How to prove that a sphere has the minimum gravitational potential energy for a given volume of uniformly dense material? [duplicate]

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Planets are spherical (roughly) in shape because a spherical configuration gives the minimum gravitational potential energy.

How does one prove that the sphere is the shape that gives minimum gravitational potential energy for a volume of uniformly dense material?

Qmechanic♦

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asked Apr 11 at 2:30

TaeNyFan

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$\begingroup$ Mathematicians: researchgate.net/publication/… Physicists: “It’s obvious!” :) $\endgroup$ – G. Smith Apr 11 at 3:15
$\begingroup$ Possible duplicate: physics.stackexchange.com/q/107584/2451 $\endgroup$ – Qmechanic♦ Apr 11 at 4:54

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