# Potential of spherical and non-spherical mass distributions?

## Homework Statement

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.

## Homework Equations

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.

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Simon Bridge
Homework Helper
The potential out of any distribution of mass is like if all the mass was in a point... at the center of mass of the distribution.

What happens to the center of mass if the distribution is not spherical?
Is the mass of spherical shells not spherically distributed?
Will a particle inside a spherical distribution of mass experience forces from non-spherical distortions?

The potential out of any distribution of mass is like if all the mass was in a point... at the center of mass of the distribution.

What happens to the center of mass if the distribution is not spherical?
Its location will be displaced fron the geometric center towards where the density is greater... Oh, wait, I am confusing a spherical distribution with a homogeneous one!
If the distribution is uniform, either spherical or not, the center of mass will coincide with the geometric center, right?

Is the mass of spherical shells not spherically distributed?
It is spherically distributed, it can vary whit radius, but shells have spherical symmetry.

Will a particle inside a spherical distribution of mass experience forces from non-spherical distortions?
Inside? Uhmmm... No... :uhh:

Simon Bridge
Homework Helper