Suppose a planet whose surface is spherical and the gravitational potential exterior to it is exactly -GM/r, like that of a point mass. Is it possible to know if the inner mass distribution is actually shperically symmetric? Can a non-spherical mass distribution produce such an external potential? If yes, give an example.
Newton's shell theorems, Gauss' law
The Attempt at a Solution
"The potential out of any spherical distribution of mass is like if all the mass was in a point", but this is true for shells of uniform density. I remember that a particle inside of the sphere doesn't feel any forces regardless the mass distribution, but outside?
If we use a "gaussian surface" to enclose such a non-spherical mass distribution, Gauss' law gives the total mass, so internal distribution wouldn't be important, but, for example, inhomogeneities in Earth's density can affect nearby planetary bodies. Then? I'm confused.