(a) Using the mathematical similarity between Coulomb’s law and Newton’s law of universal gravitation, show that Gauss’s law for gravitation can be written as where min is the net mass inside the Gaussian surface and g = Fg/m represents the gravitational field at any point on the Gaussian surface.
(b) Determine the gravitational field at a distance r from the center of the Earth where r < RE, assuming that the Earth’s mass density is uniform.