Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free.

I have been searching on the Internet but have not found a derivation of the formula for the self gravitational potential energy of a sphere. Can someone show how to do this? I assume it involved 6 nested integrals (3 for each particle $dm$ and 3 for integrating the potential energy for all other particles).

share|improve this question

1 Answer 1

up vote 2 down vote accepted

No need to make it that complicated--calculate the potential at the surface of a sphere with a uniform mass distribution with mass $M$. Then calculate the energy required to add a bit of mass with mass $dm$ and radius $dr$ to the top of this sphere. Express $M$ and $dm$ in terms of $r$ and $dr$ and integrate.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.