In this lesson, we'll discuss the foundation of Classical mechanics: namely, Newton's three laws of motion. Everything else that we discuss in Classical mechanics will be based on these principles.
Newton's law of gravity has been described as one of the greatest achievements in human thought of all time. It says that everything in the universe is, quite literally, connected. It must've been an astonishing realization to Newton that a grain of dust in his room exerts a slight "pull" on all of the stars and galaxies in the universe. In the words of Paul Dirac: "Pick a flower on Earth and you move the farthest star."
To find the gravitational force exerted by a sphere of mass \(M\) on a particle of mass \(m\) outside of that sphere, we must first subdivide that sphere into many very skinny shells and find the gravitational force exerted by anyone of those shells on \(m\). We'll see, however, that finding the gravitational force exerted by such a shell is in of itself a somewhat tedious exercise. In the end, we'll see that the gravitational force exerted by a sphere of mass \(M\) on a particle of mass \(m\) outside of the sphere (where \(D\) is the center-to-center separation distance between the sphere and the particle) is completely identical to the gravitational force exerted by a particle of mass \(M\) on the other particle of mass \(m\) such that \(D\) is there separation distance.