Newton applied his universal law of gravitation for the special case of circular orbits and obtained the full form the 3rd Law of Kepler:

          GM/(4π^2 ) T^2 = r^3

(a)Analyse the motion of a small mass, m, in uniform circular orbit about a much larger mass M, and verify this expression, where T is the period of the orbit, r is the radius of the orbit and G is the gravitational constant.

(b)Apply the result to the orbit of the Moon (m) about the Earth (M). The period of revolution for the Moon is 27.3 days and its average distance from the Earth is  3.84 × 10^5  km.   Does the equality hold (the orbit is not exactly circular)?