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## Homework Statement

Astronauts orbiting a planet find that

(i) the surface of the planet is precisely spherical.

(ii) the potential exterior to the planetary surface is [tex]\phi = \frac{-GM}{r}[/tex] exactly, that is, perfectly spherical.

Can you conclude from these observations that the mass distribution in the interior of the planet is spherically symmetric?

## Homework Equations

## The Attempt at a Solution

I think that it doesn't matter whether it is a point mass inside at the centre or whether there is a symmetric mass distribution but I don't really know why I think that!