Applying Gauss's Law for Gravitation Using Gauss's law for gravitation (derived in part (b) of Problem 22.59), show that the following statements are true:
(a) For any spherically symmetric mass distribution with total mass M, the acceleration due to gravity outside the distribution is the same as though all the mass were concentrated at the center.
(b) At any point inside a spherically symmetric shell of mass, the acceleration due to gravity is zero.
(c) If we could drill a hole through a spherically sym metric planet to its center, and if the density were uniform, we would find that the magnitude of g is directly proportional to the distance r from the center. We proved these results in Section 12.6 using some fairly strenuous analysis; the proofs using Gauss's law for gravitation are much easier.