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gupster
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This is an adaptation of question 2.1. in Galactic Dynamics by Binney and Tremaine in case anyone owns it.
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?
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!
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!