There is considerable literature on this question, and closely related variations. See:
- The Thompson problem: Which configurations of $n$ electrons on a sphere minimize the electrostatic potential energy?
- The Tammes problem: Which configurations of $n$ points on a sphere maximizes the smallest distance between any two points? Sometimes phrased as packing $n$ congruent circles on a sphere:
![DiskPacking][1]
(Image from [Paul Sutcliffe](http://www.maths.dur.ac.uk/~dma0pms/my-projects/proj4_1213.html).)