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

Asked Apr 11 '20 at 02:30

Active Apr 11 '20 at 04:52

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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?

edited Apr 11 '20 at 04:52

Qmechanic

asked Apr 11 '20 at 02:30

TaeNyFan

2

Mathematicians: https://www.researchgate.net/publication/261932086_A_Round_Ball_Uniquely_Minimizes_Gravitational_Potential_Energy Physicists: “It’s obvious!” :) – G. Smith Apr 11 '20 at 03:15
Possible duplicate: https://physics.stackexchange.com/q/107584/2451 – Qmechanic Apr 11 '20 at 04:54

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