There is considerable literature on this question, and closely related variations.
See: 

 - The [*Thompson problem*](https://en.wikipedia.org/wiki/Thomson_problem): Which configurations of $n$ electrons on a sphere minimize the electrostatic potential energy?
 - The [*Tammes problem*](https://en.wikipedia.org/wiki/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:

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![DiskPacking][1]
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(Image from [Paul Sutcliffe](http://www.maths.dur.ac.uk/~dma0pms/my-projects/proj4_1213.html).)
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[1]: https://i.sstatic.net/fxBXg.jpg