Question

The Moon can be considered to be a sphere with uniform density with mass MM and radius RM. At the (exact) center of the Moon, the gravitational force on a mass m due to the mass of the Moon is?

I know the answer is zero but want to know why using gauss' law

Answer 1

Assume that there is a certain cavity in the center of the Moon where we are going to place the mass ‘m”. Locate the Gaussian closed surface inside the Moon to enclose its central empty region. There will be nothing inside this surface => the flux of gravitational field is zero => the force (which is the product of gravitational field strength and the mass of the object) will be zero.