/G Neukum) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03792b0d9297d83e40af1c/1507664835657/space+travela+nd+colonization+thumbnail.jpg gregschool-lessons - Terraforming and Colonizing Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9079d90852294993ed09ab/1552972255054/Mars-VR-570x300%5B1%5D.jpg gregschool-lessons - Terraforming and Colonizing Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03792b0d9297d83e40af26/1502314679613/olympus.jpg gregschool-lessons - Terraforming and Colonizing Mars Poster by SpaceX https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c907b81971a186e678a4034/1552972687082/Cpw8t4nVUAA7e5L%5B1%5D.jpg gregschool-lessons - Terraforming and Colonizing Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03792b0d9297d83e40af24/1502431153897/ gregschool-lessons - Terraforming and Colonizing Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c907c79ec212d7ca9d3fb33/1552972940780/dis03_fig1_hires_0%5B1%5D.jpg gregschool-lessons - Terraforming and Colonizing Mars Mars’ south polar ice cap, as seen in April of 2000 by the Mars Odyssey mission. Credit: NASA/JPL/MSSS https://www.gregschool.org/gregschoollessons/2017/5/14/introduction-to-special-relativity-d23j8-p3zt4 monthly 0.5 2017-11-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a05c2bee2c48388cba1d71e/1510326979408/Figure_29_02_05a%5B1%5D.jpg gregschool-lessons - Introduction to Special Relativity Figure 1: A clock onboard a spacecraft or plane circumnavigating the Earth will tick more slowly than a clock on the Earth's surface. All physical processes run more slowly at very high altitudes above the Earth's surface. This is even true if the relative velocity between both objects is zero; according to Einstein's general theory of relativity, the Earth's mass warps time in such a way where the flow of time (how rapidly or how slowly the clock ticks) varies with altitude above the Earth's surface. This is a mindboggling prediction! https://www.gregschool.org/gregschoollessons/2017/5/14/8c5knwf9nztiio7uwnvvotz1pj86ht-thkb7-c33w6 monthly 0.5 2017-11-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a05d8d1e2c483f86324d3c0/1510332630437/time+dil.jpg gregschool-lessons - Time Dilation Figure 1: Right at the moment the train is passing by the observer standing at the train station, both observers clocks are synchronized; in other words, right at this moment, \(t=t'=0\). Also, right at this moment, a light source \(S'\) emits light in a direction towards a mirror (colored pink in image above) attached to the top of the train. The light beam eventually reaches the mirror and is reflected back towards \(S'\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a05cf789140b7ac4ec648dd/1510333018414/480px-Time_dilation.svg%5B1%5D.png gregschool-lessons - Time Dilation Figure 2: Using Equation (1), we can calculate the Lorenz factor for various different values of relative speed to obtain the graph above. As you can see, when the relative velocity between two reference frames is greater than 90% the speed of light, the effects of time dilation become enormous. Image by Zayani (Own work) [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0) or GFDL (http://www.gnu.org/copyleft/fdl.html)], via Wikimedia Commons https://www.gregschool.org/gregschoollessons/2017/5/15/particle-in-one-dimensional-box-dwfnl-dex28 monthly 0.5 2019-03-21 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0379520d9297d83e40bb31/1495487069613/kjkjnj.png gregschool-lessons - Time-Independant Schrodinger Equation: Free Particle and Particle in One-Dimensional Box Figure 1 (click to expand): Illustration of a free particle moving in a "one-dimensional box" which is trapped inside of an infinite potential well. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0379520d9297d83e40bb33/1495562943423/sch.png gregschool-lessons - Time-Independant Schrodinger Equation: Free Particle and Particle in One-Dimensional Box Figure 2 (click to expand): The probability amplitude of measuring the particle at a position \(x\) in the presence of a potential \(V_0\) decreases exponentially with increasing \(V_0\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0379520d9297d83e40bb37/1495487701759/ gregschool-lessons - Time-Independant Schrodinger Equation: Free Particle and Particle in One-Dimensional Box Figure 4: Illustration shows the allowed energy levels of a particle trapped inside of a one-dimensional box. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0379520d9297d83e40bb2f/1495485871466/ gregschool-lessons - Time-Independant Schrodinger Equation: Free Particle and Particle in One-Dimensional Box "A wave function that satisfies the nonrelativistic Schrödinger equation with V = 0. In other words, this corresponds to a particle traveling freely through empty space. The real part of the wave function is plotted here."\(^{[1]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0379520d9297d83e40bb35/1494831797145/ gregschool-lessons - Time-Independant Schrodinger Equation: Free Particle and Particle in One-Dimensional Box Figure 3 (click to expand): Illustration of a free particle moving in a one-dimensional box which is "pinned down" by a finite well. The probability amplitude of finding the particle outside of the box decreases exponentially as a function of distance. https://www.gregschool.org/gregschoollessons/2017/8/13/nuclear-fusion-engines-g9fdd-hjd78 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03795d085229fe447339b3/1507665154586/space+travela+nd+colonization+thumbnail.jpg gregschool-lessons - Nuclear Fusion Engines https://www.gregschool.org/gregschoollessons/2017/8/29/finding-the-integral-of-kxm-lbzkf-wtznt monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037965e2c483a1fc729396/1507419408151/author+date.jpg gregschool-lessons - Finding the integral of \(kx^m\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037965e2c483a1fc729398/1507420992695/areaoftriangle.jpg gregschool-lessons - Finding the integral of \(kx^m\) Figure 1: The area underneath the function \(f(x)=2x\) is simply just the area of a triangle. The base of the triangle is \(x\) and its height is \(f(x)=2x\). Using the formula for the area of a triangle, we find that the area underneath \(f(x)=2x\) is \(x^2\). https://www.gregschool.org/gregschoollessons/2017/8/30/capacitance-32sgr-ssdas monthly 0.5 2017-11-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a03798f71c10b1e516768b9/1507602491385/electromagnetism+thumbnaillllll+imageeee.jpg gregschool-lessons - Capacitance https://www.gregschool.org/gregschoollessons/2017/8/30/5g8xs8bx2yk4rez4xp70hkmry35965-k5dj3-6lkj3 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0379ab24a694f5e24f5ce3/1507603176920/electromagnetism+thumbnaillllll+imageeee.jpg gregschool-lessons - Calculating the amount of Electric Potential Energy Stored in a Capacitor https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0379ab24a694f5e24f5ce5/1504719624283/kkk.png gregschool-lessons - Calculating the amount of Electric Potential Energy Stored in a Capacitor Figure 1 https://www.gregschool.org/gregschoollessons/2017/5/23/math-interlude-cddln-phcd6 monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0379bd71c10b1e5167755b/1507610424966/electromagnetism+thumbnaillllll+imageeee.jpg gregschool-lessons - Quantum Mechanics: Math Interlude https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a065ff941920291503726c2/1510367229774/200px-Complex_Impedance.svg%5B1%5D.jpg gregschool-lessons - Quantum Mechanics: Math Interlude Figure 1: Any complex number \(z\) can be represented in either Cartesian coordinates as \(x+iy\) or in polar coordinates as \(re^{iθ}\). https://www.gregschool.org/gregschoollessons/2017/5/14/quantum-dynamics-2nhll-s9x7c monthly 0.5 2017-11-08 https://www.gregschool.org/gregschoollessons/2017/5/23/the-eigenvalues-of-any-observable-hatl-must-be-real-3jrk4-gja8k monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0379dd9140b70c95b26f1a/1507610471341/electromagnetism+thumbnaillllll+imageeee.jpg gregschool-lessons - The Eigenvalues of any Observable \(\hat{L}\) must be Real https://www.gregschool.org/gregschoollessons/2017/5/23/pauli-matrices-wf87n-fgty6 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0379e50d9297d83e40e669/1507610581346/electromagnetism+thumbnaillllll+imageeee.jpg gregschool-lessons - Pauli Matrices https://www.gregschool.org/gregschoollessons/2017/8/10/einstein-equivalence-principle-8j2w9-76xjn monthly 0.5 2017-11-08 https://www.gregschool.org/gregschoollessons/2017/5/23/fundamental-principles-and-postulates-of-quantum-mechanics-5hrka-4pedm monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0379f6419202d77c15f7a2/1507610679168/electromagnetism+thumbnaillllll+imageeee.jpg gregschool-lessons - Fundamental Principles and Postulates of Quantum Mechanics https://www.gregschool.org/gregschoollessons/2017/5/23/measuring-the-spin-of-an-electron-e5rzd-gmtdl monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037a10419202d77c15fe4e/1495565239455/ gregschool-lessons - Measuring the Spin of an Electron Figure 1 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037a10419202d77c15fe51/1507610719385/electromagnetism+thumbnaillllll+imageeee.jpg gregschool-lessons - Measuring the Spin of an Electron https://www.gregschool.org/gregschoollessons/2017/5/14/solving-the-frw-equation-for-the-scaling-factor-in-different-scenarios-hdsrg-6tdyy monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037a3a0d9297d83e40fabd/1509980764068/AT_7e_Figure_27_01%5B2%5D.jpg gregschool-lessons - Solving the FRW Equation for the Scaling Factor in different scenarios Figure 1: As you can see from the graph above, for the first roughly 10,000 years most of the energy density in the universe was due to the presence of radiation. During the time interval from when the universe was 10,000 years old to when it was several billion years old, the energy density of the universe was dominated by matter. In our present epoch, the energy density of the universe is dominated by dark energy (or vacuum energy). This graph has profound implications. As time progresses, dark energy will become more and more dominant and will remain the dominant source of energy in the universe; since dark energy causes everything in the universe to expand, the universe will continue to expand without ever stopping. This graph, essentially, implies the ultimate fate of the universe. The universe will continue to expand more and more until it becomes dark, empty, and lifeless. https://www.gregschool.org/gregschoollessons/2017/5/14/bentleys-and-olbers-paradoxes-e6hj4-pzpcf monthly 0.5 2017-11-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a049ed5c8302552e4b72d05/1510252249221/ gregschool-lessons - Bentley's and Olber's Paradoxes According to Olbers' paradox, if the universe is infinitely large with a uniform distribution of stars then the night sky should be blindingly bright. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a05f1f2652dea8f286e5d9d/1510339073364/Olber%27s_Paradox_-_All_Points%5B1%5D.gif gregschool-lessons - Bentley's and Olber's Paradoxes "As more distant stars are revealed in this animation depicting an infinite, homogeneous and static universe, they fill the gaps between closer stars. Olbers's paradox argues that as the night sky is dark, one of these three assumptions about the nature of the universe must be false."\(^{[1]}\) Image by Kmarinas86 [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons https://www.gregschool.org/gregschoollessons/2017/5/14/friedman-robertson-walker-frw-equation-s6f2m-ryshd monthly 0.5 2017-11-11 https://www.gregschool.org/gregschoollessons/2017/5/14/surface-of-last-scattering-blnaz-936jb monthly 0.5 2017-11-11 https://www.gregschool.org/gregschoollessons/2017/5/14/spectroscopy-9cnt6-tkzdb monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037a6ce4966bbdfaf2aed6/1494827814784/ gregschool-lessons - Spectroscopy https://www.gregschool.org/gregschoollessons/2017/6/16/formation-of-planets-and-stars-xa5hw-skf5t monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037a77652dea086dc9def3/1498195845727/ gregschool-lessons - A Brief Tour of our Milky Way Galaxy Artist's depiction of the Milky Way Galaxy. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037a77652dea086dc9def5/1498157418533/mwpan_aitoff_s.jpg gregschool-lessons - A Brief Tour of our Milky Way Galaxy Picture of the Milky Way Galaxy as seen edge on. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037a77652dea086dc9def7/1498193304895/ gregschool-lessons - A Brief Tour of our Milky Way Galaxy Inferred image of the center of the Milky Way Galaxy. (Source) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037a77652dea086dc9def9/1498195183058/430453main_crabmosaic_hst_big_full.jpg gregschool-lessons - A Brief Tour of our Milky Way Galaxy Image of Crab Nebula. (Image credit: NASA) https://www.gregschool.org/gregschoollessons/2017/5/14/dark-matter-yla9j-kgnpm monthly 0.5 2017-11-08 https://www.gregschool.org/gregschoollessons/2017/5/14/cosmic-microwave-background-radiation-lfmal-shpkt monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037a8ac830257e2fa357af/1494827005244/ gregschool-lessons - Cosmic Microwave Background Radiation https://www.gregschool.org/gregschoollessons/2017/5/14/dark-energy-exgdc-7538n monthly 0.5 2017-11-11 https://www.gregschool.org/gregschoollessons/2017/8/30/finding-the-capacitance-of-a-parallel-plate-capacitor-ajby4-584gb monthly 0.5 2017-11-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037aabe4966bbdfaf2c466/1504480094587/Fig1.jpg gregschool-lessons - Finding the Capacitance of a Parallel-Plate Capacitor Figure 1: Parallel-plate capacitor. Each conductor is a flat plate with charges \(-Q\) and \(+Q\), areas of \(A\), and separated at a distance of \(d\). Courtesy of the Department of Physics and Astronomy, Michigan State University https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037aaae4966bbdfaf2c464/1507605626845/electromagnetism+thumbnaillllll+imageeee.jpg gregschool-lessons - Finding the Capacitance of a Parallel-Plate Capacitor https://www.gregschool.org/gregschoollessons/2017/5/18/brachistochrone-problem-8bgmb-zrgw7 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037ae453450a088000d620/1507588702724/gfnf.jpg gregschool-lessons - Brachistochrone problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037ae453450a088000d624/1495304353556/ gregschool-lessons - Brachistochrone problem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037ae453450a088000d626/1495304408606/ gregschool-lessons - Brachistochrone problem Credit\(^{[3]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037ae453450a088000d622/1495304339104/ gregschool-lessons - Brachistochrone problem https://www.gregschool.org/gregschoollessons/2017/5/18/generalized-coordinates-7r5bn-wlsm4 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037aec419202d77c1644b6/1507588890423/gfnf.jpg gregschool-lessons - Generalized coordinates https://www.gregschool.org/gregschoollessons/2017/5/18/finding-the-geodesic-on-a-cylinder-mley2-h44tn monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037af4085229fe4473b195/1507588727041/gfnf.jpg gregschool-lessons - Finding the geodesic on a cylinder https://www.gregschool.org/gregschoollessons/2017/6/20/derivation-of-guasss-law-from-columns-law-mbxrn-syd52 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037afcec212d3e0f543bb5/1501802501336/guass.jpg gregschool-lessons - Derivation of Guass's Law from Column's Law Figure 1 (click to enlarge) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037afcec212d3e0f543bb7/1501804297766/ gregschool-lessons - Derivation of Guass's Law from Column's Law Figure 2 (click to enlarge) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037afcec212d3e0f543bb3/1507606994080/electromagnetism+thumbnaillllll+imageeee.jpg gregschool-lessons - Derivation of Guass's Law from Column's Law https://www.gregschool.org/gregschoollessons/2017/5/18/v7t2klwmycopiblvbhzkhyw2duujqy-bjxsk-sxxc8 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037b0653450a088000e1ba/1507588749777/gfnf.jpg gregschool-lessons - Introduction to Lagrangian Mechanics https://www.gregschool.org/gregschoollessons/2017/5/14/columns-law-7fdl2-rws49 monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037b109140b70c95b2ccd8/1507607529720/electromagnetism+thumbnaillllll+imageeee.jpg gregschool-lessons - Column's Law https://www.gregschool.org/gregschoollessons/2017/5/18/derivation-of-the-euler-lagrange-equation-s8wam-zntyn monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037b2853450a088000eb97/1507588781308/gfnf.jpg gregschool-lessons - Derivation of the Euler-Lagrange Equation https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037b2853450a088000eb99/1495304730085/ gregschool-lessons - Derivation of the Euler-Lagrange Equation Figure 1 (click to expand) https://www.gregschool.org/gregschoollessons/2017/7/20/using-guasss-law-to-find-the-electric-field-produced-by-a-single-point-charge-8m3gx-l22p3 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037b3f8165f535a0971fcb/1501807096166/ gregschool-lessons - Using Guass's Law to find the Electric Field Produced by a Single Point Charge Figure 3 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037b3f8165f535a0971fc7/1501804682969/guass.jpg gregschool-lessons - Using Guass's Law to find the Electric Field Produced by a Single Point Charge Figure 1 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037b3f8165f535a0971fc9/1501805131555/ gregschool-lessons - Using Guass's Law to find the Electric Field Produced by a Single Point Charge Figure 2 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037b3f8165f535a0971fc5/1507607040412/electromagnetism+thumbnaillllll+imageeee.jpg gregschool-lessons - Using Guass's Law to find the Electric Field Produced by a Single Point Charge https://www.gregschool.org/gregschoollessons/2017/5/14/electric-flux-enbx3-2af5w monthly 0.5 2017-11-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037b4853450a088000f2dc/1507606396620/electromagnetism+thumbnaillllll+imageeee.jpg gregschool-lessons - Electric Flux https://www.gregschool.org/gregschoollessons/2017/5/18/noethers-theorem-78d8y-89f2j monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037b53c830257e2fa3972d/1507588859663/gfnf.jpg gregschool-lessons - Noether’s Theorem https://www.gregschool.org/gregschoollessons/2017/5/18/what-do-we-mean-by-kinematics-dynamics-and-mechanics-xr2cr-fkz2j monthly 0.5 2017-11-08 https://www.gregschool.org/gregschoollessons/2017/6/20/faxkbn1icm37pyljps0j38mgdt0t22-ch2g2-plga4 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037b84652dea086dca2eb4/1507582425469/Untitled.jpg gregschool-lessons - Basic Equations of Kinematics https://www.gregschool.org/gregschoollessons/2017/8/28/newtons-law-of-gravity-ybhff-cl6dx monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037b95ec212d3e0f5465ca/1507582895064/Untitled.jpg gregschool-lessons - Newton's Law of Gravity https://www.gregschool.org/gregschoollessons/2017/5/14/introduction-to-newtonian-mechanics-25a5e-xcb9m monthly 0.5 2017-11-08 https://www.gregschool.org/gregschoollessons/2017/6/20/76hgztk8ogz149g9acwmizq62okwe4-cz2yr-m7abr monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037ba5c830257e2fa3ae1b/1501788322829/ gregschool-lessons - Position Vectors, Displacement, Velocity, and Acceleration Figure 2 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037ba5c830257e2fa3ae17/1507582470969/Untitled.jpg gregschool-lessons - Position Vectors, Displacement, Velocity, and Acceleration https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037ba5c830257e2fa3ae19/1501784000999/ gregschool-lessons - Position Vectors, Displacement, Velocity, and Acceleration Figure 1 (click to enlarge) https://www.gregschool.org/gregschoollessons/2017/8/29/newtons-three-laws-of-motion-62d9d-emyyp monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037baf24a6943d6bba4413/1507582682482/Untitled.jpg gregschool-lessons - Newton's Three Laws of Motion https://www.gregschool.org/gregschoollessons/2017/8/10/derivation-on-momentum-conservation-bxjp5-pe7wa monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037bbde2c483e53cae60f5/1507586881155/gfnf.jpg gregschool-lessons - Derivation of Momentum Conservation https://www.gregschool.org/gregschoollessons/2017/8/10/introduction-to-linear-momentum-mbs6h-a3eh4 monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037bc8419202d77c1682f3/1507586693883/gfnf.jpg gregschool-lessons - Introduction to Linear Momentum https://www.gregschool.org/gregschoollessons/2017/8/28/motion-of-objects-experiancing-air-friction-wheys-9sakr monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037bd58165f535a0974945/1507586453265/gfnf.jpg gregschool-lessons - Motion of objects experiencing air friction https://www.gregschool.org/gregschoollessons/2017/6/21/the-abstract-has-a-lot-to-say-about-the-physical-world-xk4tb-7mtn7 monthly 0.5 2017-11-08 https://www.gregschool.org/gregschoollessons/2017/5/14/xe30zrw2tke0y051q8xdpf9cxaff19-fyzrj-85zyn monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0631b824a6942e849f5e6e/1510355396579/cosmolg.jpg gregschool-lessons - Scaling Factor, Hubble's Parameter, and the Age of the Universe Figure 1: The coordinate value \(x^i\) assigned to each tick mark in the rectangular coordinate system above remains the same as the coordinate system stretches or contracts. Only the scaling factor \(a(t)\) changes when the coordinate system stretches or contracts. https://www.gregschool.org/gregschoollessons/2017/8/10/inelastic-collisions-mjsnh-ygw3m monthly 0.5 2017-11-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a05bb30652dea801332e747/1510325044804/InelCol%5B1%5D.gif gregschool-lessons - Inelastic Collisions Figure 1: An inelastic collision is when two objects collide and stick together. Each object becomes conjoined and moves away with equal velocities. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c189140b70c95b31521/1507587059265/gfnf.jpg gregschool-lessons - Inelastic Collisions https://www.gregschool.org/gregschoollessons/2017/5/14/4ufuuy7fweohxl2tk6hryzmsq50amd-a67kn-yp26b monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c1fe2c483e53cae7f87/1507588058521/gfnf.jpg gregschool-lessons - Introduction to Mechanical Waves https://www.gregschool.org/gregschoollessons/2017/5/14/rotational-kinematics-5xef2-wy987 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c29e4966bbdfaf330e9/1507588198193/gfnf.jpg gregschool-lessons - Rotational Kinematics https://www.gregschool.org/gregschoollessons/2017/5/14/introduction-to-rotational-kinetic-energy-b8hy8-dreh5 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c319140b70c95b31c75/1507588322330/gfnf.jpg gregschool-lessons - Introduction to Rotational Kinetic Energy https://www.gregschool.org/gregschoollessons/2017/5/14/torque-6zmaw-amjpk monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c42f9619a0fd0c17cc7/1507588457714/gfnf.jpg gregschool-lessons - Torque https://www.gregschool.org/gregschoollessons/2017/8/26/work-measure-of-energy-transfer-5kccp-p3dsg monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c4dec212d3e0f5498d2/1507587499632/gfnf.jpg gregschool-lessons - Work: Measure of Energy Transfer https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c4dec212d3e0f5498d0/1504544870969/ff.png gregschool-lessons - Work: Measure of Energy Transfer Figure 1: Work done on a block by a constant force of \(-10\) newtons over a displacement of \(5\) meters. https://www.gregschool.org/gregschoollessons/2017/6/21/the-dependency-of-theta-in-the-dot-product-a6rdd-m5x4z monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c55c830257e2fa3ddaa/1507587268526/gfnf.jpg gregschool-lessons - The Dependency of theta in the dot product https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c55c830257e2fa3dda8/1501801080881/ gregschool-lessons - The Dependency of theta in the dot product https://www.gregschool.org/gregschoollessons/2017/8/26/work-done-by-earths-gravity-nfmxr-wpxmy monthly 0.5 2018-09-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c66419202d77c16ad11/1507587669020/gfnf.jpg gregschool-lessons - Work done by Earth's Gravity https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c66419202d77c16ad0f/1504580902846/vv.png gregschool-lessons - Work done by Earth's Gravity Figure 1: As an object moves along the path \(\vec{R}(t)\) from an initial height of \(y_i\) to a final height of \(y_f\), the Earth's gravitational force \(-m\vec{g}\) does work on the object. https://www.gregschool.org/gregschoollessons/2017/8/27/work-done-by-force-moving-an-object-at-constant-height-dxkzp-m6742 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c6f652dea086dca6e9d/1507587696400/gfnf.jpg gregschool-lessons - Work-Kinetic Energy Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c6f652dea086dca6e9f/1504580497144/wet2.gif gregschool-lessons - Work-Kinetic Energy Theorem Figure 1: "Sunil Kumar Singh, Work - Kinetic Energy Theorem. February 2, 2013." http://cnx.org/content/m14095/latest/OpenStax CNX CC BY 3.0. https://www.gregschool.org/gregschoollessons/2017/5/14/genesis-of-the-elements-xz53h-kphyl monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c91e4966bbdfaf349c0/1509987202844/ gregschool-lessons - Genesis of the Elements Figure 4: As a star undergoes nuclear fusion in its core, it generates light. This light exerts an outward radiation pressure on the star which balances the inward gravitational forces that tend to pull the star's matter towards its center. But at the end of a star's life, nuclear fusion begins to slow down and eventually stop; this means that there is no outward radiation pressure to balance the gravitational forces exerted on the outward layers of the star and star eventually collapses. If the star is very massive, such a collapse will result in one of the most spectacular events in the universe: a supernova. The energy generated by a supernova explosion is so stupendous that it results in nuclear reactions which create the heavier elements in the period table. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c91e4966bbdfaf349ba/1509981827221/RutherfordGoilFoil+%281%29%5B1%5D.jpg gregschool-lessons - Genesis of the Elements Figure 1: Rutherford's experiment involved putting a radioactive element known as radium inside of a lead box. The radium spontaneously emitted \(α\) particles in a narrow beam through a small hole in the box. These \(α\) particles were directed towards a gold foil. Most \(α\) particles passed straight through the gold foil but occasional one would get reflected back at an acute angle with the beam of \(α\) particles. This meant that atoms must have tiny, but very dense, nuclei. Image credit: http://m.teachastronomy.com/astropedia/article/The-Structure-of-the-Atom https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c91e4966bbdfaf349bc/1509983399387/nuclear-fusion-stars%5B1%5D.png gregschool-lessons - Genesis of the Elements Figure 2: All stars in the universe generate light and energy by fusing lighter elements into heavier elements. For stars up to the mass of about that of our Sun, light and energy is created by fusing hydrogen into helium. The image above illustrates the chain of nuclear reactions which occur in small to medium sized stars and very massive stars that allow them to generate light and energy. Stellar fusion accounts for where many of the light to medium-sized elements in the periodic table come from. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c91e4966bbdfaf349be/1509985102690/ gregschool-lessons - Genesis of the Elements Figure 3: The Alpha-Beta-Gamma paper demonstrated that after the first roughly three minutes of the universe since its initial Bang, hydrogen and helium nuclei were synthesized via nuclear fusion. After about three minutes, the universe cooled enough for fusion to stop; but the universe was still so hot that all of the matter comprising the universe was a plasma and plasma's are opaque to radiation. The matter comprising the universe was in a plasma state for the first roughly 300,000 years since the Big Bang; since plasma is opaque to radiation, for the first roughly 300,000 years light could not freely travel throughout the universe without constantly "bumping into stuff (atomic nuclei)." At sometime when the universe was about 300,000 to 400,000 years old, matter cooled enough for electrons to bind to atomic nuclei and for light to freely pass through the universe. Due to the expansion of space, Alpher and Herman estimated that wavelengths of this light should now be stretched into the microwave region. https://www.gregschool.org/gregschoollessons/2017/6/12/snowball-earth-p5pbn monthly 0.5 2019-03-23 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c967da34e17b612ddddc14c/5c967f3824a694bdfd470e9a/1553366841813/cosmos_9035489_001_72dpi.jpg gregschool-lessons - Snowball Earth https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c967fed9140b79a9b3337f3/5c9680d81972fb0001fb6dd3/1553367257073/Facts-2.jpg gregschool-lessons - Snowball Earth https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037c9d53450a0880014c79/1497300036844/ gregschool-lessons - Snowball Earth Picture of Earth 750 million years ago when the supercontinent Rodinia was getting torn apart. (Click to expand.) https://www.gregschool.org/gregschoollessons/2017/5/4/colonizing-the-moon-yl6rd monthly 0.5 2019-02-22 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b98a960575d1ff027c1f3fc/5b98a9634d7a9cbbeab1dda1/1536731624539/Lunar_base_concept_drawing_s78_23252%5B1%5D.jpg gregschool-lessons - Colonizing the Moon - Lunar Mass Driver Artist’s depiction of a lunar mass driver. The physicist Gerard K. O’Neil imagined using this device to electromagnetically launch lunar material into space for the purpose of being using to construct artificial space habitats for human residence and to move most industry off the Earth and into space. Image courtesy of NASA. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b98a8770e2e72043c39e14f/1536731258919/fig0801%5B1%5D.gif gregschool-lessons - Colonizing the Moon https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5a037cb908522944d44c5796/5a037cb908522944d44c579d/1498698373172/.jpg gregschool-lessons - Colonizing the Moon The Smart Things Future Living Report https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5a037cb908522944d44c5796/5a037cb908522944d44c5797/1498698373166/LunarColonyRawlings650.jpg gregschool-lessons - Colonizing the Moon Domed lunar settlement illustration by Pat Rawlings, courtesy NASA. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5a037cb908522944d44c5796/5a037cb908522944d44c579b/1498698373171/landscape-1436809198-1197px-inflatable-habitat-s89-20084.jpg gregschool-lessons - Colonizing the Moon Artist concept of a moon colony via NASA https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5a037cb908522944d44c5796/5a037cb908522944d44c5799/1498698373169/LeapOfFaith.jpg gregschool-lessons - Colonizing the Moon Painting by Pat Rawlings courtesy NASA https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037cb908522944d44c5794/1507664167600/space+travela+nd+colonization+thumbnail.jpg gregschool-lessons - Colonizing the Moon https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b98a88b2b6a28301fa44fb2/1536731281125/fig0802%5B1%5D.gif gregschool-lessons - Colonizing the Moon https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b98a8f4562fa774edff9e54/5b98a8f44d7a9cbbeab1da5c/1536731782111/Oneilcylinder1.jpg gregschool-lessons - Colonizing the Moon O’Neill cylinders https://www.gregschool.org/gregschoollessons/2017/4/27/colonizing-the-asteroids-and-comets-of-our-solar-system-clyl4 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037ccd08522944d44c5d78/1502343637033/ gregschool-lessons - Colonizing the Asteroids and Comets of our Solar System Figure 1 (click to enlarge) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037ccd08522944d44c5d7a/1493345091357/WANDERERS_terrarium_01.jpg gregschool-lessons - Colonizing the Asteroids and Comets of our Solar System Figure 2 - click to enlarge (Source) "This shot shows the inside of the asteroid from the previous scene. Just as I wrote about that scene, this is a highly speculative vision of an impressive piece of human engineering - a concept that science fiction author Kim Stanley Robinson calls a "terraruim" in his novel "2312". It is also not unlike what Arthur C. Clarke described in his novel "Rendezvous with Rama". What we see here is the inside of a hollowed out asteroid, pressurized and filled with a breathable atmosphere. Like I described in the previous scene, the whole structure is put into a revolving rotation, simulating the effect of gravity toward the inside "walls" of the cylinder shape we see. The structure in this scene has a diameter of about 7 kilometers and revolves with a speed of 1 rotation every 2 minutes, simulating the effect of 1g (the gravity pull we feel on Earth) at the surface of the inside. This place is also filled with water, creating lakes and seas wrapped along with the landscape. An artificial sun is running along a rail in the middle of the space, simulating a daylight cycle. This scene is of course built from scratch, but I used countless satellite photos of the Earth to texture the landscape. I actually used a slightly warped world map to create the outlines between land and water, as some may notice a couple of familiar shorelines."\(^{[3]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037ccd08522944d44c5d76/1507664334394/space+travela+nd+colonization+thumbnail.jpg gregschool-lessons - Colonizing the Asteroids and Comets of our Solar System https://www.gregschool.org/gregschoollessons/2017/2/13/introduction-to-einsteins-theory-of-general-relativity-mp9y7 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037cd6652dea086dca87b2/1490733558102/ gregschool-lessons - Introduction to Einstein's Theory of General Relativity https://www.gregschool.org/gregschoollessons/2017/1/23/superconductors-the-future-of-transportation-and-electric-transmission-d5e6r monthly 0.5 2019-03-23 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037cea652dea086dca8c03/1509744550746/email+img+thumbnail.jpg gregschool-lessons - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037cea652dea086dca8bfd/1509744831827/facebook+img+thumbnail.jpg gregschool-lessons - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037cea652dea086dca8bff/1509744812574/twiiter+img+thumbnail.jpg gregschool-lessons - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037cea652dea086dca8c05/1509744531017/technology+thumbnail.png gregschool-lessons - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037cea652dea086dca8c01/1509744847045/ gregschool-lessons - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037cea652dea086dca8bfb/1509744676939/ gregschool-lessons - Superconductors: the Future of Transportation and Electric Transmission https://www.gregschool.org/gregschoollessons/2017/2/17/thermodynamics-and-the-arrow-of-time-zsgz8 monthly 0.5 2017-11-08 https://www.gregschool.org/gregschoollessons/2017/3/27/light-fidelity-li-fi-ultra-fast-wireless-communications-system-49mxf monthly 0.5 2019-03-23 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037cfde2c483e53caeb602/1509744407032/twiiter+img+thumbnail.jpg gregschool-lessons - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037cfde2c483e53caeb60a/1490641020901/ gregschool-lessons - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System Figure 1 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037cfde2c483e53caeb606/1509744154145/email+img+thumbnail.jpg gregschool-lessons - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037cfde2c483e53caeb604/1509744456561/google+img+thumbnail.jpg gregschool-lessons - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037cfde2c483e53caeb600/1509744439536/facebook+img+thumbnail.jpg gregschool-lessons - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037cfde2c483e53caeb5fc/1509744247982/share+technology++img.jpg gregschool-lessons - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037cfde2c483e53caeb608/1509744129041/technology+thumbnail.png gregschool-lessons - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System https://www.gregschool.org/gregschoollessons/2017/3/14/exponential-growth-of-information-technology-1-hkykf monthly 0.5 2017-11-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d138165f535a0979af5/1509744984223/email+img+thumbnail.jpg gregschool-lessons - Exponential Growth of Information Technology https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d138165f535a0979aed/1509745093086/share+technology++img.jpg gregschool-lessons - Exponential Growth of Information Technology https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d138165f535a0979af3/1509745212285/google+img+thumbnail.jpg gregschool-lessons - Exponential Growth of Information Technology https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d138165f535a0979aef/1509745182840/facebook+img+thumbnail.jpg gregschool-lessons - Exponential Growth of Information Technology https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d138165f535a0979af1/1509745198013/twiiter+img+thumbnail.jpg gregschool-lessons - Exponential Growth of Information Technology https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d138165f535a0979af7/1509744969681/technology+thumbnail.png gregschool-lessons - Exponential Growth of Information Technology https://www.gregschool.org/gregschoollessons/2017/5/23/calculating-the-wavefunction-collection-of-probability-amplitudes-associated-with-any-ket-vector-skh4m-ey7ag-jtfne monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d3171c10b64691e0cc8/1507610296214/electromagnetism+thumbnaillllll+imageeee.jpg gregschool-lessons - Calculating the Wavefunction Associated with any Ket Vector https://www.gregschool.org/gregschoollessons/2017/5/15/time-evolution-of-state-vectors-c6g7n-dwall monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d40ec212d3e0f54dc6d/1510107139616/1_Lwu5UJMmcuFVJLZ1Ln4E0Q%5B1%5D.png gregschool-lessons - Schrodinger's Time-Dependent Equation: Time-Evolution of State Vectors Figure 1: The motion of a simple pendulum is an example of the time-reversibility of Newton's second law. Given the initial state of the pendulum, Newton's second law can be used to determine the past or future state of the system. For example, one could determine the velocity and position of the pendulum at any past or future time given its present state. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d40ec212d3e0f54dc6f/1510108488383/photon_double_slit2%5B1%5D.gif gregschool-lessons - Schrodinger's Time-Dependent Equation: Time-Evolution of State Vectors Figure 2: Schrodinger's equation is deterministic because the past or future quantum state \(|\psi(t)⟩\) of a quantum system can be determined with infinite precision. But, in general, a quantum system can be in a superposition of many different states where the measurement of any physical quantity is uncertain. For example, if anything the size of a small molecule or smaller passes through a double-slit in a double-slit experiment, where it hits the screen (which is to say, its final position) is uncertain (see illustration above). The quantum state of a quantum system is deterministic; but the eigenvalue that you'll measure after an experiment is done is the quantity which is not deterministic in quantum mechanics. Source: http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec13.html https://www.gregschool.org/gregschoollessons/2017/6/16/overview-of-calculus-hmtnx-xzysh monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d50e2c483e53caeca88/1497934508324/ gregschool-lessons - Overview of Single-Variable Calculus Figure 2 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d50e2c483e53caeca8e/1497933579348/ gregschool-lessons - Overview of Single-Variable Calculus Figure 5 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d50e2c483e53caeca86/1497934480889/ gregschool-lessons - Overview of Single-Variable Calculus Figure 1 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d50e2c483e53caeca8c/1497933573517/ gregschool-lessons - Overview of Single-Variable Calculus Figure 4 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d50e2c483e53caeca84/1510078784067/Untitled.jpg gregschool-lessons - Overview of Single-Variable Calculus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d50e2c483e53caeca8a/1497931192368/ gregschool-lessons - Overview of Single-Variable Calculus Figure 3 https://www.gregschool.org/gregschoollessons/2017/5/15/periodic-wavefunctions-that-is-ones-that-come-back-to-themselves-have-quantized-eigenvalues-of-momenta-and-angular-momenta-2k3el-hrfk7 monthly 0.5 2017-11-08 https://www.gregschool.org/gregschoollessons/2017/5/23/the-eigenvectors-of-any-hermitian-operator-must-be-orthogonal-w2jps-fm7r7 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d6dc830257e2fa42154/1510110338040/electromagnetism+thumbnaillllll+imageeee.jpg gregschool-lessons - The Eigenvectors of any Hermitian Operator must be Orthogonal https://www.gregschool.org/gregschoollessons/2017/5/27/origin-of-structure-and-clumpyness-dbe4t-snxy5 monthly 0.5 2017-11-11 https://www.gregschool.org/gregschoollessons/2017/5/14/how-initial-states-of-definite-energy-change-with-time-5hyrx-9wkx4 monthly 0.5 2017-11-08 https://www.gregschool.org/gregschoollessons/2017/6/12/crispr-cas9-gene-editing-rz8n7 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d8ce4966bbdfaf38714/1497325314908/ gregschool-lessons - CRISPR-CAS9 Gene Editing Figure 1 Source\(^{[1]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d8ce4966bbdfaf38718/1497325759187/rrr.png gregschool-lessons - CRISPR-CAS9 Gene Editing Figure 3 Source https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d8ce4966bbdfaf38716/1497325436986/ gregschool-lessons - CRISPR-CAS9 Gene Editing Figure 2 Source https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d8ce4966bbdfaf3871a/1497325731797/ gregschool-lessons - CRISPR-CAS9 Gene Editing Figure 4 (click to enlarge) https://www.gregschool.org/gregschoollessons/2017/3/22/p-series-convergence-and-divergence-r69x7 monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d95e2c483e53caedb0e/1490229889184/ gregschool-lessons - P-Series Convergence and Divergence Figure 2 (click to enlarge) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d95e2c483e53caedb0c/1490231132628/ gregschool-lessons - P-Series Convergence and Divergence Figure 1 (click to enlarge) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037d95e2c483e53caedb0a/1507581648482/Untitled.jpg gregschool-lessons - P-Series Convergence and Divergence https://www.gregschool.org/gregschoollessons/2017/9/25/colonizing-and-terraforming-venus monthly 0.5 2018-04-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac95549352f53a44fcd4b06/1523145700558/facebook+thumbnail.jpg gregschool-lessons - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d3eb791f318d2d58af61ee/1523145700569/1.10-1024x768.jpg gregschool-lessons - Colonizing and Terraforming Venus Artist concept of lightning on Venus. Image credit: ESA https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac955750e2e72f4e58b5a70/1523145700562/google+share+thumbnail_preview.jpg gregschool-lessons - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d3e94ecd39c3acbc034421/1523145700570/venus-cloud-city.jpg gregschool-lessons - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac955652b6a289d089b266f/1523145700565/email+thumbnail_preview.jpg gregschool-lessons - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac95554562fa799825bd630/1523145700560/Twitter+thumbnail_preview.jpg gregschool-lessons - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0e3b1ec830258272ef160e/1523145700572/TerraformedVenus%5B1%5D.jpg gregschool-lessons - Colonizing and Terraforming Venus "A conceptual picture I made of Venus if it were terraformed. (Credit: Daein Ballard) Notice the interesting cloud formations and that the planet has polar caps. I decided to show the planet this way after studying Venus' atmosphere. The two Hadley cells the planet has stop at 70 degrees north and south. So the polar regions are cut off from the warm air. Also the slow rotation of the planet causes the clouds to whip around the planet very fast, especially at the equator, to balance out the temperature difference between day and night sides of the planet."\(^{[5]}\) Image credit: Ittiz at the English language Wikipedia [GFDL (http://www.gnu.org/copyleft/fdl.html) or CC-BY-SA-3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac956f2575d1fd39324a769/1523145700556/share+b.jpg gregschool-lessons - Colonizing and Terraforming Venus https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac9553b1ae6cf686ab9a720/1523145700566/space+colon+author+date.jpg gregschool-lessons - Colonizing and Terraforming Venus https://www.gregschool.org/gregschoollessons/2017/9/10/how-to-produce-water-and-oxygen-on-mars monthly 0.5 2018-04-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac957c588251b5348314cf2/1523144855332/Twitter+thumbnail_preview.jpg gregschool-lessons - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0e4a8ff9619ae2895df378/1523144855341/mars3%5B1%5D.jpg gregschool-lessons - How to Produce Water and Oxygen on Mars The rover above is capable of releasing frozen water from regolith by heating it using microwaves. Credit: SUTD/Gilmour Space Corporation https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac957baaa4a998f3f318895/1523144855330/facebook+thumbnail.jpg gregschool-lessons - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac957d46d2a73d3a0cfeaa9/1523144855336/email+thumbnail_preview.jpg gregschool-lessons - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac957ea88251b53483151a0/1523144855334/google+share+thumbnail_preview.jpg gregschool-lessons - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0e549de2c48384bd2b1733/1523144855339/extracting+water+from+Mars%27+regolith.jpg gregschool-lessons - How to Produce Water and Oxygen on Mars "Truck, oven, and slag pile system for extracting water from Martian soil."\(^{[2]}\) Artwork by Michael Carroll. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac957a603ce649b2a21efee/1523144855328/share+b.jpg gregschool-lessons - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac9579188251b534831466e/1523144855337/space+colon+author+date.jpg gregschool-lessons - How to Produce Water and Oxygen on Mars https://www.gregschool.org/gregschoollessons/2017/9/24/introduction-to-double-integrals-1-9ekxy monthly 0.5 2018-04-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac97c64aa4a998f3f360dd8/1523154033161/sharee.png gregschool-lessons - Introduction to Double Integrals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac979d703ce649b2a262570/1523153372892/Calculus+thumbnail.png gregschool-lessons - Introduction to Double Integrals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac97a212b6a289d089fb811/1523153455649/email+thumbnail.jpg gregschool-lessons - Introduction to Double Integrals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac97782aa4a998f3f357921/1509398380899/riemann_boxes_m.jpg gregschool-lessons - Introduction to Double Integrals Figure 1: When we were deriving an expression for the definite integral in terms of the Riemann sum, we first approximated the area underneath \(f(x)\) by summing the areas of many very skinny rectangles as illustrated in (A). To define a double integral in terms of a Riemann sum, we first approximate the volume underneath a surface by summing the volumes of many very skinny columns as depicted in (C). The width and depth of each column is given by \(Δx\) and \(Δy\) and the height of each rectangle is given by the surface \(f(x,y)\) as shown in (B). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac97a598a922dc773a333b2/1523153505711/Twitter+thumbnail.jpg gregschool-lessons - Introduction to Double Integrals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac97a3e70a6adaedb1bc88f/1523153478181/google+share+thumbnail.jpg gregschool-lessons - Introduction to Double Integrals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac979fa0e2e72f4e58fe720/1523153418455/facebook+thumbnail.jpg gregschool-lessons - Introduction to Double Integrals https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac97782aa4a998f3f357923/1507232588323/partial+der.jpg gregschool-lessons - Introduction to Double Integrals Figure 2: The volume underneath the surface \(f(x,y)\) can be approximated by summing the volumes of an \(nm\) number of columns underneath the surface. As these columns become infinitesimally skinny and as the number \(nm\) of them approaches infinity, this sum gives the exact volume underneath the surface \(f(x,y)\). https://www.gregschool.org/gregschoollessons/2017/10/30/gravitational-force-exerted-by-a-sphere monthly 0.5 2018-09-03 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca50c388251b5348496a63/1523209296664/google+share+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca5005562fa79982741607/1523209296666/classical+mechanics+thumbnail.png gregschool-lessons - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca50748a922dc773b6f742/1523209296657/facebook+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca508d562fa79982742ae9/1523209296659/Twitter+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca503cf950b74252052b4b/1523209296655/sharee.png gregschool-lessons - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca50a7352f53a44fe5ac6e/1523209296661/email+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5aca42ec88251b5348475405/1523209296668/sphere+force.png gregschool-lessons - Gravitational Force Exerted by a Sphere Figure 1: A shell can be subdivided into many very skinny rings. Anyone of these rings can be represented by the ring \(QRR_1Q_1\) illustrated above. Image credit\(^{[1]}\). https://www.gregschool.org/gregschoollessons/2017/11/2/gravitational-force-exerted-by-a-rod-zf4pf-np6lw monthly 0.5 2019-02-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb88c56d2a73d3a014005d/1523287944108/facebook+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb88c56d2a73d3a0140061/1523287988805/google+share+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb88c56d2a73d3a0140067/1509666905146/rod.png gregschool-lessons - Gravitational Force Exerted by a Rod Figure 1: A rod of mass \(M\) and a particle of mass \(m\) are separated from each other by a distance of \(d\) along the \(x\)-axis. Each mass element \(dm\) comprising the rod is located at some position \(x\) along the \(x\)-axis and is separated from the particle \(m\) by some amount \(r\). By summing all the gravitational forces \(d\vec{F}_g\) exerted by each mass element \(dm\) comprising the rod, we can find the total gravitational force exerted on \(m\) by the entire rod. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb88c56d2a73d3a0140063/1523287964387/email+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb88c56d2a73d3a014005f/1523288004050/Twitter+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb88c56d2a73d3a014005b/1523288053202/sharee.png gregschool-lessons - Gravitational Force Exerted by a Rod https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5acb88c56d2a73d3a0140065/1523287857170/classical+mechanics+thumbnail.png gregschool-lessons - Gravitational Force Exerted by a Rod https://www.gregschool.org/gregschoollessons/2017/9/30/proof-of-greens-theorem monthly 0.5 2018-09-03 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3455ab0e2e7239ad71b4df/1530163356513/twiiter+img+thumbnail.jpg gregschool-lessons - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d01a96f43b5501b2e62104/1530163356523/429px-Green%27s-theorem-simple-region.svg.png gregschool-lessons - Proof of Green's Theorem Figure 1: The curve \(C=C_1+C_2+C_3+C_4\) is piece-wise smooth. It is "piece-wise" because it is split up into an \(n=4\) number of separate curves with an \(n=4\) number of "edges." It is "smooth" because each individual curve itself is smooth without any sharp edges or cusps. This curve is also positively-oriented because its direction goes counter-clockwise. Image by Cronholm 144. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3454030e2e7239ad717c15/1530163356508/share+calculus+img.png gregschool-lessons - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b345559aa4a993c62182e23/1530163356510/facebook+img+thumbnail.jpg gregschool-lessons - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b34556970a6adf2d7660311/1530163356518/email+img+thumbnail.jpg gregschool-lessons - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3453e70e2e7239ad7177f7/1530163356521/Calculus+thumbnail.png gregschool-lessons - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b3557262b6a28a0366206ba/1530222380477/images.png gregschool-lessons - Proof of Green's Theorem Figure 3: We can break up the curve \(c\) into the two separate curves, \(c_1\) and \(c_2\). This also allows us to break up the function \(x(y)\) into the two separate functions, \(x_1(y)\) and \(x_2(y)\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b34559303ce644e1dd08077/1530163356516/google+img+thumbnail.jpg gregschool-lessons - Proof of Green's Theorem https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b355639575d1f7d68cd861b/1530222142601/images.png gregschool-lessons - Proof of Green's Theorem Figure 2: We can split the curve \(c\) into two separate curves, \(c_1\) and \(c_2\). This also allows us to split the function \(y(x)\) into the two separate functions, \(y_1(x)\) and \(y_2(x)\). https://www.gregschool.org/gregschoollessons/2017/11/14/drakes-equation monthly 0.5 2018-07-19 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff7c4562fa778928bbc13/1532041164233/astronomy+and+cosmology+thumbnail.png gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5a0cacc4e4966b4ad90d9612/5a0cacc49140b7e76cf5e3b3/1532041164240/20131102_cosmos-episode-2-jovian-life-full%5B1%5D.jpg gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way Hunters, Floaters, and Sinkers "This painting speculates about possible forms of life on a Jupiter-like gas giant. Airbrushed water-based acrylic."\(^{[4]}\) Image by Adolf Schaller. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5a0cacc4e4966b4ad90d9612/5a0cad818165f525ba090942/1532041164243/20131102_cosmos-episode-2-hfs-floater-close-up%5B1%5D.jpg gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way A "Floater" from Cosmos, Episode 2 "Part of the larger mural, "Hunters, Floaters, and Sinkers" painted for the series."\(^{[4]}\) Image by Adolf Schaller. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5a0cacc4e4966b4ad90d9612/5a0cae0824a6944522e4ff4d/1532041164245/20131102_cosmos-episode-2-hfs-herd-of-floaters%5B1%5D.jpg gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way A Lazy Herd of Floaters "An updated digital restoration by Adolf Schaller of detail in his original Hunters, Floaters, Sinkers mural which appeared on Cosmos, Episode 2, which speculates about life in the atmosphere of a gas-giant planet."\(^{[4]}\) Image by Adolf Schaller. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5a0cacc4e4966b4ad90d9612/5a0cba949140b72564c34318/1532041164247/20131102_cosmos-episode-2-hfs-a-hunter-close-up%5B1%5D.jpg gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way A Hunter "A speculative hunter animal evolved in the atmosphere of a gas-giant planet. Developed for Cosmos, Episode 2."\(^{[4]}\) Image by Adolf Schaller. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff80103ce6465a2fd5fea/1532041164225/facebook+img+thumbnail.jpg gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0e1c3f24a694cb082c79a2/1532041164252/Habitable-zone%5B1%5D.jpg gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way The habitable zone is a range of orbital distances (between an exoplanet and the star it orbits) where the planet is neither too hot nor too cold. This is also sometimes called the Goldilocks zone. In order for a planet to be truly "Earth-like," it must also have a mass 1-2 times that of the Earth, have an atmosphere, and orbit in a stable elliptical orbit that is not too essentric. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0e06eaf9619adb9189c6ca/1532041164256/Heic0612b_H%5B1%5D.jpg gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way Artist's depiction of an exoplanet crossing our line of sight in front of its home-star. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff8316d2a735162171c29/1532041164227/twiiter+img+thumbnail.jpg gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff8151ae6cfa99e5b20c4/1532041164231/email+img+thumbnail.jpg gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0cabc20d9297328dca11b9/1532041164238/75C0D4ADBC26486DAD4D19D3CBCEB9E1%5B1%5D.jpg gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way "Mr. Spock (Leonard Nimoy), communicating with the Horta through a Vulcan mind meld."\(^{[3]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0dc6d64192020bbec9dded/1532041164264/qiao-chen-ship9-3%5B1%5D.jpg gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way An artist's depiction of the starship proposed by Project Daedalus.\(^{[5]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff822f950b763cde2be1d/1532041164230/ gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4ff7e870a6ad94de39f830/1532041164222/share+astronomy+and+cosmology+img.png gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5a0e1fd4419202f344874dce/5a0e201f24a694cb082d3777/1532041164261/HT-trappist-1-star-surface-3-jt-170221_4x3_992%5B1%5D.jpg gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way Imagine standing on the surface of the exoplanet TRAPPIST-1f. This artist's concept is one interpretation of what it could look like. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5a0e1fd4419202f344874dce/5a0e1fd5f9619ae28956d607/1532041164258/proximasurface%5B1%5D.jpg gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way "This artist’s impression shows a view of the surface of the planet Proxima b orbiting the red dwarf star Proxima Centauri, the closest star to the solar system. The double star Alpha Centauri AB also appears in the image. Proxima b is a little more massive than the Earth and orbits in the habitable zone around Proxima Centauri, where the temperature is suitable for liquid water to exist on its surface."\(^{[1]}\) https://www.nasa.gov/feature/jpl/eso-discovers-earth-size-planet-in-habitable-zone-of-nearest-star Credits: ESO/M. Kornmesser https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b4cf448758d463a3bf9d754/1532041164249/pular+planet.png gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way Artist's depiction of an exoplanet orbiting a pulsar. Due to the pulsar's radiation, the exoplanet glows. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a0e1f27419202f344872e8d/1532041164254/Kepler_spacecraft_artist_render_%28crop%29%5B1%5D.jpg gregschool-lessons - Drake's Equation and Searching for Life in the Milky Way Artist's depiction of the Kepler space telescope. https://www.gregschool.org/gregschoollessons/2017/6/8/early-earth-history-5mbef monthly 0.5 2017-11-08 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037caff9619a0fd0c194f1/1497031483687/ gregschool-lessons - Early Earth History Click to enlarge - (Source\(^{[2]}\)) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037caff9619a0fd0c194f5/1497222105007/ gregschool-lessons - Early Earth History Modern stromatolites in Shark Bay, Western Australia. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a037caff9619a0fd0c194f3/1497030292093/Archean.png gregschool-lessons - Early Earth History Click to enlarge - (Source\(^{[2]}\)) https://www.gregschool.org/gregschoollessons/utopia-life-in-the-year-2100 monthly 0.5 2019-03-22 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c228b0d6d2a7362341e50a2/5c228b0d6d2a7362341e50a7/1544408466566/WANDERERS_verona_rupes_03%5B1%5D.jpg gregschool-lessons - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c228b0d6d2a7362341e50a2/5c228b0d6d2a7362341e50a3/1553278214216/WANDERERS_verona_rupes_01%5B1%5D.jpg gregschool-lessons - Utopia: Life in the Year 2100 “Base jumping off the tallest cliff in the Solar System, located on Uranus' moon Miranda. Uranus itself, along with a few other moons (from the top left to bottom right: Ariel (here on the far side of Uranus), Belinda, Puck and Portia) are seen in the background of the last shot. On Uranus´small moon Miranda lies a monumental cliff wall believed to be the tallest in the Solar System. It is called Verona Rupes. Observations are limited but it is certain that the cliffs rise at least 5 kilometers above the ground below. Maybe even twice as much. This extreme height combined with Miranda´s low gravity (0,018g) would make for a spectacular base-jump. After taking the leap from the top edge you could fall for at least 12 minutes and, with the help of a small rocket to brake your fall toward the bottom, end up landing safely on your feet. Miranda´s close orbit around giant Uranus also makes a magnificent huge cyan ball in the sky. The scene is built mostly in CG, except for the people who are shot live action and composited into the environment, and the foreground cliffs in the first shot which are made from several photos of a place in Norway known as "The Pulpit Rock". For building the landscape I used (amongst others) this satellite photo of Verona Rupes, taken by NASAs Voyager 2 during the flyby of Uranus in 1986. For the color and texture of Uranus I used this photo as reference. Also by Voyager 2, NASA.”\({[4]}\) Source: http://www.erikwernquist.com/wanderers/gallery_verona_rupes.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c228b0d6d2a7362341e50a2/5c228b0d6d2a7362341e50a5/1544408463612/WANDERERS_verona_rupes_02%5B1%5D.jpg gregschool-lessons - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c299a9221c67c14302feca2/1553278760133/2483808_landscape.jpg gregschool-lessons - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c228b0d6d2a7362341e5098/1544156143514/central+dome+super+computer.jpg gregschool-lessons - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c228b0d6d2a7362341e50aa/1544073254525/26166483_911930292319504_5468126342370460385_n%5B1%5D.jpg gregschool-lessons - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c29a899758d46566d036a11/1553278760164/large_-085MyVwIWu7CejYdKdZJ_6R-zaYCURcCPnuQyPhrbA.jpg gregschool-lessons - Utopia: Life in the Year 2100 ”Flipping good ... the Japanese cuisine machine hasn't dropped a pancake yet.”\(^{[3]}\) Image: Huis Ten Bosch/Facebook https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c2998ea70a6adae0b2b46b4/5c2998ea575d1f0c317ebfb5/1553278760127/1*ekxLnZoSewL3p7pVUrMEhQ.jpeg gregschool-lessons - Utopia: Life in the Year 2100 Robert McCall, “The Prologue and the Promise” https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c228b0d6d2a7362341e509a/1546233660364/11908915_472363736276164_3837059669263559235_o%5B1%5D.jpg gregschool-lessons - Utopia: Life in the Year 2100 Image (click to enlarge) of lab-grown meat. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c2d216940ec9ae70fd9b9c0/5c2d216903ce64d68f4b5590/1553278760150/The-Venus-Project-Architecture-1-889x500%5B1%5D.jpg gregschool-lessons - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c2d216940ec9ae70fd9b9c0/5c2d216a4ae2373e5b77f816/1553278760154/The-Venus-Project-Buildings-889x493%5B1%5D.jpg gregschool-lessons - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c2d216940ec9ae70fd9b9c0/5c2d216a4ae2373e5b77f825/1553278760157/The-Venus-Project-Design-889x500%5B1%5D.jpg gregschool-lessons - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c2d216940ec9ae70fd9b9c0/5c2d216c40ec9ae70fd9ba1f/1553278760160/The-Venus-Project-Restaurant-889x544%5B1%5D.jpg gregschool-lessons - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c228b0d6d2a7362341e509c/5c228b0d6d2a7362341e509d/1544408785580/benjamin-parker-fleetovermiranda-render-wip.jpg gregschool-lessons - Utopia: Life in the Year 2100 “Civilians watch a small fleet orbit around Uranus' moon Miranda.” Credit: https://www.artstation.com/artwork/mqZVx9 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c228b0d6d2a7362341e509c/5c228b0d6d2a7362341e509f/1544408724395/benjamin-parker-fleetovermiranda-render-k.jpg gregschool-lessons - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c93285f971a1866cb5cdfe2/1553278760138/Diorama%2C_cavemen_-_National_Museum_of_Mongolian_History%5B1%5D.jpg gregschool-lessons - Utopia: Life in the Year 2100 “A diorama showing Homo erectus, the earliest human species that is known to have controlled fire, from inside the National Museum of Mongolian History in Ulaanbaatar, Mongolia.”\(^{[1]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c932b4041920263332ff208/1553278760142/goddardtsiolkovsky%5B1%5D.jpg gregschool-lessons - Utopia: Life in the Year 2100 Photographs of the two pioneers of rocketry science, Konstantin Tsiolkovsky (left) and Robert Goddard (right). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2ab77d2b6a28bef1af0bf3/1553278760167/42276747_2080497328640659_4459771513339379712_o%5B1%5D.jpg gregschool-lessons - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9520e79140b7f2bbf8d473/1553278760146/Neolithic-revolution-ancient-farmers.jpg gregschool-lessons - Utopia: Life in the Year 2100 The Neolithic Revolution (which began, independently, in multiple different civilization 10 to 12 thousand years ago) occurred when, for the first time, we humans began to domesticate plants and animals. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c952de7104c7bde94c94c4e/1553280493180/13312851_249672685423630_2457750922315756964_n.jpg gregschool-lessons - Utopia: Life in the Year 2100 https://www.gregschool.org/gregschoollessons/orbital-rings-and-planet-building monthly 0.5 2019-06-01 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff647d1/1535610747216/med_venus2.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "Terraformed Venus is surrounded by a Dynamic Orbital Ring, mosty constructed from carbon extracted from its original atmosphere."\(^{[24]}\) Image by Steve Bowers. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64810/5b8b4bd10ebbe8ab9ff64817/1535487396885/alexey+shirokikh.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Designer Planet Artist’s depiction of a designer planet. Artwork by Alexey Shirokikh. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64810/5b8b4bd10ebbe8ab9ff64815/1535487329539/Dreamsphere.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System “A Dreamsphere, a suprastellar shell completely surrounding a brown dwarf in the Stellar Umma region.” Image from Steve Bowers. Image can also be found on Orion’s Arm. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64810/5b8b4bd10ebbe8ab9ff64813/1535352753554/med_suprajupiter.png gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System “A suprajovian ring suspended above the gas giant Mungo.” Image from Steve Bowers. Image can also be found at Orion’s Arm. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64810/5b8b4bd10ebbe8ab9ff64811/1535352742220/Athelan.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System “Athelan, a suprashell erected around the gas giant Uranus in the Old Solar System.” Image from Steve Bowers. Image can also be found on Orion’s Arm. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff64789/1535328074668/405001%5B1%5D.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "The High Frontier: Human Colonies in Space is a 1976 book by Gerard K. O'Neill. It envisions large manned habitats in the Earth-Moon system, especially near stable Lagrangian points. Three designs are proposed: Island one (a modified Bernal sphere), Island two (a Stanford torus), and Island 3, two O'Neill cylinders. These would be constructed using raw materials from the lunar surface launched into space using a mass driver and from near-Earth asteroids. The habitats were to spin for simulated gravity and be illuminated and powered by the sun. Solar power satellites were proposed as a possible industry to support the habitats. The book won the 1977 Phi Beta Kappa Award in Science."\(^{[9]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647fb/5b8b4bd10ebbe8ab9ff647fc/1535354345044/1pAZfg0WDtvCEBWpd997Kr9YV49FlqTHnQMz55sxqPc.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of a Matrioshka brain. Image retrieved from: https://www.reddit.com/r/Futurology/comments/zu399/this_day_will_come_the_matrioshka_brain/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff6481c/5b8b4bd10ebbe8ab9ff6481d/1536720334659/jeremy-jozwik-ia-coljupiter-comp2-raw-jpeg-0214.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Fusion Candles Artist's impression of Fusion Candles which could be used to move Jupiter and its moons across interstellar or even intergalactic space and away from our solar system. Spaceship Jupiter! Artwork by Jeremy Jozwik from Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff64797/1535329695987/the-verge-lightfarm-studios.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64800/5b8b4bd10ebbe8ab9ff64801/1537231651609/jakub-grygier-005-matrioshka-brain-ab.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Matrioshka Brain Artist's impression of a Matrioshka Brain. Artwork by Jakub Grygier who is also a member of the SFIA production team. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647a3/5b8b4bd10ebbe8ab9ff647aa/1535329173143/neil-blevins-megastructures-7-star-lifter-color-sketch.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647a3/5b8b4bd10ebbe8ab9ff647a4/1535329245230/neil-blevins-megastructures-7-star-lifter-3d-sketch.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647a3/5b8b4bd10ebbe8ab9ff647a6/1535329228095/neil-blevins-neil-blevins-megastructures-7-star-lifter-3.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647a3/5b8b4bd10ebbe8ab9ff647a8/1535329080141/neil-blevins-megastructures-7-star-lifter-1-b.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff647bf/1535355718877/med_bronx4.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "The inner and outer static orbital rings around Bronx are linked to a central geostationary ring by carbon nanotube cables. The inner ring is only 265km above the clouds, while the outer ring is 75,600km from the planet's core."\(^{[19]}\) Image from Steve Bowers. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64769/5b8b4bd10ebbe8ab9ff6477a/1535343290369/sergio-botero-tflp-damocles-presentation-freight-cab-web.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64769/5b8b4bd10ebbe8ab9ff64778/1535343288243/sergio-botero-tflp-damocles-presentation-large-cab-dims.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64769/5b8b4bd10ebbe8ab9ff64776/1535343284499/sergio-botero-tflp-damocles-comp-1-v3-web.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64769/5b8b4bd10ebbe8ab9ff64774/1535343280086/sergio-botero-tflp-damocles-comp-5-web.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64769/5b8b4bd10ebbe8ab9ff64770/1535343280153/sergio-botero-tflp-damocles-comp-2-v1-web.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64769/5b8b4bd10ebbe8ab9ff64772/1535343280933/sergio-botero-tflp-damocles-presentation-large-cab-web.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64769/5b8b4bd10ebbe8ab9ff6476c/1535343274958/sergio-botero-tflp-damocles-comp-3-web.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64769/5b8b4bd10ebbe8ab9ff6476a/1535825798962/sergio-botero-tflp-damocles-comp-4-v1-web.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "Damocles is a large space port and elevator hub with stations fixed on [E]arth, located in an enormous, peaceful and very prosperous city, in a not-so-distant future.”\(^{[2]}\) In the year 2117 the most economical way to send people and cargo to outer space is using a space elevator. It’s not the quickest option but a very practical and effective one. Just like other similar Orbitowers placed on the Equator, the Damocles elevator hub provides this service. Space freight elevators are crucial to carry large components of interplanetary and the earlier interstellar vehicles into orbit, so they can be assembled in space instead of being launched by rockets. Autonomous trucks and cars arrive at the base’s ground to take passengers and cargo to the space elevator cabs. Flying vehicles land on the pads. The building itself is headquarters for many logistics companies, there are some offices and a hotel."\(^{[2]}\) Artwork by Sergio Botero at Artstation.\(^{[2]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64769/5b8b4bd10ebbe8ab9ff6476e/1535343276062/sergio-botero-tflp-damocles-presentation-freight-cab-dims.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff647cf/1534192981005/ gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist's depiction of solar panels attached to a space elevator. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff64795/1535327450524/glenn-clovis-spec-sheet-island-3-by-glennclovis-d5jj93n.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist's depiction of a Model 3 O'Neil cylinder which would be capable of supporting millions of a people, a complete biosphere, and all of the Earth's natural habitats. An O'Neil cylinder could also be used as an arc ship (sometimes also called a generation ship) to travel to other stars or galaxies. Image by Glenn Clovis from Artstation.\(^{[11]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647ef/5b8b4bd10ebbe8ab9ff647f0/1535351435005/shell_world_by_johnmalcolm1970.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of atlas towers connecting two separate shells in a shell world. Image credit: https://www.deviantart.com/johnmalcolm1970/art/Shell-World-114062545 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff647ad/1535488475236/3001TheFinalOdyssey%5B1%5D.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "Arthur C. Clarke’s 3001: The Final Odyssey features an orbital ring held aloft by four enormous inhabitable towers (assumed successors to space elevators) at the Equator."\(^{[15]}\) For book summary, see: https://en.wikipedia.org/wiki/3001:_The_Final_Odyssey https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff64767/1535847641084/gggggggggggggggggggggggg.png gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff6478b/5b8b4bd10ebbe8ab9ff64792/1535827428335/Spacecolony3edit.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Interior of an O'Neill cylinder\(^{[10]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff6478b/5b8b4bd10ebbe8ab9ff6478e/1535827424197/Internal_view_of_the_O%27Neill_cylinder.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Solar eclipse inside an O'Neill cylinder\(^{[10]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff6478b/5b8b4bd10ebbe8ab9ff6478c/1535827420148/Spacecolony4.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Interior of an O'Neill cylinder\(^{[10]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff6478b/5b8b4bd10ebbe8ab9ff64790/1535827414502/Spacecolony1.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System O'Neill cylinders\(^{[10]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647b5/5b8b4bd10ebbe8ab9ff647b6/1535355566180/1492030052266.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of an orbital ring. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff647a1/1535609604928/c58d9cac14778ce30b60c5c6d63fee2a.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647e7/5b8b4bd10ebbe8ab9ff647e8/1535356149316/espen-saetervik-rings.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of hoop worlds (also known as ring worlds). These megastructures can be built by building many adjacent orbital rings next to each other, side by side, and laying a surface down over those orbital rings. Image retrieved from https://www.iamag.co/espen-olsen-saetervik/espen-saetervik-rings/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff647b9/1535355196399/Kohlenstoffnanoroehre_Animation.gif gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Animation of a sheet of pure graphene rolled up into a carbon nanotube. Credit: https://commons.wikimedia.org/wiki/File:Kohlenstoffnanoroehre_Animation.gif https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64763/5b8b4bd10ebbe8ab9ff64764/1535427182885/espen-saetervik-rings%5B2%5D.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff647c1/1535309001976/Stanford_Torus_interior+highhd.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist's depiction of the interior of a Stanford torus. Painted by Donald E. Davis. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff647c5/1535309881848/Nikola-Tesla.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Image above portrays Nikola Tesla, the famous inventor who first conceived of the notion of orbital rings in the 1870s shortly after recovering from malaria. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff647ed/1534192981013/cities+dangling+from+shell+world.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "Full cities could hang from the top of the shell that holds in the newly terraformed world's atmosphere."\(^{[27]}\) Image uploaded Oct. 7, 2013. Credit: Ken Roy/Tennessee Valley Interstellar Workshop https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff647e1/1535738151212/Kepler_spacecraft_artist_render_%28crop%29%5B1%5D.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist's conception of the Kepler Space Telescope. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647f3/5b8b4bd10ebbe8ab9ff647f8/1535351231677/ringworld.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Larry Niven's Ringworld. Image credit: https://bargainbin4u.wordpress.com/2008/07/14/ringworld-by-larry-niven/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647f3/5b8b4bd10ebbe8ab9ff647f6/1535350325687/ringworld_engineers_by_tomislavtikulin-db0bei8.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of a ring world. Image credit: https://www.deviantart.com/tomislavtikulin/art/Ringworld-Engineers-665659952 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647f3/5b8b4bd10ebbe8ab9ff647f4/1535350338882/halcyon_days_by_julian_faylona-d70cz32.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of a ring world. Image credit: https://www.deviantart.com/julian-faylona/art/Halcyon-Days-423868574 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff647eb/1534192981008/shell+world.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "An engineer suggests building a roof over a small planet so that Earthlike conditions could be maintained."\(^{[26]}\) The Shell World could be used to maintain Earth-like conditions on the surface of an alien planet or moon; hanging cities could be suspended from the interior wall of the shell world; or the outer-surface of the Shell World could be engineered to closely resemble the Earth. Some combination of all of the above could be possible, albeit only to a certain extent. Credit: by Karl Tate, Infographics Artist https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647c7/5b8b4bd10ebbe8ab9ff647c8/1535355930567/4304_1105960212_large_tiff.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647bb/5b8b4bd10ebbe8ab9ff647bc/1535827690138/earthring_1024.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of an orbital ring which appeared in Issue 7 of the magazine, All About Space. Image by Adrian Mann.\(^{[18]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff64781/1535354657587/ gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Public Area "The public area would be assembled into a complex structure in the form of a truncated octahedron. It would have a great room consisting of a lobby, restaurant, entertainment room, and other spaces where people could enjoy a dining experience, sports, and a variety of amusements under low-gravity conditions."\(^{[4}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff6477f/1535354651593/ gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Guest Room Module "A module with 104 individual rooms, including 64 guest rooms, would be arranged on a ring that is 140 meters in diameter. The ring would generate an artificial gravity field of 0.7 G by rotating around three times per minute, so people could relax almost in the same manner as on earth."\(^{[4]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff6477d/1535354571685/img_index_01.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System "Since ancient times, people have always dreamed of going to space. Only astronauts have been able to go until now, but progress has been made on efforts to enable even private citizens to experience space, and space travel is finally about to become an industry. Shimizu foresaw the era of space travel early on, and has proposed a space hotel concept."\(^{[4]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff6479d/1535568397254/13220830_239617033095862_8671672187626094751_n%5B1%5D.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64822/5b8b4bd10ebbe8ab9ff64825/1535827901771/hades__star___warp_lane_hub_by_gabriel_bs-db8y989.png gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System “Two hubs that can connect to create a temporary Warp Lane in your system The Warp Lane Hub can be connected to another Hub for one day, for a fixed Hydrogen cost. Once connected, ships can travel between the two end points instantly and without consuming Hydrogen.”\(^{[31]}\) Image credit: https://www.deviantart.com/gabrielbstiernstrom/art/Hades-Star-Warp-Lane-Hub-680163129 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64822/5b8b4bd10ebbe8ab9ff64823/1535827892994/gateway_hub_04_by_lorddoomhammer-d9u3226.png gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s scifi depiction of a galactic empire using portals to travel across space.\(^{[30]}\) Image credit: https://www.deviantart.com/lorddoomhammer/art/Galactic-Network-594726702 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64799/5b8b4bd10ebbe8ab9ff6479a/1535827448497/space-colony-ix.png gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist’s depiction of an O’Neil cylinder. Artwork by Bruno Xavier.\(^{[12]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647cb/5b8b4bd10ebbe8ab9ff647cc/1537231595568/SpaceX+crew+Big+Falcon+Rocket+%28BFR%29+launching+from+Earth.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Anywhere in the World in Under an Hour Elon Musk proposed using BFR rockets (see image above) as a planetary transportation system which could get you anywhere in the world in under one hour. Image courtesy of Space X. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647af/5b8b4bd10ebbe8ab9ff647b0/1535864456094/Lunar_base_concept_drawing_s78_23252%5B1%5D.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Lunar Mass Driver Artist’s depiction of a lunar mass driver. The physicist Gerard K. O’Neil imagined using this device to electromagnetically launch lunar material into space for the purpose of being using to construct artificial space habitats for human residence and to move most industry off the Earth and into space. Image courtesy of NASA. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647af/5b8b4bd10ebbe8ab9ff647b2/1535919854915/moon+mass+drive-finished-jayproductspainting%5B1%5D.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Lunar Mass Driver Artist’s depiction of a Lunar mass driver. Artwork by Jay Wong. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647d3/5b8b4bd10ebbe8ab9ff647d6/1535505607498/1016944456%5B1%5D.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647d3/5b8b4bd10ebbe8ab9ff647da/1535505936223/3N0rREtorxM8g6vSXCRG_Shimizu5%5B1%5D.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647d3/5b8b4bd10ebbe8ab9ff647d4/1535505602288/EeJcpqLjdfReW4kJ22xE_Shimizu3%5B1%5D.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647d3/5b8b4bd10ebbe8ab9ff647d8/1535505613347/P8_centre_shaft_sh_3115154k.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647d3/5b8b4bd10ebbe8ab9ff647de/1535505977487/A2ljC-Qaok-kAJvzyNWu_Shimizu2%5B1%5D.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System The concept of the Ocean Spiral was first unveiled by Shimizu Corporation, in conjunction with Tokyo University and Japan Agency for Marine-Earth Science and Technology, in 2014. The company excepts it to take 5 years to build an Ocean Spiral. The company expects the project to cost ¥3 trillion (approximately £20 billion). The company claims it could be ready for human habitation by 2030. Learn more by reading the article, Ocean Spiral is a conceptual city proposed beneath the surface of the ocean. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff647d3/5b8b4bd10ebbe8ab9ff647dc/1535505946498/tP0RZDSgdsNPw8Z245OD_Shimizu7%5B1%5D.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff6479f/1535609875282/final-frontier.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Final Frontier Voyager (2007), George Grie. Óleo sobre lienzo.\(^{[13]}\)Credit: https://commons.wikimedia.org/wiki/File:Final-Frontier.jpg https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff6481a/1535415737889/677_gas_interiors%5B1%5D.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Illustration showing the rocky, icy, metallic cores of the four Jovian planets. Credit: NASA/Lunar and Planetary Institute Retrieved from: https://solarsystem.nasa.gov/resources/677/gas-giant-interiors-2003/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff64820/1535500914749/main-qimg-c723f245065082e7f3de09cd458d893e%5B1%5D.png gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System The infographic above shows the differences between a Type I (or K1), a Type II (or K2), and a Type III (or K3) civilization. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff647c3/1535309406755/bigggstandfordtoruss.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Cut-away view of the interior of a Standford Torus. Image courtesy of NASA Ames Research Center. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64783/5b8b4bd10ebbe8ab9ff64784/1535827236841/space-elevator%5B1%5D.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Space Elevator Depiction of a space elevator. Artwork by Glenn Clovis at Artstation.\(^{[6]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64783/5b8b4bd10ebbe8ab9ff64786/1535827243822/seattle_space_elevator_observatory_by_alterbr33d-d5j8j2p-750x375%402x%5B1%5D.png gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System - Copy of Space Elevator Depiction of a space elevator.\(^{[7]}\) Artwork retrieved from: http://prospective-tourisme.com/index.php/2017/08/10/entretien-laurent-queige-directeur-welcome-city-lab/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b8b4bd10ebbe8ab9ff647e3/1535611314042/Oceanplanet_lucianomendez.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artist's illustration of a hypothetical ocean planet with two natural satellites. Image credit: https://commons.wikimedia.org/wiki/File:Oceanplanet_lucianomendez.JPG https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64808/5b8b4bd10ebbe8ab9ff6480b/1535487143670/neil-blevins-megastructures-9-gas-giant-refinery-color-sketch.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64808/5b8b4bd10ebbe8ab9ff6480d/1535923719046/jeremy-jozwik-ia-neptune-comp2-0000.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System Artists depictions of gas giant refineries on two different gas giant planets. The gas giants depicted in these images are suspended by large blimps which hold a lifting gas. But it would also be possible, as we discuss in this article, to attach those gas giant refineries to the ceiling of a shell world or orbital ring. Artwork by Neil Blevins (top) and Jeremy Jozwik (bottom) at Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b8b4bd10ebbe8ab9ff64808/5b8b4bd10ebbe8ab9ff64809/1535351657862/neil-blevins-megastructures-9-gas-giant-refinery-design-packet.jpg gregschool-lessons - Orbital Rings and Planet Building: Prelude to Colonizing the Solar System https://www.gregschool.org/gregschoollessons/2017/10/30/gravitational-force-exerted-by-a-sphere-rdyjt-dcss2 monthly 0.5 2018-09-14 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9c0ca1758d46af9e69fa29/1523208363916/email+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9c0ca1758d46af9e69fa25/1523208313862/facebook+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9c0ca1758d46af9e69fa2d/1523208206453/classical+mechanics+thumbnail.png gregschool-lessons - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9c0ca1758d46af9e69fa2f/1523204866420/sphere+force.png gregschool-lessons - Gravitational Force Exerted by a Sphere Figure 1: A shell can be subdivided into many very skinny rings. Anyone of these rings can be represented by the ring \(QRR_1Q_1\) illustrated above. Image credit\(^{[1]}\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9c0ca1758d46af9e69fa27/1523208340227/Twitter+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9c0ca1758d46af9e69fa2b/1523208400289/google+share+thumbnail.jpg gregschool-lessons - Gravitational Force Exerted by a Sphere https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9c0ca1758d46af9e69fa23/1523217470590/sharee.png gregschool-lessons - Gravitational Force Exerted by a Sphere https://www.gregschool.org/gregschoollessons/technological-revolutions monthly 0.5 2019-03-23 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2e90b1cd8366ce524fb483/1553287768070/ gregschool-lessons - Technological Revolutions “Smithsonian scientists and their Chinese colleagues found this and other handaxes in the same sediment layer with tektites, small rocks that formed during a meteor impact 803,000 years ago. Since the handaxes and tektites were in the same layer, both are the same age. Early humans must have moved into the area right after the impact. They may have made the handaxes from rocks that were exposed when forests burned.”\(^{[1]}\) Image Credit: James Di Loreto, & Donald H. Hurlbert, Smithsonian Institution https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2fc9862b6a28ff22bd5c66/1553287768116/Meissner_effect_p1390048%5B1%5D.jpg gregschool-lessons - Technological Revolutions “A magnet levitating above a high-temperature superconductor, cooled with liquid nitrogen. Persistent electric current flows on the surface of the superconductor, acting to exclude the magnetic field of the magnet (Faraday's law of induction). This current effectively forms an electromagnet that repels the magnet.” Image source: https://en.wikipedia.org/wiki/Superconductivity#/media/File:Meissner_effect_p1390048.jpg https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2fba140e2e72f08ab291af/1553287768105/Newcomens_Dampfmaschine_aus_Meyers_1890%5B1%5D.png gregschool-lessons - Technological Revolutions “Newcomen's steam-powered atmospheric engine was the first practical piston steam engine. Subsequent steam engines were to power the Industrial Revolution.”\(^{[7]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c2fa74888251b069d1ca774/5c2fa748758d46fb365b0a9e/1553287768088/392448062_orig%5B1%5D.jpg gregschool-lessons - Technological Revolutions Artist’s depiction of nanobots patroling the human bloodstream. Image retrieved from: https://www.cnet.com/news/nanobots-can-now-swarm-like-fish-to-perform-complex-medical-tasks/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954d8a9b747a5c37086ff1/5c954e0a71c10b6eca224078/1553288732301/nanotechn.jpg gregschool-lessons - Technological Revolutions Image source : Google https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2d25e688251be3e0ed5117/1553287768119/stock-photo-concept-of-magnetic-levitation-train-moving-on-the-sky-way-in-vacuum-tunnel-across-the-city-modern-755107045%5B1%5D.jpg gregschool-lessons - Technological Revolutions The image above portrays how large buildings (which could be arcologies that people live in) could be connected by maglev trains operating within evacuated tunnels. Image Credit: https://www.shutterstock.com/image-illustration/concept-magnetic-levitation-train-moving-on-755107045 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2fb3ad70a6adad0a563e6a/1553287768096/ gregschool-lessons - Technological Revolutions “The Principia states Newton's laws of motion, forming the foundation of classical mechanics; Newton's law of universal gravitation; and a derivation of Kepler's laws of planetary motion (which Kepler first obtained empirically). The Principia is considered one of the most important works in the history of science.”\(^{[5]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2fb74fc2241b2a8d20d99d/1553287768103/Joule%27s_Apparatus_%28Harper%27s_Scan%29%5B1%5D.png gregschool-lessons - Technological Revolutions “Engraving of James Joule's apparatus for measuring the mechanical equivalent of heat, in which altitude potential energy from the weight on the right is converted into heat at the left, through stirring of water.”\(^{[7]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2faeb4758d463079f878eb/1553287768093/shopping%5B2%5D.jpg gregschool-lessons - Technological Revolutions In the book, Life 3.0, the cosmologist and AI researcher Max Tegmark explores the implications of AI and robotics. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2fb5104ae2370b648878aa/1553287768099/Newtons_laws_in_latin%5B1%5D.jpg gregschool-lessons - Technological Revolutions “Newton's First and Second laws, in Latin, from the original 1687 Principia Mathematica”\(^{[6]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2e93d9032be47ea48ca0fc/1553287768076/Life-expectancy-GDP-capita.png gregschool-lessons - Technological Revolutions This graph illustrates the increase in standards of living and life expectancy that occurred during the time of the first two industrial revolutions.\(^{[3]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c2fbb690e2e72f08ab2aba3/5c2fbb6c2b6a28c2e447c3a4/1553287768109/Bane-Boon-1280x640%5B1%5D.jpg gregschool-lessons - Technological Revolutions Image retrieved from: https://iconshots.com/concept/the-future-of-technology-should-we-be-worried/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2e963d21c67c6b2564ed53/1553287768079/Ending_Aging%5B1%5D.jpg gregschool-lessons - Technological Revolutions Credit: https://en.wikipedia.org/wiki/File:Ending_Aging.jpg https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2e8a740ebbe8aa628a113f/1553287768125/stock-photo-the-train-moving-on-the-overpass-and-the-city-on-the-water-concept-of-modern-transport-futuristic-769589683%5B1%5D.jpg gregschool-lessons - Technological Revolutions Arcologies on the surface of the sea could be connected by maglev transportation systems. As we discuss in the article, How to Colonize the Earth?, these sea-steading towers would extend within the depths of the oceans; the cities underneath the sea surface could also be connected by maglev monorail systems. Image Credit: https://www.shutterstock.com/image-illustration/train-moving-on-overpass-city-water-769589683?src=l4eCjvmchovnXUJuJH_WrQ-1-29 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2d2531c2241b63e32537dd/1553287768122/furureofcities1%5B1%5D.jpg gregschool-lessons - Technological Revolutions https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c2fa5480e2e728e6b090183/5c2fa549cd8366903646c7f0/1553287768082/Artificial-Intelligence-2%5B1%5D.jpg gregschool-lessons - Technological Revolutions https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2fa63b0ebbe85c974e933b/1553287768085/Moore%27s_Law_Transistor_Count_1971-2016%5B1%5D.png gregschool-lessons - Technological Revolutions A plot of CPU transistor counts against dates of introduction. Source URL: https://commons.wikimedia.org/wiki/File:Moore%27s_Law_Transistor_Count_1971-2016.png https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2e92944ae23708582cc0a0/1553287768074/Maler_der_Grabkammer_des_Sennudem_001.jpg gregschool-lessons - Technological Revolutions “Ploughing with a yoke of horned cattle in Ancient Egypt. Painting from the burial chamber of Sennedjem, c. 1200 BC.”\(^{[2]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2fc6fe032be405050dfba3/1553287768113/superconductors.png gregschool-lessons - Technological Revolutions The following graph reflects the empirical fact that as time has progressed, we have achieved superconductivity at higher and higher temperatures. Credit: Pia Jensen Ray https://www.gregschool.org/gregschoollessons/spaceship-comets-and-highways-through-space monthly 0.5 2019-02-28 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9b4258032be4e77bce6e5a/1551045244884/yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy.png gregschool-lessons - Spaceship Comets and Highways Through Space “Each of the hexagons in this figure represents one of the mirror farms shown in [previous image]. The dots are schematic representations of the habitats occupied by each twent-five-member “band.” in reality the habitats would probably be much too small to be seen on this scale.”\(^{[37]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9a8f792b6a288509fa8086/5b9a8f7b88251b25f1c0c4f2/1551045244790/alphacentfix2%5B1%5Dkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk.jpg gregschool-lessons - Spaceship Comets and Highways Through Space - Trip to Alpha Centauri using a Starshot Probe SCMP Graphic: Dennis Wong, Dang Elland Sources: Universe Today, SIMBAD Dacabase, SCMP research https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9b2f652b6a28b42974812f/1551045244858/jhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh.jpg gregschool-lessons - Spaceship Comets and Highways Through Space “This artist's concept puts solar system distances in perspective. The scale bar is in astronomical units, with each set distance beyond 1 AU representing 10 times the previous distance. One AU is the distance from the Sun to the Earth, which is about 93 million miles or 150 million kilometers. Neptune, the most distant planet from the Sun, is about 30 AU.”\(^{[4]}\) Image Credit: NASA/JPL-Caltech https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9c89e9758d46cdbe67d11b/1551045244754/41WSCf9QqtL._SX333_BO1%2C204%2C203%2C200_.jpg gregschool-lessons - Spaceship Comets and Highways Through Space Robert Zubrin’s book, Entering Space, covers topics ranging from colonizing Mars and the solar system and explores the feasibility of interstellar travel with known physics.\(^{[1]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9994110e2e7257287e7252/5b9994110e2e7257287e7253/1536859707540/Asteroid+Mining+Station+by+Bas+Ruhe%5B1%5D.jpg gregschool-lessons - Spaceship Comets and Highways Through Space - Asteroid Mining Station Artist’s depicion of a colonized asteroid. Artwork by Bas Ruhe from Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9a8559352f53b5e0113094/5b9a855b70a6adaccf7d3f62/1551045244775/Untitled.png gregschool-lessons - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9a8559352f53b5e0113094/5b9a855b21c67caa96292535/1551045244773/lunaring.png gregschool-lessons - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9a8559352f53b5e0113094/5b9a85596d2a73dd96de8b17/1551045244762/lunar-ring_2748879k.jpg gregschool-lessons - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2c35e81ae6cf9b886471f4/1551045244820/swe12_10836_coverbackgroundshadowport_mattbradbury%5B1%5D.jpg gregschool-lessons - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9a85398985830bc3e99661/5b9a853af950b779d561617c/1551045244757/lunar-mining-base.jpg gregschool-lessons - Spaceship Comets and Highways Through Space The power requirements of buried human habitats and propellant production plants could be met by the widely spaced solar power panels shown above. Image: anna.j.nesterova@gmail.com https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9b2b8eaa4a99c088e81d4f/5b9b2b8f03ce645245ef8963/1551045244800/Superlaser2.jpg gregschool-lessons - Spaceship Comets and Highways Through Space - Death Star Artist’s depiction of a death star. By building a shell world of the kind described by the scientist Paul Birch around a faint dead star (i.e. a brown dwarf), the faint radiation which that star gives off could be collected and used to power a gigantic laser mounted on the surface of a shell world. Thus, as far fetched as the idea might seem, it isn’t totally implausable. Image retrieved from: Artist’s depiction of a comet being used as a spaceship. Image retrieved from: http://earth-chronicles.ru/news/2014-04-21-63940 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5bb53c1df9619a42ac84d81f/5bb53c1eeef1a13f1f49c5c4/1551045244887/1_hHjG69bPm3VrMyUG2idPKg.jpeg gregschool-lessons - Spaceship Comets and Highways Through Space “Conceptual model of a growing and evolving asteroid starship. The image of comet 67P by ESA is used as a placeholder for a large asteroid.”\(^{[6]}\) Composite image by Francisco Muñoz and Anton Dobrevski https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9a86ce1ae6cfe40ee3b274/5b9a86cecd836605b06731ac/1551045244781/790097132176630087%5B2%5D.jpg gregschool-lessons - Spaceship Comets and Highways Through Space - Spaceship Asteroid “The concept of turning an asteroid into a spacecraft is not entirely new: conceptual designer Bryan Versteeg has been working with the Mars One Team to imagine how we could use large asteroids for mining, transportation and habitat.”\(^{[2]}\) Credit: http://www.spacehabs.com/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9a9578f950b779d5623c32/1551045244797/alphacentfix2%5B1%5Dkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk.jpg gregschool-lessons - Spaceship Comets and Highways Through Space Image Source: https://i4is.org/wp-content/uploads/2018/05/Principium21.pdf https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9c6ca3b8a0455bce242a7f/1551045244878/pale+blue+dottttttttttttttttttttttttttttttttttttttttttttttttttt.jpg gregschool-lessons - Spaceship Comets and Highways Through Space In Carl Sagan’s book, Pale Blue Dot, he talked about the possibility of interstellar human communities living in comets in the Kuiper belt, the Oort cloud, and beyond. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9a9ef26d2a73dd96dfe486/5b9a9ef288251b25f1c197c9/1551045244815/evolvingaste%5B1%5D.jpg gregschool-lessons - Spaceship Comets and Highways Through Space Credit: Nils Faber & Angelo Vermeulen https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5bb65ce91905f417c5811af6/1551045244892/1449-enz.jpg gregschool-lessons - Spaceship Comets and Highways Through Space The map above shows the migration patterns and timeline of the Polynesians who traveled from Asia to America by hopping from one tiny archipelago to another. Our descendants who travel from the Earth to the exoplanet Proxima B might adopt an analogous strategy by hopping from one comet to another until they reach their final destination. Image retrieved from: https://teara.govt.nz/en/map/1449/map-of-pacific-migrations https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9d626421c67c45060ca19c/1551045244861/energy-from-space-1.jpg gregschool-lessons - Spaceship Comets and Highways Through Space Using a nuclear reactor to fuse together deuterium and helium-3 would generate a lot of energy; that energy would be transferred to a shock absorber on the rear of a spaceship which would give the spaceship thrust thereby causing it to accelerate. Image retrieved from: https://science.howstuffworks.com/environmental/green-science/energy-from-space.htm https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7308e8eb39313412dcb4c5/5c7308eb6e9a7f1fd2a3f354/1551045244748/space-travel-1200x675%5B1%5D.jpg gregschool-lessons - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5ba077b6f950b71d81b7855b/5be8c0681ae6cfbdd7a9234d/1551045244856/ksr-04.png gregschool-lessons - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5ba077b6f950b71d81b7855b/5ba077e770a6ad5a1e8f2b1e/1551045244851/kkkk.png gregschool-lessons - Spaceship Comets and Highways Through Space Infographics represent a visual explanation of the so-called terrariums discussed in Kim Stanley Robinsons, 2312. Also, there is a slight error in the last infographic: the asteroid does not spin, rather a cylinder inside of the hollowed out asteroid is the thing which is actually spinning. Infographics created by Pablo Defendini. Infographics retrieved from: http://www.defendini.com/2312.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5ba077b6f950b71d81b7855b/5ba077beaa4a994c4158ebe1/1551045244837/livinginasteroidd.png gregschool-lessons - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5ba077b6f950b71d81b7855b/5ba077bb758d46f894b6d80d/1551045244843/hhhhh.png gregschool-lessons - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9994110e2e7257287e7256/1537145174696/9780553373356-uk%5B1%5D.jpg gregschool-lessons - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9b36efc2241bee33f749ab/5b9b36f0f950b7a67a389b6c/1551045244865/liian1htqo3l6hvx4kkj%5B1%5D.jpg gregschool-lessons - Spaceship Comets and Highways Through Space Concept art for DSI's "Harvestor" craft. Credit and Copyright: Bryan Versteeg / DSI. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9b36efc2241bee33f749ab/5b9b36f021c67c95e70f2a44/1551045244874/jhm27etrwqj7fgpuxvuj%5B1%5D.jpg gregschool-lessons - Spaceship Comets and Highways Through Space Asteroid settlement concept. Credit and Copyright: Bryan Versteeg / DSI. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9994110e2e7257287e7241/5b9994110e2e7257287e7242/1537229057732/maxresdefault.jpg gregschool-lessons - Spaceship Comets and Highways Through Space - Starshot Probe Depiction of a Starshot probe being accellerated by Earth-based lasers. Credit: Breakthrough Starshot https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9aa6a103ce64cdc8584059/5b9aa6a28985830bc3eb66fd/1551045244809/d00fccc571b621e809cb4ef1b9b98ee7_full.jpg gregschool-lessons - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9994110e2e7257287e7258/5b9994110e2e7257287e725b/1536987150213/MarsAndTheSpaceElevator%5B1%5D.jpg gregschool-lessons - Spaceship Comets and Highways Through Space “Here is a new montage showing the base of the space elevator on the tented town called "Sheffield", built on the summit of Pavonis Mons volcano (see Red Mars). The cable is supposed to be 10m thick, which means here that Sheffield city is very big here, at a large level of development. On the foreground, you can see colored urban lights. I imagine the main entry to the planet's surface would be like a rich and welcoming show for new settlers. I also imagine the tent' skin would be blue, to balance the red and grey landscape.”\(^{[59]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9994110e2e7257287e7258/5b9994110e2e7257287e7259/1537230346111/SheffieldAndTheSpaceElevator%5B1%5D.jpg gregschool-lessons - Spaceship Comets and Highways Through Space Artist’s impression of a space elevator connecting to the domed over city, Sheifeild, located on Pvonic Mons in Kim Robinson’s Mars trilogy. Images retrieved from: http://davinci-marsdesign.blogspot.com/2012/04/sheffield-and-space-elevator.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9a85b00ebbe8e940a26378/1551045244778/ephemeralizationnnnnn.jpg gregschool-lessons - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9b2dfa8a922db50d250061/5b9b2dfac2241bee33f6fa1b/1551045244826/colony19%5B1%5D.jpg gregschool-lessons - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9994110e2e7257287e7262/5b9994110e2e7257287e7263/1536717071163/jeremy-jozwik-ia-kuiperbeltterrain-comp2-0084.jpg gregschool-lessons - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9b3f2a4fa51ab31e474767/1551045244881/hexagonal+array.png gregschool-lessons - Spaceship Comets and Highways Through Space “This hexagonal array of starlight mirrors might support a co-living group of twenty-five adults and children. Each of the mirrors is about the size of the continental United States, and the entire mirror “farm” is about 30,000 kilometers across.”\(^{[37]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9994110e2e7257287e723f/1536288589788/Skylab-73-HC-440HR%5B1%5D.jpg gregschool-lessons - Spaceship Comets and Highways Through Space Image of the Saturn V rocket launching to space. Image courtesy of NASA. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9994110e2e7257287e7245/5b9994110e2e7257287e7246/1536889609120/jakub-grygier-026-interstellar-travel-ad.jpg gregschool-lessons - Spaceship Comets and Highways Through Space - Interstellar Spaceship Artist’s depiction of an interstellar spaceship accellerated by laser beams. Artwork by Jakub Grygier from Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ba307c78a922d016ed60bc8/1551045244786/alphacentfix2%5B1%5D.jpg gregschool-lessons - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5bb65e1b9140b778c67d3963/1551045244895/photosynthesis-process-2.jpg gregschool-lessons - Spaceship Comets and Highways Through Space The infographic above shows how plants, via the process of photosynethesis, use light (sunlight or artificial light), carbon dioxide and water to produce breathable oxygen. https://www.gregschool.org/gregschoollessons/2018/5/23/preliminary-interstellar-missions-prelude-to-the-stars monthly 0.5 2019-02-24 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b99a05b6d2a73dd96d65225/1549254809125/mars_hs-2016-15-a-full_tif%5B1%5D.jpg gregschool-lessons - Preliminary Interstellar Missions: Prelude to the Stars “This Hubble Space Telescope image of Mars shows details 20 to 30 miles across. A solar gravitational lens telescope would get even sharper views of exoplanets up to 100 light years away.”\(^{[4]}\) (STScI/AURA), J. Bell (ASU), and M. Wolff) Source URL: https://www.airspacemag.com/daily-planet/ultimate-space-telescope-would-use-sun-lens-180962499/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2c135a40ec9ab2ea4478e5/1549254809129/NASA-WhatBiosignaturesDoesLifeProduce-20180625%5B1%5D.jpg gregschool-lessons - Preliminary Interstellar Missions: Prelude to the Stars The combination of certain molecules and the absence of certain molecules in an exoplanet’s atmosphere is only likely if life is inhabited on that world: such combinations are called disequilibrium mixtures. As the light emitted from a star passes through an exoplanet’s atmosphere, the molecules in that exoplanet’s atmosphere absorb only certain wavelengths. Given which wavelengths were absorbed, we can determine whether or not disequilibrium mixtures are present in that exoplanet’s atmosphere and, consequently, assess the likelihood that extraterrestrial life inhabits that world. NASA/Aaron Gronsta https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ba1d2840e2e7243afb3dd5a/1549254809133/Great+Oxidization+Event.jpg gregschool-lessons - Preliminary Interstellar Missions: Prelude to the Stars Diagram of the evolution of atmospheric oxygen concentration during the history of the planet. © Ido, Pierre Sans-Jofre https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2aabb270a6adae0b34a7d6/1549254809137/Welcome_to_the_Universe_by_Neil_deGrasse_Tyson%3B_book_cover.jpg gregschool-lessons - Preliminary Interstellar Missions: Prelude to the Stars Welcome to the Universe: An Astrophysical Tour is a popular science book by Neil deGrasse Tyson, Michael A. Strauss, and J. Richard Gott, based on an introductory astrophysics course they co-taught at Princeton University. The book was published by the Princeton University Press on September 20, 2016.\(^{[6]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9999c38985830bc3e13e16/1536791569946/3E58320900000578-0-image-a-2_1489702334064%5B1%5D.jpg gregschool-lessons - Preliminary Interstellar Missions: Prelude to the Stars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5ba46a530d9297e050b0b8cc/5ba46a53f4e1fcbe9171f5b1/1549254809127/1280px-Artist%27s_impression_of_the_planet_Ross_128_b%5B1%5D.jpg gregschool-lessons - Preliminary Interstellar Missions: Prelude to the Stars Artist's impression of the planet Ross 128 b, with the star Ross 128 visible in the background\(^{[1]}\) Credit: European Southern Observatory https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b9b4509b8a045be53c6dc77/1549254809143/microwave-sail-starwisp-n.jpg gregschool-lessons - Preliminary Interstellar Missions: Prelude to the Stars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ba2df660ebbe8e7950982fd/1549254809135/50lys%5B1%5D.gif gregschool-lessons - Preliminary Interstellar Missions: Prelude to the Stars The image above is a map of a small fraction of nearby stars in our stellar neighborhood. It is a map of 130 stars located within 50 lightyears of us which are visible with the naked eye. This map shows only a tiny percent of that stars within 50 lightyears away from the Sun. There are in fact 1,800 known stars within this volume of space. To eliminate the threat of nearby supernovae, our descendants will one day visit all of these stars, either directly in which case their species actually arrives at the star, or indirectly by sending spacecraft and robots to those stars. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2ab1408a922d1c5eac7c06/1549254809139/013532_med%5B1%5D.jpg gregschool-lessons - Preliminary Interstellar Missions: Prelude to the Stars Illustration of the James Webb Space Telescope, current as of September 2009. Top side. Image Source: https://web.archive.org/web/20100527230418/http://www.jwst.nasa.gov/images_artist13532.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ba3e12d4785d325a53ca4b9/1549254809131/Stromatolites_in_Sharkbay%5B1%5D.jpg gregschool-lessons - Preliminary Interstellar Missions: Prelude to the Stars The stromatolites shown in the photograph above are fossils which were produced by cyanobacteria 3.5 billion years in Shark Bay, Australia. Cyanobacteria - a simple, single-celled lifeform - produced large amounts of oxygen via photosynthesis causing the first major oxygenation even in Earth’s history. Photograph taken by Paul Harrison. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b9999c38985830bc3e13e12/5b9999c38985830bc3e13e13/1537289631769/grav_lens_telescope%5B1%5D.jpg gregschool-lessons - Preliminary Interstellar Missions: Prelude to the Stars A gravitational lens telescope, as envisioned by Claudio Maccone in his 2009 book Deep Space Flight and Communications. (Claudio Maccone) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5ba2fcd48985837c2df40ed1/5ba2ff790e2e7299a6f5ccdf/1549254809141/dvv.jpg gregschool-lessons - Preliminary Interstellar Missions: Prelude to the Stars Infographic above is from Time Magazine April 10, 2000. https://www.gregschool.org/gregschoollessons/2018/5/23/star-lifting-colonizing-the-stars-and-the-galaxies monthly 0.5 2019-03-19 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b999c2e4ae23743aeeb3b66/5b999c2e4ae23743aeeb3b67/1536890841527/jeremy-jozwik-ia-kuiperbeltterrain-comp2-0084.jpg gregschool-lessons - Star Lifting: Colonizing the Stars and the Galaxies - Kuiper Belt Laser Array Artist’s impression of an array of lasers built on a comet in the Kuiper Belt. These laser stations would also be built on comets within Oort clouds (not jude our own) and interstellar space to create an interstellar highway. Artwork by Jeremy Jozwik from Artstation who is also a member of the SFIA production team. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c8ea63ce4966b4eaee53ab5/1552945894119/Local_Group_and_nearest_galaxies%5B1%5D.jpg gregschool-lessons - Star Lifting: Colonizing the Stars and the Galaxies https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b999c2e4ae23743aeeb3b72/1528412559259/star+lifter.jpg gregschool-lessons - Star Lifting: Colonizing the Stars and the Galaxies Figure 2 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c8eca1341920294c29e2339/1552960357080/neil-blevins-megastructures-9-gas-giant-refinery-5.jpg gregschool-lessons - Star Lifting: Colonizing the Stars and the Galaxies Artist’s depiction of gas giant refineries used to extract materials such as helium-3 and deuterium from the atmosphere of one of the Jovian planets. Artwork by Neil Blevins at Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b999c2e4ae23743aeeb3b74/5b999c2e4ae23743aeeb3b75/1536791569975/neil-blevins-megastructures-1-ringworld-color-sketch%5B1%5D.jpg gregschool-lessons - Star Lifting: Colonizing the Stars and the Galaxies Artist’s depiction of a ring world. Artwork by Neil Blevins. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b999c2e4ae23743aeeb3b74/5b999c2e4ae23743aeeb3b77/1536791569979/neil-blevins-megastructures-1-ringworld-design-packet%5B1%5D.jpg gregschool-lessons - Star Lifting: Colonizing the Stars and the Galaxies https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c8ecef271c10b4ed9c9920f/1552945894113/lzlsart9qi311%5B1%5D.jpg gregschool-lessons - Star Lifting: Colonizing the Stars and the Galaxies Nicoll-Dyson Beam “Unleashing The Nicoll-Dyson Beam from Gigastructural Engineering & More. Inward Perfection has never been so easy when you can delete your enemies Capital systems with the press of a button. Edit: It also has multiple settings. Ranging from reducing all infrastructure to rubble to Solar System Deleter.” Image retrieved from: https://www.reddit.com/r/Stellaris/comments/8qgwe9/fear_me_for_i_am_your_apocalypse/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b99cb580ebbe8e9409c31c5/5b99cb59b8a045cb6c9ee62c/1552945894093/neil-blevins-megastructures-7-star-lifter-3d-sketch.jpg gregschool-lessons - Star Lifting: Colonizing the Stars and the Galaxies - Star Lifting “A star lifter removes mass from a star for either raw materials or to change the nature of the star itself. For example, you may remove mass from the star to collect hydrogen or other elements. Or you could remove mass in order to extend the life of the star, to make the star dimmer, or reduce the chances of a super nova.” Artwork by Neil Blevins from Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c8ed502f9619a653708c330/1552945894116/Von-Neumann-Probe.jpg gregschool-lessons - Star Lifting: Colonizing the Stars and the Galaxies Concept art by Mark Molnar https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b999c2e4ae23743aeeb3b62/5b999c2e4ae23743aeeb3b63/1536791569963/Oneilcylinder1.jpg gregschool-lessons - Star Lifting: Colonizing the Stars and the Galaxies https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c90091aee6eb0728acc7659/5c90091a0d929794c36ecafe/1552970568823/1080p-Space-Desktop-Background-hd-desktop-wallpapers-cool-images-hd-apple-background-wallpapers-colourfull-free-display-lovely-wallpapers.jpg gregschool-lessons - Star Lifting: Colonizing the Stars and the Galaxies Image retrieved from: https://thewallpaper.co/preview/?wallpaper=1080p-space-desktop-background-hd-desktop-wallpapers-cool-images-hd-apple-background-wallpapers-colourfull-free-display-lovely-wallpapers-1920x1080 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b999c2e4ae23743aeeb3b6e/1528407608550/Star_lifting_1.svg%5B1%5D.png gregschool-lessons - Star Lifting: Colonizing the Stars and the Galaxies Figure 1: A star lifter would consist of a ring of solar power stations and ion accelerators distributed around a star in the shape of a ring. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c8ecc64ec212d73478cc97a/5c8ecc6541920294c29e3aa2/1552945894108/neil-blevins-megastructures-12-nicoll-dyson-laser-design-packet.jpg gregschool-lessons - Star Lifting: Colonizing the Stars and the Galaxies Artist’s depiction of a Nicoll-Dyson Laser. Artwork by Neil Blevins at ArtStation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b999c2e4ae23743aeeb3b70/1536791569973/Physics_of_the_future_Kaku_2011%5B1%5D.jpg gregschool-lessons - Star Lifting: Colonizing the Stars and the Galaxies "Physics of the Future: How Science Will Shape Human Destiny and Our Daily Lives by the Year 2100 is a 2011 book by theoretical physicist Michio Kaku, author of Hyperspace and Physics of the Impossible. In it Kaku speculates about possible future technological development over the next 100 years. He interviews notable scientists about their fields of research and lays out his vision of coming developments in medicine, computing, artificial intelligence, nanotechnology, and energy production. The book was on the New York Times Bestseller List for five weeks." https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b999c2e4ae23743aeeb3b6a/5b999c2e4ae23743aeeb3b6b/1536791569970/megastructures_7_star_lifter_3%5B1%5D.jpg gregschool-lessons - Star Lifting: Colonizing the Stars and the Galaxies Artist’s depiction of a star lifter. Artwork by Neil Blevins. https://www.gregschool.org/gregschoollessons/string-theory-and-colonizing-the-multiverse monthly 0.5 2019-03-21 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c90816453450a5d43f2c56c/1553136306229/universeismath.jpg gregschool-lessons - String Theory and Colonizing the Multiverse https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5be8c89403ce64619f88957f/1553136306240/shutterstock_84250684.jpg gregschool-lessons - String Theory and Colonizing the Multiverse Our universe may be one of many, physicists say. Credit: Shutterstock/Victor Habbick https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c91d122e4966b53e036d921/1553136306245/CERN_LHC%5B1%5D.jpg gregschool-lessons - String Theory and Colonizing the Multiverse The image above shows a section of the LHC (Large Hadron Collider). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c91c81753450a802a19682f/1553136306234/calabi-yau7%5B1%5D.gif gregschool-lessons - String Theory and Colonizing the Multiverse “String Theory predicts the existence of more than the 3 space dimensions and 1 time dimension we are all familiar with. According to string theory, there are additional dimensions that we are unfamiliar with because they are curled up into tiny complicated shapes that can only be seen on tiny scales. If we could shrink to this tiny, Planck-sized scale we could see that at every 3D point in space, we can also explore 6 additional dimensions. This animation shows an array of Calabi-Yau spaces which are projections of these higher dimensions into the more familiar dimensions we are aware of.”\(^{[2]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c931b0c4e17b65e89803aa0/1553144603597/T8F5x4MeyrzMFMXieSkmmL-970-80%5B1%5D.jpg gregschool-lessons - String Theory and Colonizing the Multiverse “An artist's interpretation of utilizing a wormhole to travel through space, Thorne kick-started a serious discussion among scientists about whether or wormhole travel is possible.”\(^{[1]}\) (Image: © NASA) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c91c69224a694ccc84b4b6f/1553136306232/four_forces%5B1%5D.jpg gregschool-lessons - String Theory and Colonizing the Multiverse Image Credit: https://physicswithsampurkis.files.wordpress.com/2014/01/four_forces.jpg https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c91c9678165f5b9be0f4a49/1553136306237/crystal_to_string%5B1%5D.jpg gregschool-lessons - String Theory and Colonizing the Multiverse The image above shows how various different small objects compare to each other in terms of size. Image retrieved from: http://www.particlecentral.com/strings_page.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b99c907758d4663942abb33/5b99c9074d7a9ce10e1433c9/1553136306225/gateway_hub_04_by_lorddoomhammer-d9u3226.png gregschool-lessons - String Theory and Colonizing the Multiverse https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c91d09d7817f72e2c2ce7f4/1553136306242/LeonardSusskindStanford2009_cropped%5B1%5D.jpg gregschool-lessons - String Theory and Colonizing the Multiverse Leonard Susskind https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c91d2624e17b673ce265308/1553136306249/matrioshka+brainnnn.png gregschool-lessons - String Theory and Colonizing the Multiverse “A matrioshka brain is a hypothetical megastructure proposed by Robert Bradbury, based on the Dyson sphere, of immense computational capacity. It is an example of a Class B stellar engine, employing the entire energy output of a star to drive computer systems.”\(^{[3]}\) Image from Steve Bowers https://www.gregschool.org/gregschoollessons/2018/7/20/space-based-solar-power-6fp9c monthly 0.5 2019-04-07 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b71efdb70a6ad96d8884229/1534192981034/archh.png gregschool-lessons - Inward Bound: How Should We Colonize the Earth? Depiction of arcologies located on the surface of the sea. (Click image to enlarge.) Image credit: https://www.shimz.co.jp/en/topics/dream/content03/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b71efdb70a6ad96d888422f/1534192981042/untitledddddss.png gregschool-lessons - Inward Bound: How Should We Colonize the Earth? Illustrations of a floating city concept. Images Credit: https://www.shimz.co.jp/en/topics/dream/content03/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ca936b17817f75f41e83c78/1554593461999/ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc.png gregschool-lessons - Inward Bound: How Should We Colonize the Earth? Illustration of the Casimir effect Image Credit: https://commons.wikimedia.org/wiki/File:Casimir_plates.svg https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b71efdb70a6ad96d888422d/1534192981040/archepelago.png gregschool-lessons - Inward Bound: How Should We Colonize the Earth? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b71efdb70a6ad96d8884221/5b71efdb70a6ad96d8884226/1534192981030/180714_Analemma_Earth-from-space_1600_c.jpg gregschool-lessons - Inward Bound: How Should We Colonize the Earth? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b71efdb70a6ad96d8884221/5b71efdb70a6ad96d8884224/1534192981027/161130_PU_Comet_on_20_November_NavCam_1600_c.jpg gregschool-lessons - Inward Bound: How Should We Colonize the Earth? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5b71efdb70a6ad96d8884221/5b71efdb70a6ad96d8884222/1534192981023/180714_Analemma_hot-air-balloon_1600_c.jpg gregschool-lessons - Inward Bound: How Should We Colonize the Earth? Depiction of a skyscraper attached to an asteroid. Such a skyscraper could be an Atlas tower supported by active support; that is, projectiles which run through a closed-loop chamber which imparted momentum on the structure in order to keep the structure suspended in the air. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b71efdb70a6ad96d888422b/1534192981037/ddd.png gregschool-lessons - Inward Bound: How Should We Colonize the Earth? This infographic depicts the Ocean Spiral: a vast helical-shaped structure which would extend from the surface of the sea to the sea floor. (Click image to enlarge.) Image Credit: https://www.shimz.co.jp/en/topics/dream/content01/ https://www.gregschool.org/gregschoollessons/rotational-inertia monthly 0.5 2019-03-23 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d816fc4c326d0fa4a490fc/1553304546553/rotational+inertiaimg.jpg gregschool-lessons - Rotational Inertia Figure 1: The rotational inertia of a hollow sphere is given by \(I=\frac{2}{3}MR^2\) and the rotational inertia of a solid ball is given by \(\frac{2}{5}MR^2\). Since the lever arms \(r\) (perpendicular distance from the axis of rotation) of each mass element in the solid sphere is smaller (because each mass is closer to the axis of rotation) than the lever arms in the hollow sphere (since each mass is farther away from the axis of rotation), the solid sphere must have a smaller rotational inertia. According to Equation (2), if \(r\) is smaller, then the function \(r^2\) that we are taking the area under is smaller. https://www.gregschool.org/gregschoollessons/super-intelligence-rise-of-the-machines monthly 0.5 2019-03-21 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c03389d2b6a28df2b7d173b/1553140043479/1541094535342-shutterstock_680929729%5B1%5D.jpg gregschool-lessons - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c0303c3575d1f6d6b3d995b/1553140043463/lg-airport-robot-9.jpg gregschool-lessons - Super Intelligence: Rise of the Machines The two robots above help clean the floor and give directions to passengers at the Seoul-Incheon International Airport. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c032db40ebbe8cd4bb98096/1553140043465/how-intelligent-will-aI-get-3%5B1%5D.jpg gregschool-lessons - Super Intelligence: Rise of the Machines Infographic source: https://www.huawei.com/en/about-huawei/publications/winwin-magazine/ai/how-intelligent-will-ai-get https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c032c1e4d7a9cc088dc56ca/1553140043472/tumblr_inline_p95ps0lvcV1scxxly_500%5B1%5D.png gregschool-lessons - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c03334c4d7a9cc088dcadff/1553140043474/staircase1%5B1%5D.png gregschool-lessons - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c02fb7d562fa71d4c7e537b/5c02fb7ec2241b1a4540382c/1553140043460/androids%5B1%5D.jpg gregschool-lessons - Super Intelligence: Rise of the Machines Cover art from the Sci-Fi Masterworks edition of Do Androids Dream of Electric Sheep? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c0323e46d2a738dea691847/1553140043470/Knowledge%252520Timeline%5B1%5D.gif gregschool-lessons - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c040a6bf950b754a35235b5/1553140043481/1541094406003-Untitled%5B1%5D.jpg gregschool-lessons - Super Intelligence: Rise of the Machines An example environment fed to the AI physicist. Here, the field of view is divided into four quadrants, each of which is governed by a different physical effect, such as gravity or an electromagnetic field. The dots and lines represent the ball’s trajectory through the environment. Based on how a ball moves through the environment, the AI must use the strategies it was given to describe the physical laws that are governing the ball’s motion. Image: Tegmark and Wu/arXiv https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c040ce9352f531f774053c4/1553140043483/central+dome+super+computer.jpg gregschool-lessons - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c0333694d7a9cc088dcaf46/1553140043476/staircase2%5B1%5D.png gregschool-lessons - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c03235070a6ad79cd1d6e31/1553140043467/TrainingTime-Graph-171019-r01%5B1%5D.gif gregschool-lessons - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c760281eb393114c85c6111/5c760281ee6eb02ae93cdd9f/1553140043456/Savvycom-AI-Lab%5B1%5D.jpg gregschool-lessons - Super Intelligence: Rise of the Machines https://www.gregschool.org/gregschoollessons/robots-and-their-uses monthly 0.5 2019-03-22 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c0f13080e2e726dadf11b14/5c0f130988251b1f81187596/1545767693598/arcologies.jpg gregschool-lessons - Robots and their Uses https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c0edb03c2241b1fedba9d7a/5c0edb0440ec9a0c615d48e8/1545767693602/iStock-660606914-804x1024%5B1%5D.jpg gregschool-lessons - Robots and their Uses https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c08aba388251b592172432b/5c08aba31ae6cfd1dd5467e8/1545767693595/luis-dourado-670d7641531557-57a9f2970415e.jpg gregschool-lessons - Robots and their Uses https://www.artstation.com/artwork/YxRbq https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c08b7f9f950b7c33192da63/1545767693608/if-you-could-visualize-grahams-curiosity-number-your-head-would-6200771.png gregschool-lessons - Robots and their Uses https://me.me/i/if-you-could-visualize-grahams-curiosity-number-your-head-would-3896085 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c0896b3032be44dcbeffda7/5c0896b340ec9a67bf39403c/1545767693571/neil-blevins-inc-the-robot-14-textured-poses1%5B1%5D.jpg gregschool-lessons - Robots and their Uses https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c089593cd8366f8b7572cab/5c08959370a6ad40348ee7df/1545767693565/524246%5B1%5D.jpg gregschool-lessons - Robots and their Uses Image retrieved from: https://wall.alphacoders.com/big.php?i=524246 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c0ee5f3758d464fd6809052/1545767693606/Atlas_from_boston_dynamics%5B1%5D.jpg gregschool-lessons - Robots and their Uses Atlas from Boston Dynamics https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c0f0050758d46ceef973400/1545767693610/any-sufficiently-advanced-technology-is-indistinguishable-from-magic-arthur-c-14468433.png gregschool-lessons - Robots and their Uses https://www.gregschool.org/articles-page-11 daily 0.75 2019-03-21 https://www.gregschool.org/articles-page-11/2017/5/23/pauli-matrices-wf87n monthly 0.5 2018-04-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc4fa57131a52388a462c6/1510177253510/electromagnetism+thumbnaillllll+imageeee.jpg Articles page 11 - Pauli Matrices https://www.gregschool.org/articles-page-11/2017/5/23/the-eigenvalues-of-any-observable-hatl-must-be-real-3jrk4 monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc4f61ccc5c55311706d9c/1510177245093/electromagnetism+thumbnaillllll+imageeee.jpg Articles page 11 - The Eigenvalues of any Observable \(\hat{L}\) must be Real https://www.gregschool.org/articles-page-11/2017/5/14/introduction-to-special-relativity-d23j8 monthly 0.5 2017-11-09 https://www.gregschool.org/articles-page-11/2017/6/28/8fldcv2rgvjvjwb42w67qh0ude4ii0-3yepp monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dd39f480bd5e3fd04102cd/1510177013572/space+travela+nd+colonization+thumbnail.jpg Articles page 11 - Alcubierre Warp Drive https://www.gregschool.org/articles-page-11/2017/6/19/introduction-to-limits-wyfhl monthly 0.5 2017-11-07 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a01d50fec212dc9f58d2911/1510076742404/limitss.jpg Articles page 11 - Introduction to Limits and Derivatives Figure 1: Above, I have graphed some arbitrary function \(g(x)\). At the point \(g(x_0)\), the slope or steepness of the curve is very small (indeed, it is zero) whereas at the point \(g(x_1)\) the slope of the curve is comparitevely large. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a01eb6b419202ecf43391b8/1510076742406/limit3.jpg Articles page 11 - Introduction to Limits and Derivatives Table 1: Values of \(f(x)\) as \(x→2\) and as \(Δx→0\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a01e4e871c10b4521168624/1510076742410/limits2.jpg Articles page 11 - Introduction to Limits and Derivatives Figure 3 (click to enlarge): Graph of arbitrary function \(f(x)\). If we let \(h(x)=\frac{f(x+ Δx)-f(x)}{(x+Δx)-x}\), then the function \(h(x)\) gives us the slope of the line obtained by drawing a straight line through the two points \((x,f(x))\) and \((x+Δx,f(x+Δx))\). For example if \(Δx=Δx_1\), then \(h(x)=\frac{f(x+ Δx_1)-f(x)}{(x+Δx_1)-x}\) gives the slope of the line \(AB_1\) (dark green line) in the graph above. As the value of \(Δx\) gets closer and closer to equaling zero, the value of \(h(x)\) gets closer and closer to equaling the slope of the grey line in the graph above. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a01edd70d92971b474082b9/1510076742408/limits1.jpg Articles page 11 - Introduction to Limits and Derivatives Figure 2: Graph of the function \(f(x)=x^2\). As the values of \(x\) get closer and closer to equaling \(2\), the values of \(x^2\) get closer and closer to equaling \(4\). https://www.gregschool.org/articles-page-11/2017/8/10/einstein-equivalence-principle-8j2w9 monthly 0.5 2017-11-09 https://www.gregschool.org/articles-page-11/2017/9/10/how-to-produce-water-and-oxygen-on-mars-njmkh monthly 0.5 2018-04-07 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac958971ae6cf686aba16f1/1523144648835/Twitter+thumbnail_preview.jpg Articles page 11 - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac958971ae6cf686aba16f5/1523144671889/email+thumbnail_preview.jpg Articles page 11 - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac958971ae6cf686aba16fb/1511021201272/mars3%5B1%5D.jpg Articles page 11 - How to Produce Water and Oxygen on Mars The rover above is capable of releasing frozen water from regolith by heating it using microwaves. Credit: SUTD/Gilmour Space Corporation https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac958971ae6cf686aba16f7/1523144599773/space+colon+author+date.jpg Articles page 11 - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac958971ae6cf686aba16f3/1523144687004/google+share+thumbnail_preview.jpg Articles page 11 - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac958971ae6cf686aba16ef/1523144639537/facebook+thumbnail.jpg Articles page 11 - How to Produce Water and Oxygen on Mars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac958971ae6cf686aba16f9/1510888610952/extracting+water+from+Mars%27+regolith.jpg Articles page 11 - How to Produce Water and Oxygen on Mars "Truck, oven, and slag pile system for extracting water from Martian soil."\(^{[2]}\) Artwork by Michael Carroll. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5ac95ad503ce649b2a22599f/1523147007558/share+b.jpg Articles page 11 - How to Produce Water and Oxygen on Mars https://www.gregschool.org/articles-page-11/2017/5/23/math-interlude-cddln monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc4f34f9a61e6c50c00f76/1510177213821/electromagnetism+thumbnaillllll+imageeee.jpg Articles page 11 - Quantum Mechanics: Math Interlude https://www.gregschool.org/articles-page-11/2017/8/30/capacitance-32sgr monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc398546c3c48d67794e72/1507602491385/electromagnetism+thumbnaillllll+imageeee.jpg Articles page 11 - Capacitance https://www.gregschool.org/articles-page-11/2017/8/30/finding-the-electric-field-produced-by-a-parallel-plate-capacitor-kpyfb monthly 0.5 2017-10-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc399fa8b2b02864cc415e/1507602728755/electromagnetism+thumbnaillllll+imageeee.jpg Articles page 11 - Finding the Electric Field produced by a Parallel-Plate Capacitor https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc399fa8b2b02864cc4162/1504719611731/sf.png Articles page 11 - Finding the Electric Field produced by a Parallel-Plate Capacitor Figure 2 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc399fa8b2b02864cc4164/1504719611734/ddfdf.png Articles page 11 - Finding the Electric Field produced by a Parallel-Plate Capacitor https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc399fa8b2b02864cc4160/1504719611725/ddd.png Articles page 11 - Finding the Electric Field produced by a Parallel-Plate Capacitor https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc399fa8b2b02864cc4166/1504719611739/fff.png Articles page 11 - Finding the Electric Field produced by a Parallel-Plate Capacitor https://www.gregschool.org/new-blog-47 daily 0.75 2018-07-20 https://www.gregschool.org/new-blog-47/2018/7/5/proof-of-the-theorem-fracsinxx1-t6c3x-kz4ll monthly 0.5 2018-07-19 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121cb88251bcb129f195e/1531966026247/facebook+img+thumbnail.jpg Limits - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121cb88251bcb129f1960/1531965974433/ Limits - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121cb88251bcb129f1966/1531965646813/Calculus+thumbnail.png Limits - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121cb88251bcb129f196a/1530817217237/squeezzeee.png Limits - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) Figure 2: As you can see graphically, for values of \(ϴ\) in the range \(\frac{-π}{2}<ϴ<\frac{π}{2}\), the following inequalities are true \(1≥\frac{sinϴ}{ϴ}≥cosϴ\). Notice that as \(ϴ\) approaches zero from both the negative and positive directions, the function \(\frac{sinϴ}{ϴ}\) gets "squeezed" into the same point on the graph. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121cb88251bcb129f1964/1531965935466/email+img+thumbnail.jpg Limits - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121cb88251bcb129f1968/1531244510817/Limit_of_Sine_of_X_over_X-Proof_3.png Limits - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) Figure 1: The wedge \(⪦OBA\) (colored blue) comprises a portion of the unit circle. The lengths \(AB\) and \(AC\) are the radius of the unit circle and are therefore equal to one. The heights of the triangles \(△OBA\) and \(△OCA\) can be found using basic trigonometry. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121cb88251bcb129f1962/1531965921845/twiiter+img+thumbnail.jpg Limits - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5121cb88251bcb129f195c/1531965731847/share+calculus+img.png Limits - Proof of the Theorem: \(\lim_{ϴ→0}\frac{sinϴ}{ϴ}=1\) https://www.gregschool.org/new-blog-47/2017/6/19/introduction-to-limits-wyfhl-ppzfc-e3np3 monthly 0.5 2018-07-20 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5125d970a6ade9ec7a0759/1510075871512/limits1.jpg Limits - Introduction to Limits and Derivatives Figure 2: Graph of the function \(f(x)=x^2\). As the values of \(x\) get closer and closer to equaling \(2\), the values of \(x^2\) get closer and closer to equaling \(4\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5125d970a6ade9ec7a075b/1510074097073/limits2.jpg Limits - Introduction to Limits and Derivatives Figure 3 (click to enlarge): Graph of arbitrary function \(f(x)\). If we let \(h(x)=\frac{f(x+ Δx)-f(x)}{(x+Δx)-x}\), then the function \(h(x)\) gives us the slope of the line obtained by drawing a straight line through the two points \((x,f(x))\) and \((x+Δx,f(x+Δx))\). For example if \(Δx=Δx_1\), then \(h(x)=\frac{f(x+ Δx_1)-f(x)}{(x+Δx_1)-x}\) gives the slope of the line \(AB_1\) (dark green line) in the graph above. As the value of \(Δx\) gets closer and closer to equaling zero, the value of \(h(x)\) gets closer and closer to equaling the slope of the grey line in the graph above. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5125d970a6ade9ec7a0755/1510069531644/limitss.jpg Limits - Introduction to Limits and Derivatives Figure 1: Above, I have graphed some arbitrary function \(g(x)\). At the point \(g(x_0)\), the slope or steepness of the curve is very small (indeed, it is zero) whereas at the point \(g(x_1)\) the slope of the curve is comparitevely large. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5b5125d970a6ade9ec7a0757/1510075248757/limit3.jpg Limits - Introduction to Limits and Derivatives Table 1: Values of \(f(x)\) as \(x→2\) and as \(Δx→0\). https://www.gregschool.org/new-blog-45 daily 0.75 2018-07-20 https://www.gregschool.org/new-blog-45/2017/10/22/partial-derivatives monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe26fe8e7b0f1f9f7e5323/1509828728481/twiiter+img+thumbnail.jpg Derivatives - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59f677c427ef2d09a24002fa/1509828728490/partial+derivatives.jpg Derivatives - Introduction to Partial Derivatives Figure 2: The entire blue surface is given by the function \(f(x,y)=x^2+y^2\). By letting \(y=1\), we that \(y^2=1\) and \(f(x,1)=x^2+1\) giving us a parabola shifted up one unit along the \(z\)-axis. That is how we can analytically obtain the parabola \(f(x,y)\). We can also obtain \(f(x,1)\) by passing the plane \(y=1\) (illustrated as the black plane above) through the surface \(f(x,y)\). The points at which the two surfaces (the surface \(f(x,y)\) and the plane \(y=1\)) intersect form the red parabola drawn in the image above. Image credit: By IkamusumeFan (Own work) [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe27cbec212d4734986096/1509828728477/share+calculus+img.png Derivatives - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe26e00d929758eafe1ed0/1509828728479/facebook+img+thumbnail.jpg Derivatives - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe26a224a6943fd0cc16bc/1509828728487/Calculus+thumbnail.png Derivatives - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe26ba24a6943fd0cc1a0d/1509828728485/email+img+thumbnail.jpg Derivatives - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fe26f353450a448c72dc7a/1509828728483/google+img+thumbnail.jpg Derivatives - Introduction to Partial Derivatives https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ed4b5ab7411cd96fcdb29b/1509828728488/MSP5083101ccb77dc1c84hg00003d8bb0b0083b496c.gif Derivatives - Introduction to Partial Derivatives Figure 1: Graph of the surface \(f(x,y)=x^2+y^2\). Image courtesy of Wolfram Alpha. https://www.gregschool.org/new-blog-45/2017/6/19/introduction-to-limits-wyfhl-ppzfc monthly 0.5 2017-11-07 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a01f14671c10b9fdcfa2d12/1510074097073/limits2.jpg Derivatives - Introduction to Limits and Derivatives Figure 3 (click to enlarge): Graph of arbitrary function \(f(x)\). If we let \(h(x)=\frac{f(x+ Δx)-f(x)}{(x+Δx)-x}\), then the function \(h(x)\) gives us the slope of the line obtained by drawing a straight line through the two points \((x,f(x))\) and \((x+Δx,f(x+Δx))\). For example if \(Δx=Δx_1\), then \(h(x)=\frac{f(x+ Δx_1)-f(x)}{(x+Δx_1)-x}\) gives the slope of the line \(AB_1\) (dark green line) in the graph above. As the value of \(Δx\) gets closer and closer to equaling zero, the value of \(h(x)\) gets closer and closer to equaling the slope of the grey line in the graph above. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a01f14671c10b9fdcfa2d0c/1510069531644/limitss.jpg Derivatives - Introduction to Limits and Derivatives Figure 1: Above, I have graphed some arbitrary function \(g(x)\). At the point \(g(x_0)\), the slope or steepness of the curve is very small (indeed, it is zero) whereas at the point \(g(x_1)\) the slope of the curve is comparitevely large. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a01f14671c10b9fdcfa2d10/1510075871512/limits1.jpg Derivatives - Introduction to Limits and Derivatives Figure 2: Graph of the function \(f(x)=x^2\). As the values of \(x\) get closer and closer to equaling \(2\), the values of \(x^2\) get closer and closer to equaling \(4\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5a01f14671c10b9fdcfa2d0e/1510075248757/limit3.jpg Derivatives - Introduction to Limits and Derivatives Table 1: Values of \(f(x)\) as \(x→2\) and as \(Δx→0\). https://www.gregschool.org/new-blog-32 daily 0.75 2018-09-15 https://www.gregschool.org/new-blog-32/2018/9/15/nuclear-fusion-engines monthly 0.5 2018-09-15 https://www.gregschool.org/month-1 daily 0.75 2019-01-02 https://www.gregschool.org/month-2 daily 0.75 2019-01-20 https://www.gregschool.org/month-3 daily 0.75 2019-01-21 https://www.gregschool.org/new-blog-75 daily 0.75 2019-01-02 https://www.gregschool.org/new-blog-72 daily 0.75 2019-01-21 https://www.gregschool.org/new-blog-52 daily 0.75 2018-11-25 https://www.gregschool.org/new-blog-6 daily 0.75 2018-12-04 https://www.gregschool.org/superconducters-post-in-article daily 0.75 2019-01-02 https://www.gregschool.org/superconducters-post-in-article/2017/1/23/superconductors-the-future-of-transportation-and-electric-transmission-d5e6r-7zcs4 monthly 0.5 2019-01-02 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2d286a562fa78fef791cfc/1509744831827/facebook+img+thumbnail.jpg Superconducterrss - posst in article - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2d286a562fa78fef791d00/1509744847045/ Superconducterrss - posst in article - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2d286a562fa78fef791d02/1509744550746/email+img+thumbnail.jpg Superconducterrss - posst in article - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2d286a562fa78fef791cfa/1509744676939/ Superconducterrss - posst in article - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2d286a562fa78fef791d04/1509744531017/technology+thumbnail.png Superconducterrss - posst in article - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c2d286a562fa78fef791cfe/1509744812574/twiiter+img+thumbnail.jpg Superconducterrss - posst in article - Superconductors: the Future of Transportation and Electric Transmission https://www.gregschool.org/new-blog-62 daily 0.75 2019-01-04 https://www.gregschool.org/new-blog-62/2019/1/4/paralyzed-monkeys-regain-control-of-their-legs-after-brain-implants monthly 0.5 2019-01-04 https://www.gregschool.org/new-blog-62/tag/CNN monthly 0.5 https://www.gregschool.org/new-blog-62/tag/Meera+Senthilingam monthly 0.5 https://www.gregschool.org/outward-bound-2 daily 0.75 2019-03-21 https://www.gregschool.org/outward-bound-2/2018/5/23/preliminary-interstellar-missions-prelude-to-the-stars-tlm8g monthly 0.5 2019-02-24 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c722c4cb208fc188c75330d/1549254809125/mars_hs-2016-15-a-full_tif%5B1%5D.jpg New Blog - Preliminary Interstellar Missions: Prelude to the Stars “This Hubble Space Telescope image of Mars shows details 20 to 30 miles across. A solar gravitational lens telescope would get even sharper views of exoplanets up to 100 light years away.”\(^{[4]}\) (STScI/AURA), J. Bell (ASU), and M. Wolff) Source URL: https://www.airspacemag.com/daily-planet/ultimate-space-telescope-would-use-sun-lens-180962499/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c722c4cb208fc188c753315/1549254809131/Stromatolites_in_Sharkbay%5B1%5D.jpg New Blog - Preliminary Interstellar Missions: Prelude to the Stars The stromatolites shown in the photograph above are fossils which were produced by cyanobacteria 3.5 billion years in Shark Bay, Australia. Cyanobacteria - a simple, single-celled lifeform - produced large amounts of oxygen via photosynthesis causing the first major oxygenation even in Earth’s history. Photograph taken by Paul Harrison. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c722c4cb208fc188c75331f/5c722c4cb208fc188c753320/1549254809141/dvv.jpg New Blog - Preliminary Interstellar Missions: Prelude to the Stars Infographic above is from Time Magazine April 10, 2000. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c722c4cb208fc188c753313/1549254809129/NASA-WhatBiosignaturesDoesLifeProduce-20180625%5B1%5D.jpg New Blog - Preliminary Interstellar Missions: Prelude to the Stars The combination of certain molecules and the absence of certain molecules in an exoplanet’s atmosphere is only likely if life is inhabited on that world: such combinations are called disequilibrium mixtures. As the light emitted from a star passes through an exoplanet’s atmosphere, the molecules in that exoplanet’s atmosphere absorb only certain wavelengths. Given which wavelengths were absorbed, we can determine whether or not disequilibrium mixtures are present in that exoplanet’s atmosphere and, consequently, assess the likelihood that extraterrestrial life inhabits that world. NASA/Aaron Gronsta https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c722c4cb208fc188c753317/1549254809133/Great+Oxidization+Event.jpg New Blog - Preliminary Interstellar Missions: Prelude to the Stars Diagram of the evolution of atmospheric oxygen concentration during the history of the planet. © Ido, Pierre Sans-Jofre https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c722c4cb208fc188c753319/1549254809135/50lys%5B1%5D.gif New Blog - Preliminary Interstellar Missions: Prelude to the Stars The image above is a map of a small fraction of nearby stars in our stellar neighborhood. It is a map of 130 stars located within 50 lightyears of us which are visible with the naked eye. This map shows only a tiny percent of that stars within 50 lightyears away from the Sun. There are in fact 1,800 known stars within this volume of space. To eliminate the threat of nearby supernovae, our descendants will one day visit all of these stars, either directly in which case their species actually arrives at the star, or indirectly by sending spacecraft and robots to those stars. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c722c4cb208fc188c75331d/1549254809139/013532_med%5B1%5D.jpg New Blog - Preliminary Interstellar Missions: Prelude to the Stars Illustration of the James Webb Space Telescope, current as of September 2009. Top side. Image Source: https://web.archive.org/web/20100527230418/http://www.jwst.nasa.gov/images_artist13532.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c722c4cb208fc188c753323/1549254809143/microwave-sail-starwisp-n.jpg New Blog - Preliminary Interstellar Missions: Prelude to the Stars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c722c4cb208fc188c75330f/5c722c4cb208fc188c753310/1549254809127/1280px-Artist%27s_impression_of_the_planet_Ross_128_b%5B1%5D.jpg New Blog - Preliminary Interstellar Missions: Prelude to the Stars Artist's impression of the planet Ross 128 b, with the star Ross 128 visible in the background\(^{[1]}\) Credit: European Southern Observatory https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c722c4cb208fc188c75331b/1549254809137/Welcome_to_the_Universe_by_Neil_deGrasse_Tyson%3B_book_cover.jpg New Blog - Preliminary Interstellar Missions: Prelude to the Stars Welcome to the Universe: An Astrophysical Tour is a popular science book by Neil deGrasse Tyson, Michael A. Strauss, and J. Richard Gott, based on an introductory astrophysics course they co-taught at Princeton University. The book was published by the Princeton University Press on September 20, 2016.\(^{[6]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c722c4cb208fc188c75330b/1536791569946/3E58320900000578-0-image-a-2_1489702334064%5B1%5D.jpg New Blog - Preliminary Interstellar Missions: Prelude to the Stars https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c722c4cb208fc188c753307/5c722c4cb208fc188c753308/1537289631769/grav_lens_telescope%5B1%5D.jpg New Blog - Preliminary Interstellar Missions: Prelude to the Stars A gravitational lens telescope, as envisioned by Claudio Maccone in his 2009 book Deep Space Flight and Communications. (Claudio Maccone) https://www.gregschool.org/outward-bound-2/2019/2/7/leaving-the-solar-system-f2tx3 monthly 0.5 2019-02-24 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c722d9b9140b72b900de5e0/5c722d9b9140b72b900de5e1/1550429768539/This-is-How-Earth-Moves-1.jpg New Blog - Leaving the Solar System: Introduction to the Outward Bound Series This image illustrates the fact that the Sun is actually moving through space relative to the Milky Way galaxy; from this frame of reference, the Earth is moving in a spiral-shaped path. Of course, we can actually alter this path as well as the Sun’s speed using a type of megastructure known as a Shkadov thruster; you could, in fact, give the Sun (and the Earth which goes around it) a radically different path which heads off-course away from the galaxy. Image retrieved from: https://wordlesstech.com/this-is-how-earth-moves/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c722d9b9140b72b900de5de/1550429768537/wright_brothers%5B1%5D.jpg New Blog - Leaving the Solar System: Introduction to the Outward Bound Series The Wright brothers on the steps of their boyhood home at 7 Hawthorn St. in Dayton.\(^{[1]}\) Carillon Historical Park https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c722d9b9140b72b900de5d6/5c722d9b9140b72b900de5d7/1550429768528/034-035_AAS_024%5B1%5D.jpg New Blog - Leaving the Solar System: Introduction to the Outward Bound Series Infographic retrieved from: https://www.spaceanswers.com/issue-previews/5025/5025/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c722d9b9140b72b900de5d0/1550429768522/WH-Phoebe-1024x599%5B1%5D.jpg New Blog - Leaving the Solar System: Introduction to the Outward Bound Series Image retrieved from: https://crossingzebras.com/wormhole-space-after-phoebe/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c722d9b9140b72b900de5d2/1550429768524/quote-the-moral-landscape-is-the-framework-i-use-for-thinking-about-questions-of-morality-sam-harris-12-51-41%5B1%5D.jpg New Blog - Leaving the Solar System: Introduction to the Outward Bound Series Quote by Sam Harris, author of the book, The Moral Landscape. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c722d9b9140b72b900de5d4/1550429768526/maxresdefault.jpg New Blog - Leaving the Solar System: Introduction to the Outward Bound Series https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c722d9b9140b72b900de5e4/1550429768542/grav_lens_telescope%5B1%5D%5B1%5D.jpg New Blog - Leaving the Solar System: Introduction to the Outward Bound Series A gravitational lens telescope, as envisioned by Claudio Maccone in his 2009 book Deep Space Flight and Communications. (Claudio Maccone) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c722d9b9140b72b900de5da/5c722d9b9140b72b900de5db/1550429768532/every_thing_that_comes_to_end.jpg New Blog - Leaving the Solar System: Introduction to the Outward Bound Series https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c722d9b9140b72b900de5cc/5c722d9b9140b72b900de5cd/1550429768519/84v8X%5B1%5D.jpg New Blog - Leaving the Solar System: Introduction to the Outward Bound Series https://www.gregschool.org/outward-bound-2/spaceship-comets-and-highways-through-space-5ec48-mpl83 monthly 0.5 2019-02-24 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c7312bf0d9297df0c46ebac/1546401363659/swe12_10836_coverbackgroundshadowport_mattbradbury%5B1%5D.jpg New Blog - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46ebba/5c7312bf0d9297df0c46ebbd/1536987150213/MarsAndTheSpaceElevator%5B1%5D.jpg New Blog - Spaceship Comets and Highways Through Space “Here is a new montage showing the base of the space elevator on the tented town called "Sheffield", built on the summit of Pavonis Mons volcano (see Red Mars). The cable is supposed to be 10m thick, which means here that Sheffield city is very big here, at a large level of development. On the foreground, you can see colored urban lights. I imagine the main entry to the planet's surface would be like a rich and welcoming show for new settlers. I also imagine the tent' skin would be blue, to balance the red and grey landscape.”\(^{[59]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46ebba/5c7312bf0d9297df0c46ebbb/1537230346111/SheffieldAndTheSpaceElevator%5B1%5D.jpg New Blog - Spaceship Comets and Highways Through Space Artist’s impression of a space elevator connecting to the domed over city, Sheifeild, located on Pvonic Mons in Kim Robinson’s Mars trilogy. Images retrieved from: http://davinci-marsdesign.blogspot.com/2012/04/sheffield-and-space-elevator.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46eb90/5c7312bf0d9297df0c46eb91/1536889609120/jakub-grygier-026-interstellar-travel-ad.jpg New Blog - Spaceship Comets and Highways Through Space - Copy of Copy of Interstellar Spaceship Artist’s depiction of an interstellar spaceship accellerated by laser beams. Artwork by Jakub Grygier from Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46eb72/5c7312bf0d9297df0c46eb73/1551042796892/space-travel-1200x675%5B1%5D.jpg New Blog - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46eb9c/5c7312bf0d9297df0c46eb9d/1536896112581/Superlaser2.jpg New Blog - Spaceship Comets and Highways Through Space - Copy of Copy of Death Star Artist’s depiction of a death star. By building a shell world of the kind described by the scientist Paul Birch around a faint dead star (i.e. a brown dwarf), the faint radiation which that star gives off could be collected and used to power a gigantic laser mounted on the surface of a shell world. Thus, as far fetched as the idea might seem, it isn’t totally implausable. Image retrieved from: Artist’s depiction of a comet being used as a spaceship. Image retrieved from: http://earth-chronicles.ru/news/2014-04-21-63940 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46ebae/5c7312bf0d9297df0c46ebaf/1536717071163/jeremy-jozwik-ia-kuiperbeltterrain-comp2-0084.jpg New Blog - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c7312bf0d9297df0c46eb7c/1536985604633/41WSCf9QqtL._SX333_BO1%2C204%2C203%2C200_.jpg New Blog - Spaceship Comets and Highways Through Space Robert Zubrin’s book, Entering Space, covers topics ranging from colonizing Mars and the solar system and explores the feasibility of interstellar travel with known physics.\(^{[1]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c7312bf0d9297df0c46ebb8/1537145174696/9780553373356-uk%5B1%5D.jpg New Blog - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46ebda/5c7312bf0d9297df0c46ebdb/1538604155467/1_hHjG69bPm3VrMyUG2idPKg.jpeg New Blog - Spaceship Comets and Highways Through Space “Conceptual model of a growing and evolving asteroid starship. The image of comet 67P by ESA is used as a placeholder for a large asteroid.”\(^{[6]}\) Composite image by Francisco Muñoz and Anton Dobrevski https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46eb7e/5c7312bf0d9297df0c46eb7f/1536986254211/lunar-mining-base.jpg New Blog - Spaceship Comets and Highways Through Space The power requirements of buried human habitats and propellant production plants could be met by the widely spaced solar power panels shown above. Image: anna.j.nesterova@gmail.com https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46ebce/5c7312bf0d9297df0c46ebcf/1536898850377/jhm27etrwqj7fgpuxvuj%5B1%5D.jpg New Blog - Spaceship Comets and Highways Through Space Asteroid settlement concept. Credit and Copyright: Bryan Versteeg / DSI. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46ebce/5c7312bf0d9297df0c46ebd1/1536898837446/liian1htqo3l6hvx4kkj%5B1%5D.jpg New Blog - Spaceship Comets and Highways Through Space Concept art for DSI's "Harvestor" craft. Credit and Copyright: Bryan Versteeg / DSI. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c7312bf0d9297df0c46eb76/1536288589788/Skylab-73-HC-440HR%5B1%5D.jpg New Blog - Spaceship Comets and Highways Through Space Image of the Saturn V rocket launching to space. Image courtesy of NASA. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46eba0/5c7312bf0d9297df0c46eba1/1536861860343/d00fccc571b621e809cb4ef1b9b98ee7_full.jpg New Blog - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c7312bf0d9297df0c46eb94/1537411163921/alphacentfix2%5B1%5D.jpg New Blog - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c7312bf0d9297df0c46ebde/1538678002285/1449-enz.jpg New Blog - Spaceship Comets and Highways Through Space The map above shows the migration patterns and timeline of the Polynesians who traveled from Asia to America by hopping from one tiny archipelago to another. Our descendants who travel from the Earth to the exoplanet Proxima B might adopt an analogous strategy by hopping from one comet to another until they reach their final destination. Image retrieved from: https://teara.govt.nz/en/map/1449/map-of-pacific-migrations https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c7312bf0d9297df0c46eb9a/1536857488613/alphacentfix2%5B1%5Dkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk.jpg New Blog - Spaceship Comets and Highways Through Space Image Source: https://i4is.org/wp-content/uploads/2018/05/Principium21.pdf https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c7312bf0d9297df0c46ebca/1536896886414/jhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh.jpg New Blog - Spaceship Comets and Highways Through Space “This artist's concept puts solar system distances in perspective. The scale bar is in astronomical units, with each set distance beyond 1 AU representing 10 times the previous distance. One AU is the distance from the Sun to the Earth, which is about 93 million miles or 150 million kilometers. Neptune, the most distant planet from the Sun, is about 30 AU.”\(^{[4]}\) Image Credit: NASA/JPL-Caltech https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46eb96/5c7312bf0d9297df0c46eb97/1536856111055/alphacentfix2%5B1%5Dkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk.jpg New Blog - Spaceship Comets and Highways Through Space - Copy of Copy of Trip to Alpha Centauri using a Starshot Probe SCMP Graphic: Dennis Wong, Dang Elland Sources: Universe Today, SIMBAD Dacabase, SCMP research https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46eba4/5c7312bf0d9297df0c46eba5/1536859913266/evolvingaste%5B1%5D.jpg New Blog - Spaceship Comets and Highways Through Space Credit: Nils Faber & Angelo Vermeulen https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46ebb2/5c7312bf0d9297df0c46ebb3/1536896535625/colony19%5B1%5D.jpg New Blog - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c7312bf0d9297df0c46eb8a/1536853434848/ephemeralizationnnnnn.jpg New Blog - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c7312bf0d9297df0c46ebd6/1536900915403/hexagonal+array.png New Blog - Spaceship Comets and Highways Through Space “This hexagonal array of starlight mirrors might support a co-living group of twenty-five adults and children. Each of the mirrors is about the size of the continental United States, and the entire mirror “farm” is about 30,000 kilometers across.”\(^{[37]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46ebc0/5c7312bf0d9297df0c46ebc1/1541980302277/ksr-04.png New Blog - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46ebc0/5c7312bf0d9297df0c46ebc3/1537243146946/livinginasteroidd.png New Blog - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46ebc0/5c7312bf0d9297df0c46ebc5/1537243162729/hhhhh.png New Blog - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46ebc0/5c7312bf0d9297df0c46ebc7/1537243316507/kkkk.png New Blog - Spaceship Comets and Highways Through Space Infographics represent a visual explanation of the so-called terrariums discussed in Kim Stanley Robinsons, 2312. Also, there is a slight error in the last infographic: the asteroid does not spin, rather a cylinder inside of the hollowed out asteroid is the thing which is actually spinning. Infographics created by Pablo Defendini. Infographics retrieved from: http://www.defendini.com/2312.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46eba8/5c7312bf0d9297df0c46eba9/1536859707540/Asteroid+Mining+Station+by+Bas+Ruhe%5B1%5D.jpg New Blog - Spaceship Comets and Highways Through Space - Copy of Copy of Asteroid Mining Station Artist’s depicion of a colonized asteroid. Artwork by Bas Ruhe from Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c7312bf0d9297df0c46ebcc/1537041005162/energy-from-space-1.jpg New Blog - Spaceship Comets and Highways Through Space Using a nuclear reactor to fuse together deuterium and helium-3 would generate a lot of energy; that energy would be transferred to a shock absorber on the rear of a spaceship which would give the spaceship thrust thereby causing it to accelerate. Image retrieved from: https://science.howstuffworks.com/environmental/green-science/energy-from-space.htm https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46eb8c/5c7312bf0d9297df0c46eb8d/1537229707309/790097132176630087%5B2%5D.jpg New Blog - Spaceship Comets and Highways Through Space - Copy of Copy of Spaceship Asteroid “The concept of turning an asteroid into a spacecraft is not entirely new: conceptual designer Bryan Versteeg has been working with the Mars One Team to imagine how we could use large asteroids for mining, transportation and habitat.”\(^{[2]}\) Credit: http://www.spacehabs.com/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c7312bf0d9297df0c46ebd8/1536901738138/yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy.png New Blog - Spaceship Comets and Highways Through Space “Each of the hexagons in this figure represents one of the mirror farms shown in [previous image]. The dots are schematic representations of the habitats occupied by each twent-five-member “band.” in reality the habitats would probably be much too small to be seen on this scale.”\(^{[37]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46eb78/5c7312bf0d9297df0c46eb79/1537229057732/maxresdefault.jpg New Blog - Spaceship Comets and Highways Through Space - Copy of Copy of Starshot Probe Depiction of a Starshot probe being accellerated by Earth-based lasers. Credit: Breakthrough Starshot https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c7312bf0d9297df0c46ebd4/1536978228964/pale+blue+dottttttttttttttttttttttttttttttttttttttttttttttttttt.jpg New Blog - Spaceship Comets and Highways Through Space In Carl Sagan’s book, Pale Blue Dot, he talked about the possibility of interstellar human communities living in comets in the Kuiper belt, the Oort cloud, and beyond. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46eb82/5c7312bf0d9297df0c46eb87/1536853356980/Untitled.png New Blog - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46eb82/5c7312bf0d9297df0c46eb85/1536853340541/lunar-ring_2748879k.jpg New Blog - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c7312bf0d9297df0c46eb82/5c7312bf0d9297df0c46eb83/1536853352265/lunaring.png New Blog - Spaceship Comets and Highways Through Space https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c7312bf0d9297df0c46ebe0/1538678306195/photosynthesis-process-2.jpg New Blog - Spaceship Comets and Highways Through Space The infographic above shows how plants, via the process of photosynethesis, use light (sunlight or artificial light), carbon dioxide and water to produce breathable oxygen. https://www.gregschool.org/outward-bound-2/2018/5/23/star-lifting-colonizing-the-stars-and-the-galaxies-5mjpt monthly 0.5 2019-03-19 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9012e5c83025591f884fae/5c9012e5c83025591f884faf/1536791569975/neil-blevins-megastructures-1-ringworld-color-sketch%5B1%5D.jpg New Blog - Star Lifting: Colonizing the Stars and the Galaxies Artist’s depiction of a ring world. Artwork by Neil Blevins. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9012e5c83025591f884fae/5c9012e5c83025591f884fb1/1536791569979/neil-blevins-megastructures-1-ringworld-design-packet%5B1%5D.jpg New Blog - Star Lifting: Colonizing the Stars and the Galaxies https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9012e5c83025591f884f8c/5c9012e5c83025591f884f8d/1552959889824/jeremy-jozwik-ia-kuiperbeltterrain-comp2-0084.jpg New Blog - Star Lifting: Colonizing the Stars and the Galaxies - Kuiper Belt Laser Array Artist’s impression of an array of lasers built on a comet in the Kuiper Belt. These laser stations would also be built on comets within Oort clouds (not jude our own) and interstellar space to create an interstellar highway. Artwork by Jeremy Jozwik from Artstation who is also a member of the SFIA production team. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9012e5c83025591f884faa/1536791569973/Physics_of_the_future_Kaku_2011%5B1%5D.jpg New Blog - Star Lifting: Colonizing the Stars and the Galaxies "Physics of the Future: How Science Will Shape Human Destiny and Our Daily Lives by the Year 2100 is a 2011 book by theoretical physicist Michio Kaku, author of Hyperspace and Physics of the Impossible. In it Kaku speculates about possible future technological development over the next 100 years. He interviews notable scientists about their fields of research and lays out his vision of coming developments in medicine, computing, artificial intelligence, nanotechnology, and energy production. The book was on the New York Times Bestseller List for five weeks." https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9012e5c83025591f884fac/1528412559259/star+lifter.jpg New Blog - Star Lifting: Colonizing the Stars and the Galaxies Figure 2 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9012e5c83025591f884f90/5c9012e5c83025591f884f91/1536791569963/Oneilcylinder1.jpg New Blog - Star Lifting: Colonizing the Stars and the Galaxies https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9012e5c83025591f884fb4/1552852554589/Local_Group_and_nearest_galaxies%5B1%5D.jpg New Blog - Star Lifting: Colonizing the Stars and the Galaxies https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9012e5c83025591f884fa2/1552864521733/Von-Neumann-Probe.jpg New Blog - Star Lifting: Colonizing the Stars and the Galaxies Concept art by Mark Molnar https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9012e5c83025591f884f94/1552861724343/neil-blevins-megastructures-9-gas-giant-refinery-5.jpg New Blog - Star Lifting: Colonizing the Stars and the Galaxies Artist’s depiction of gas giant refineries used to extract materials such as helium-3 and deuterium from the atmosphere of one of the Jovian planets. Artwork by Neil Blevins at Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9012e5c83025591f884f96/5c9012e5c83025591f884f97/1552943531025/1080p-Space-Desktop-Background-hd-desktop-wallpapers-cool-images-hd-apple-background-wallpapers-colourfull-free-display-lovely-wallpapers.jpg New Blog - Star Lifting: Colonizing the Stars and the Galaxies Image retrieved from: https://thewallpaper.co/preview/?wallpaper=1080p-space-desktop-background-hd-desktop-wallpapers-cool-images-hd-apple-background-wallpapers-colourfull-free-display-lovely-wallpapers-1920x1080 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9012e5c83025591f884f87/5c9012e5c83025591f884f88/1552959875428/neil-blevins-megastructures-7-star-lifter-3d-sketch.jpg New Blog - Star Lifting: Colonizing the Stars and the Galaxies - Star Lifting “A star lifter removes mass from a star for either raw materials or to change the nature of the star itself. For example, you may remove mass from the star to collect hydrogen or other elements. Or you could remove mass in order to extend the life of the star, to make the star dimmer, or reduce the chances of a super nova.” Artwork by Neil Blevins from Artstation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9012e5c83025591f884fa4/5c9012e5c83025591f884fa5/1536791569970/megastructures_7_star_lifter_3%5B1%5D.jpg New Blog - Star Lifting: Colonizing the Stars and the Galaxies Artist’s depiction of a star lifter. Artwork by Neil Blevins. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9012e5c83025591f884f9e/1552862976200/lzlsart9qi311%5B1%5D.jpg New Blog - Star Lifting: Colonizing the Stars and the Galaxies Nicoll-Dyson Beam “Unleashing The Nicoll-Dyson Beam from Gigastructural Engineering & More. Inward Perfection has never been so easy when you can delete your enemies Capital systems with the press of a button. Edit: It also has multiple settings. Ranging from reducing all infrastructure to rubble to Solar System Deleter.” Image retrieved from: https://www.reddit.com/r/Stellaris/comments/8qgwe9/fear_me_for_i_am_your_apocalypse/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c9012e5c83025591f884f9a/5c9012e5c83025591f884f9b/1552862368589/neil-blevins-megastructures-12-nicoll-dyson-laser-design-packet.jpg New Blog - Star Lifting: Colonizing the Stars and the Galaxies Artist’s depiction of a Nicoll-Dyson Laser. Artwork by Neil Blevins at ArtStation. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9012e5c83025591f884fa8/1528407608550/Star_lifting_1.svg%5B1%5D.png New Blog - Star Lifting: Colonizing the Stars and the Galaxies Figure 1: A star lifter would consist of a ring of solar power stations and ion accelerators distributed around a star in the shape of a ring. https://www.gregschool.org/outward-bound-2/string-theory-and-colonizing-the-multiverse-mbzy6 monthly 0.5 2019-03-21 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fab2e2c48315988ac4a4/1553060486672/matrioshka+brainnnn.png New Blog - String Theory and Colonizing the Multiverse “A matrioshka brain is a hypothetical megastructure proposed by Robert Bradbury, based on the Dyson sphere, of immense computational capacity. It is an example of a Class B stellar engine, employing the entire energy output of a star to drive computer systems.”\(^{[2]}\) Image from Steve Bowers https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fab2e2c48315988ac4a2/1553060137245/CERN_LHC%5B1%5D.jpg New Blog - String Theory and Colonizing the Multiverse The image above shows a section of the LHC (Large Hadron Collider). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fab2e2c48315988ac498/1553057433719/four_forces%5B1%5D.jpg New Blog - String Theory and Colonizing the Multiverse Image Credit: https://physicswithsampurkis.files.wordpress.com/2014/01/four_forces.jpg https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fab2e2c48315988ac49c/1553058165874/crystal_to_string%5B1%5D.jpg New Blog - String Theory and Colonizing the Multiverse The image above shows how various different small objects compare to each other in terms of size. Image retrieved from: http://www.particlecentral.com/strings_page.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fab2e2c48315988ac49e/1541982430321/shutterstock_84250684.jpg New Blog - String Theory and Colonizing the Multiverse Our universe may be one of many, physicists say. Credit: Shutterstock/Victor Habbick https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c92fab2e2c48315988ac492/5c92fab2e2c48315988ac493/1536805148903/gateway_hub_04_by_lorddoomhammer-d9u3226.png New Blog - String Theory and Colonizing the Multiverse https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fab2e2c48315988ac496/1552974215990/universeismath.jpg New Blog - String Theory and Colonizing the Multiverse https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fab2e2c48315988ac49a/1553057859737/calabi-yau7%5B1%5D.gif New Blog - String Theory and Colonizing the Multiverse “String Theory predicts the existence of more than the 3 space dimensions and 1 time dimension we are all familiar with. According to string theory, there are additional dimensions that we are unfamiliar with because they are curled up into tiny complicated shapes that can only be seen on tiny scales. If we could shrink to this tiny, Planck-sized scale we could see that at every 3D point in space, we can also explore 6 additional dimensions. This animation shows an array of Calabi-Yau spaces which are projections of these higher dimensions into the more familiar dimensions we are aware of.”\(^{[1]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c92fab2e2c48315988ac4a0/1553060002632/LeonardSusskindStanford2009_cropped%5B1%5D.jpg New Blog - String Theory and Colonizing the Multiverse Leonard Susskind https://www.gregschool.org/articles-page-12 daily 0.75 2019-03-23 https://www.gregschool.org/articles-page-12/2017/5/23/fundamental-principles-and-postulates-of-quantum-mechanics-5hrka monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc502c37c581029a93b3a2/1510177270687/electromagnetism+thumbnaillllll+imageeee.jpg articles page 12 - Fundamental Principles and Postulates of Quantum Mechanics https://www.gregschool.org/articles-page-12/2017/5/23/measuring-the-spin-of-an-electron-e5rzd monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af78ca6f4ca3de31c2902b/1495565239455/ articles page 12 - Measuring the Spin of an Electron Figure 1 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dc505bcd0f68a14030a6df/1510177296554/electromagnetism+thumbnaillllll+imageeee.jpg articles page 12 - Measuring the Spin of an Electron https://www.gregschool.org/articles-page-12/2017/8/29/finding-the-integral-of-kxm-lbzkf monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d96c1ae5dd5b95993631d0/1507420992695/areaoftriangle.jpg articles page 12 - Finding the integral of \(kx^m\) Figure 1: The area underneath the function \(f(x)=2x\) is simply just the area of a triangle. The base of the triangle is \(x\) and its height is \(f(x)=2x\). Using the formula for the area of a triangle, we find that the area underneath \(f(x)=2x\) is \(x^2\). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59d96c1ae5dd5b95993631ce/1507419408151/author+date.jpg articles page 12 - Finding the integral of \(kx^m\) https://www.gregschool.org/articles-page-12/2017/3/22/p-series-convergence-and-divergence monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/58d3173386e6c09c7e8faaf2/1510178197451/ articles page 12 - P-Series Convergence and Divergence Figure 1 (click to enlarge) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59dbdeca80bd5e687ee62e0c/1510178197448/Untitled.jpg articles page 12 - P-Series Convergence and Divergence https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/58d31a7bb3db2b1c58bd3285/1510178197455/ articles page 12 - P-Series Convergence and Divergence Figure 2 (click to enlarge) https://www.gregschool.org/articles-page-12/2017/3/14/exponential-growth-of-information-technology-1 monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce1bf0d929715f69032d4/1510178067154/share+technology++img.jpg articles page 12 - Exponential Growth of Information Technology https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce17bf9619ae4de047a8c/1510178067158/twiiter+img+thumbnail.jpg articles page 12 - Exponential Growth of Information Technology https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce15d64265f1222b36604/1510178067156/facebook+img+thumbnail.jpg articles page 12 - Exponential Growth of Information Technology https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce146419202d6b98cbd73/1510178067164/technology+thumbnail.png articles page 12 - Exponential Growth of Information Technology https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce15524a694f81f94f5f5/1510178067162/email+img+thumbnail.jpg articles page 12 - Exponential Growth of Information Technology https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fce16e64265f1222b36835/1510178067160/google+img+thumbnail.jpg articles page 12 - Exponential Growth of Information Technology https://www.gregschool.org/articles-page-12/2017/2/17/thermodynamics-and-the-arrow-of-time monthly 0.5 2017-11-09 https://www.gregschool.org/articles-page-12/2017/3/27/light-fidelity-li-fi-ultra-fast-wireless-communications-system monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcde46652dea01783117e6/1510178046012/twiiter+img+thumbnail.jpg articles page 12 - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcde7324a694f81f94852f/1510178046005/share+technology++img.jpg articles page 12 - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcde35e2c483b3c8a6efd7/1510178046015/google+img+thumbnail.jpg articles page 12 - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcde16ec212df7e4a943af/1510178046017/email+img+thumbnail.jpg articles page 12 - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/58d96066197aeab5831c665b/1510178046021/ articles page 12 - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System Figure 1 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcde2608466526e1ae5922/1510178046009/facebook+img+thumbnail.jpg articles page 12 - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59fcddfcec212df7e4a93f81/1510178046019/technology+thumbnail.png articles page 12 - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System https://www.gregschool.org/articles-page-12/2017/5/14/spectroscopy-9cnt6 monthly 0.5 2017-11-11 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59af7af446c3c4202e76ee78/1494827814784/ articles page 12 - Spectroscopy https://www.gregschool.org/articles-page-12/2017/5/14/surface-of-last-scattering-blnaz monthly 0.5 2017-11-11 https://www.gregschool.org/articles-page-12/2017/6/16/formation-of-planets-and-stars-xa5hw monthly 0.5 2017-11-09 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/598cd26c46c3c4cee1b81766/1498195845727/ articles page 12 - A Brief Tour of our Milky Way Galaxy Artist's depiction of the Milky Way Galaxy. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/598cd26c46c3c4cee1b8176a/1498193304895/ articles page 12 - A Brief Tour of our Milky Way Galaxy Inferred image of the center of the Milky Way Galaxy. (Source) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/598cd26c46c3c4cee1b81768/1498157418533/mwpan_aitoff_s.jpg articles page 12 - A Brief Tour of our Milky Way Galaxy Picture of the Milky Way Galaxy as seen edge on. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/598cd26c46c3c4cee1b8176c/1498195183058/430453main_crabmosaic_hst_big_full.jpg articles page 12 - A Brief Tour of our Milky Way Galaxy Image of Crab Nebula. (Image credit: NASA) https://www.gregschool.org/clarketech daily 0.75 2019-03-23 https://www.gregschool.org/clarketech/technological-revolutions-98ybg-esscz monthly 0.5 2019-03-22 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954eed4192028641aca1bc/1546630127945/ Clarketech - Technological Revolutions “The Principia states Newton's laws of motion, forming the foundation of classical mechanics; Newton's law of universal gravitation; and a derivation of Kepler's laws of planetary motion (which Kepler first obtained empirically). The Principia is considered one of the most important works in the history of science.”\(^{[5]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954eed4192028641aca1d0/1546553988948/stock-photo-the-train-moving-on-the-overpass-and-the-city-on-the-water-concept-of-modern-transport-futuristic-769589683%5B1%5D.jpg Clarketech - Technological Revolutions Arcologies on the surface of the sea could be connected by maglev transportation systems. As we discuss in the article, How to Colonize the Earth?, these sea-steading towers would extend within the depths of the oceans; the cities underneath the sea surface could also be connected by maglev monorail systems. Image Credit: https://www.shutterstock.com/image-illustration/train-moving-on-overpass-city-water-769589683?src=l4eCjvmchovnXUJuJH_WrQ-1-29 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954eed4192028641aca1cc/1546462732450/stock-photo-concept-of-magnetic-levitation-train-moving-on-the-sky-way-in-vacuum-tunnel-across-the-city-modern-755107045%5B1%5D.jpg Clarketech - Technological Revolutions The image above portrays how large buildings (which could be arcologies that people live in) could be connected by maglev trains operating within evacuated tunnels. Image Credit: https://www.shutterstock.com/image-illustration/concept-magnetic-levitation-train-moving-on-755107045 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954eed4192028641aca1c0/1546631010156/Joule%27s_Apparatus_%28Harper%27s_Scan%29%5B1%5D.png Clarketech - Technological Revolutions “Engraving of James Joule's apparatus for measuring the mechanical equivalent of heat, in which altitude potential energy from the weight on the right is converted into heat at the left, through stirring of water.”\(^{[7]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954eed4192028641aca1ce/1546462673761/furureofcities1%5B1%5D.jpg Clarketech - Technological Revolutions https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954eed4192028641aca1ac/1546556387544/Life-expectancy-GDP-capita.png Clarketech - Technological Revolutions This graph illustrates the increase in standards of living and life expectancy that occurred during the time of the first two industrial revolutions.\(^{[3]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954eed4192028641aca1ba/1546628848879/shopping%5B2%5D.jpg Clarketech - Technological Revolutions In the book, Life 3.0, the cosmologist and AI researcher Max Tegmark explores the implications of AI and robotics. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954eed4192028641aca1ca/1546635697448/Meissner_effect_p1390048%5B1%5D.jpg Clarketech - Technological Revolutions “A magnet levitating above a high-temperature superconductor, cooled with liquid nitrogen. Persistent electric current flows on the surface of the superconductor, acting to exclude the magnetic field of the magnet (Faraday's law of induction). This current effectively forms an electromagnet that repels the magnet.” Image source: https://en.wikipedia.org/wiki/Superconductivity#/media/File:Meissner_effect_p1390048.jpg https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954eed4192028641aca1c8/1546635037806/superconductors.png Clarketech - Technological Revolutions The following graph reflects the empirical fact that as time has progressed, we have achieved superconductivity at higher and higher temperatures. Credit: Pia Jensen Ray https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954eed4192028641aca1b0/5c954eed4192028641aca1b1/1546626382657/Artificial-Intelligence-2%5B1%5D.jpg Clarketech - Technological Revolutions https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954eed4192028641aca1be/1546630451461/Newtons_laws_in_latin%5B1%5D.jpg Clarketech - Technological Revolutions “Newton's First and Second laws, in Latin, from the original 1687 Principia Mathematica”\(^{[6]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954eed4192028641aca1b6/5c954eed4192028641aca1b7/1546627071014/392448062_orig%5B1%5D.jpg Clarketech - Technological Revolutions Artist’s depiction of nanobots patroling the human bloodstream. Image retrieved from: https://www.cnet.com/news/nanobots-can-now-swarm-like-fish-to-perform-complex-medical-tasks/ https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954eed4192028641aca1aa/1546556065103/Maler_der_Grabkammer_des_Sennudem_001.jpg Clarketech - Technological Revolutions “Ploughing with a yoke of horned cattle in Ancient Egypt. Painting from the burial chamber of Sennedjem, c. 1200 BC.”\(^{[2]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954eed4192028641aca1c2/1546631734569/Newcomens_Dampfmaschine_aus_Meyers_1890%5B1%5D.png Clarketech - Technological Revolutions “Newcomen's steam-powered atmospheric engine was the first practical piston steam engine. Subsequent steam engines were to power the Industrial Revolution.”\(^{[7]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954eed4192028641aca1ae/1546556994722/Ending_Aging%5B1%5D.jpg Clarketech - Technological Revolutions Credit: https://en.wikipedia.org/wiki/File:Ending_Aging.jpg https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954eed4192028641aca1b4/1546626649805/Moore%27s_Law_Transistor_Count_1971-2016%5B1%5D.png Clarketech - Technological Revolutions A plot of CPU transistor counts against dates of introduction. Source URL: https://commons.wikimedia.org/wiki/File:Moore%27s_Law_Transistor_Count_1971-2016.png https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954eed4192028641aca1a8/1546555589793/ Clarketech - Technological Revolutions “Smithsonian scientists and their Chinese colleagues found this and other handaxes in the same sediment layer with tektites, small rocks that formed during a meteor impact 803,000 years ago. Since the handaxes and tektites were in the same layer, both are the same age. Early humans must have moved into the area right after the impact. They may have made the handaxes from rocks that were exposed when forests burned.”\(^{[1]}\) Image Credit: James Di Loreto, & Donald H. Hurlbert, Smithsonian Institution https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954eed4192028641aca1c4/5c954eed4192028641aca1c5/1546632086035/Bane-Boon-1280x640%5B1%5D.jpg Clarketech - Technological Revolutions Image retrieved from: https://iconshots.com/concept/the-future-of-technology-should-we-be-worried/ https://www.gregschool.org/clarketech/robots-and-their-uses-br26w-dpmrl monthly 0.5 2019-03-23 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f03ec212d705142e85f/1545767693610/any-sufficiently-advanced-technology-is-indistinguishable-from-magic-arthur-c-14468433.png Clarketech - Robots and their Uses https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f03ec212d705142e857/5c954f03ec212d705142e858/1545767693602/iStock-660606914-804x1024%5B1%5D.jpg Clarketech - Robots and their Uses https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f03ec212d705142e84f/5c954f03ec212d705142e850/1545767693595/luis-dourado-670d7641531557-57a9f2970415e.jpg Clarketech - Robots and their Uses https://www.artstation.com/artwork/YxRbq https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f03ec212d705142e84b/5c954f03ec212d705142e84c/1545767693571/neil-blevins-inc-the-robot-14-textured-poses1%5B1%5D.jpg Clarketech - Robots and their Uses https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f03ec212d705142e85d/1545767693608/if-you-could-visualize-grahams-curiosity-number-your-head-would-6200771.png Clarketech - Robots and their Uses https://me.me/i/if-you-could-visualize-grahams-curiosity-number-your-head-would-3896085 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f03ec212d705142e847/5c954f03ec212d705142e848/1545767693565/524246%5B1%5D.jpg Clarketech - Robots and their Uses Image retrieved from: https://wall.alphacoders.com/big.php?i=524246 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f03ec212d705142e853/5c954f03ec212d705142e854/1545767693598/arcologies.jpg Clarketech - Robots and their Uses https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f03ec212d705142e85b/1545767693606/Atlas_from_boston_dynamics%5B1%5D.jpg Clarketech - Robots and their Uses Atlas from Boston Dynamics https://www.gregschool.org/clarketech/utopia-life-in-the-year-2100-4e9ga-y24xn monthly 0.5 2019-03-23 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f160852293821458b93/1553277163807/Neolithic-revolution-ancient-farmers.jpg Clarketech - Utopia: Life in the Year 2100 The Neolithic Revolution (which began, independently, in multiple different civilization 10 to 12 thousand years ago) occurred when, for the first time, we humans began to domesticate plants and animals. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f160852293821458b97/5c954f160852293821458b98/1544066498793/524246%5B1%5D.jpg Clarketech - Utopia: Life in the Year 2100 Image retrieved from: https://wall.alphacoders.com/big.php?i=524246 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f160852293821458b9f/5c954f160852293821458ba2/1546461550632/The-Venus-Project-Restaurant-889x544%5B1%5D.jpg Clarketech - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f160852293821458b9f/5c954f160852293821458ba0/1546461550188/The-Venus-Project-Design-889x500%5B1%5D.jpg Clarketech - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f160852293821458b9f/5c954f160852293821458ba6/1546461554396/The-Venus-Project-Buildings-889x493%5B1%5D.jpg Clarketech - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f160852293821458b9f/5c954f160852293821458ba4/1546461550216/The-Venus-Project-Architecture-1-889x500%5B1%5D.jpg Clarketech - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f160852293821458bad/1546234016988/large_-085MyVwIWu7CejYdKdZJ_6R-zaYCURcCPnuQyPhrbA.jpg Clarketech - Utopia: Life in the Year 2100 ”Flipping good ... the Japanese cuisine machine hasn't dropped a pancake yet.”\(^{[3]}\) Image: Huis Ten Bosch/Facebook https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f160852293821458b8f/1553148030627/Diorama%2C_cavemen_-_National_Museum_of_Mongolian_History%5B1%5D.jpg Clarketech - Utopia: Life in the Year 2100 “A diorama showing Homo erectus, the earliest human species that is known to have controlled fire, from inside the National Museum of Mongolian History in Ulaanbaatar, Mongolia.”\(^{[1]}\) https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f160852293821458bab/1546233660364/11908915_472363736276164_3837059669263559235_o%5B1%5D.jpg Clarketech - Utopia: Life in the Year 2100 Image (click to enlarge) of lab-grown meat. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f160852293821458baf/5c954f160852293821458bb0/1544408785580/benjamin-parker-fleetovermiranda-render-wip.jpg Clarketech - Utopia: Life in the Year 2100 “Civilians watch a small fleet orbit around Uranus' moon Miranda.” Credit: https://www.artstation.com/artwork/mqZVx9 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f160852293821458baf/5c954f160852293821458bb2/1544408724395/benjamin-parker-fleetovermiranda-render-k.jpg Clarketech - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f160852293821458bb5/5c954f160852293821458bba/1553278214216/WANDERERS_verona_rupes_01%5B1%5D.jpg Clarketech - Utopia: Life in the Year 2100 “Base jumping off the tallest cliff in the Solar System, located on Uranus' moon Miranda. Uranus itself, along with a few other moons (from the top left to bottom right: Ariel (here on the far side of Uranus), Belinda, Puck and Portia) are seen in the background of the last shot. On Uranus´small moon Miranda lies a monumental cliff wall believed to be the tallest in the Solar System. It is called Verona Rupes. Observations are limited but it is certain that the cliffs rise at least 5 kilometers above the ground below. Maybe even twice as much. This extreme height combined with Miranda´s low gravity (0,018g) would make for a spectacular base-jump. After taking the leap from the top edge you could fall for at least 12 minutes and, with the help of a small rocket to brake your fall toward the bottom, end up landing safely on your feet. Miranda´s close orbit around giant Uranus also makes a magnificent huge cyan ball in the sky. The scene is built mostly in CG, except for the people who are shot live action and composited into the environment, and the foreground cliffs in the first shot which are made from several photos of a place in Norway known as "The Pulpit Rock". For building the landscape I used (amongst others) this satellite photo of Verona Rupes, taken by NASAs Voyager 2 during the flyby of Uranus in 1986. For the color and texture of Uranus I used this photo as reference. Also by Voyager 2, NASA.”\({[4]}\) Source: http://www.erikwernquist.com/wanderers/gallery_verona_rupes.html https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f160852293821458bb5/5c954f160852293821458bb6/1544408466566/WANDERERS_verona_rupes_03%5B1%5D.jpg Clarketech - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f160852293821458bb5/5c954f160852293821458bb8/1544408463612/WANDERERS_verona_rupes_02%5B1%5D.jpg Clarketech - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f160852293821458ba9/1544156143514/central+dome+super+computer.jpg Clarketech - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f160852293821458b91/1553148746362/goddardtsiolkovsky%5B1%5D.jpg Clarketech - Utopia: Life in the Year 2100 Photographs of the two pioneers of rocketry science, Konstantin Tsiolkovsky (left) and Robert Goddard (right). https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f160852293821458b9b/5c954f160852293821458b9c/1544066745624/neil-blevins-inc-the-robot-14-textured-poses1%5B1%5D.jpg Clarketech - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f160852293821458bbf/1546303365164/42276747_2080497328640659_4459771513339379712_o%5B1%5D.jpg Clarketech - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f160852293821458b8d/1546230422424/2483808_landscape.jpg Clarketech - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f160852293821458bbd/1544073254525/26166483_911930292319504_5468126342370460385_n%5B1%5D.jpg Clarketech - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f160852293821458b95/1544143467767/8a6f20acd6bb4d346443d8872dec9649.jpg Clarketech - Utopia: Life in the Year 2100 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f160852293821458b89/5c954f160852293821458b8a/1546230084517/1*ekxLnZoSewL3p7pVUrMEhQ.jpeg Clarketech - Utopia: Life in the Year 2100 Robert McCall, “The Prologue and the Promise” https://www.gregschool.org/clarketech/super-intelligence-rise-of-the-machines-btkn7-kghy3 monthly 0.5 2019-03-23 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f2c8165f590a8d04f22/1543768690328/1541094406003-Untitled%5B1%5D.jpg Clarketech - Super Intelligence: Rise of the Machines An example environment fed to the AI physicist. Here, the field of view is divided into four quadrants, each of which is governed by a different physical effect, such as gravity or an electromagnetic field. The dots and lines represent the ball’s trajectory through the environment. Based on how a ball moves through the environment, the AI must use the strategies it was given to describe the physical laws that are governing the ball’s motion. Image: Tegmark and Wu/arXiv https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f2c8165f590a8d04f18/1543709737491/Knowledge%252520Timeline%5B1%5D.gif Clarketech - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f2c8165f590a8d04f1e/1543713651396/staircase2%5B1%5D.png Clarketech - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f2c8165f590a8d04f0a/5c954f2c8165f590a8d04f0b/1551237763911/Savvycom-AI-Lab%5B1%5D.jpg Clarketech - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f2c8165f590a8d04f24/1543769327376/central+dome+super+computer.jpg Clarketech - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f2c8165f590a8d04f20/1543714992397/1541094535342-shutterstock_680929729%5B1%5D.jpg Clarketech - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f2c8165f590a8d04f12/1543701465710/lg-airport-robot-9.jpg Clarketech - Super Intelligence: Rise of the Machines The two robots above help clean the floor and give directions to passengers at the Seoul-Incheon International Airport. https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f2c8165f590a8d04f16/1543709544581/TrainingTime-Graph-171019-r01%5B1%5D.gif Clarketech - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f2c8165f590a8d04f1c/1543713631011/staircase1%5B1%5D.png Clarketech - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f2c8165f590a8d04f1a/1543711783089/tumblr_inline_p95ps0lvcV1scxxly_500%5B1%5D.png Clarketech - Super Intelligence: Rise of the Machines https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c954f2c8165f590a8d04f0e/5c954f2c8165f590a8d04f0f/1543700155460/androids%5B1%5D.jpg Clarketech - Super Intelligence: Rise of the Machines Cover art from the Sci-Fi Masterworks edition of Do Androids Dream of Electric Sheep? https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c954f2c8165f590a8d04f14/1543712186611/how-intelligent-will-aI-get-3%5B1%5D.jpg Clarketech - Super Intelligence: Rise of the Machines Infographic source: https://www.huawei.com/en/about-huawei/publications/winwin-magazine/ai/how-intelligent-will-ai-get https://www.gregschool.org/clarketech/2017/1/23/superconductors-the-future-of-transportation-and-electric-transmission-d5e6r-ancwd monthly 0.5 2019-03-23 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9587eb5bfa3f0001d2cd19/1509744676939/ Clarketech - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9587eb5bfa3f0001d2cd2b/1509744812574/twiiter+img+thumbnail.jpg Clarketech - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9587eb5bfa3f0001d2cd31/1509744531017/technology+thumbnail.png Clarketech - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9587eb5bfa3f0001d2cd2d/1509744847045/ Clarketech - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9587eb5bfa3f0001d2cd29/1509744831827/facebook+img+thumbnail.jpg Clarketech - Superconductors: the Future of Transportation and Electric Transmission https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c9587eb5bfa3f0001d2cd2f/1509744550746/email+img+thumbnail.jpg Clarketech - Superconductors: the Future of Transportation and Electric Transmission https://www.gregschool.org/clarketech/2017/8/21/our-future-as-cyborgs-lfz6p-2rlfh monthly 0.5 2019-03-23 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c95882a53450a28e41da975/1510175161926/technology+thumbnail.png Clarketech - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c95882a53450a28e41da979/1510175161930/04-17-Asimo-Grand-Marshall-HIGPA%5B1%5D.jpg Clarketech - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c95882a53450a28e41da96d/1510250950786/facebook+img+thumbnail.jpg Clarketech - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c95882a53450a28e41da977/1510175161928/bionic_v2.png Clarketech - Our Future as Cyborgs https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c95882a53450a28e41da973/1510249455185/email+img+thumbnail.jpg Clarketech - Our Future as Cyborgs 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Ultra-Fast, Wireless Communications System Figure 1 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c95886ef9619a337b767762/1509744439536/facebook+img+thumbnail.jpg Clarketech - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c95886ef9619a337b767769/1509744154145/email+img+thumbnail.jpg Clarketech - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c95886ef9619a337b767760/1509744247982/share+technology++img.jpg Clarketech - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/5c95886ef9619a337b767767/1509744456561/google+img+thumbnail.jpg Clarketech - Light Fidelity (Li-Fi): Ultra-Fast, Wireless Communications System 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https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/5c72fe77fa0d600773be0e06/5c72fe78ec212dd3a564c11e/1551040124039/Galactic_Hitman_Artwork_2%5B1%5D.jpg Space Travel & Colonization https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ffb0d78e7b0f1f9fa1179c/1509929178460/space%5B1%5D.jpg Space Travel & Colonization https://www.gregschool.org/special-general-relativity-1 daily 0.75 2017-08-10 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ffacfb8165f5564ad2f0eb/1509928193062/grmontage%5B1%5D.jpg Special & General Relativity https://www.gregschool.org/singlevariable-calculus-1 daily 0.75 2018-07-20 https://static1.squarespace.com/static/58757ed7f5e231cc32494a1b/t/59ffb17af9619a4291aa3a3b/1509929344532/calc+banner.jpg Calculus https://www.gregschool.org/classical-mechanics-lecture-1 daily 0.75 2017-09-05 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