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

Ask Question

Asked 9 months ago

Active 9 months ago

Viewed 29 times

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♦

142k19 gold badges327 silver badges1677 bronze badges

asked Apr 11 '20 at 2:30

TaeNyFan

2,7793 silver badges30 bronze badges

2

$\begingroup$ Mathematicians: researchgate.net/publication/… Physicists: “It’s obvious!” :) $\endgroup$ – G. Smith Apr 11 '20 at 3:15
$\begingroup$ Possible duplicate: physics.stackexchange.com/q/107584/2451 $\endgroup$ – Qmechanic♦ Apr 11 '20 at 4:54

add a comment |

0 Browse other questions tagged newtonian-gravity lagrangian-formalism potential-energy variational-principle variational-calculus or ask your own question.