Question: Newton's law of gravity says that the gravitational force between two bodies is attractive and given by
F = GMm/r2,
Where G is the gravitational constant, m and M are the masses of the two bodies, and r is the distance between them. This is the famous inverse square law. For a falling body, we take M to be the mass of the earth and r to be the distance from the body to the center of the earth. So, actually, r changes as the body falls, but for anything we can easily observe (say, a ball dropped from the Tower of Pisa), it won't change significantly over the course of the motion. Hence, as an approximation, it is reasonable to assume that the force is constant. According to Newton's second law, acceleration is caused by a force and Force = Mass × Acceleration.
(a) Find the differential equation for the position, s of a moving body as a function of time.
(b) Explain how the differential equation shows the acceleration of the body is independent of its mass.