A spherical planet of radius $R$ is inhabited by $n\ge 2$ aliens. Due to the emergence of a novel deadly virus, the aliens must practice social distancing, staying away as far as possible of each other. What is the maximum distance that can be achieved in terms of $R$ and $n$?
If Euclidean distance is used (not Geodesic), the answer for $n=2,3,4$ the answer should be $2R$, $\frac{R}{\sqrt{3}}$, and $\frac{R\sqrt{6}}{4}$ respectively.
Note: this problem is about maximum distance to the nearest neighbor, not about total distance, as wrongly marked as a duplicate.