Central configurations in spatial n-body problem for n = 5, 6 with equal masses

TL;DR

This paper provides a comprehensive computer-assisted classification of all central configurations in the spatial n-body problem for n=5 and 6 with equal masses, including symmetry details and counts near the equal mass case.

Contribution

It offers the first complete listing of central configurations for these cases, including symmetry analysis and counts for configurations close to equal masses.

Findings

Full list of central configurations for n=5,6 with equal masses

Symmetry classifications for each configuration

Exact counts of configurations near equal mass cases

Abstract

We present a computer assisted proof of the full listing of central configurations for spatial n-body problem for n = 5 and 6, with equal masses. For each central configuration we give a full list of its euclidean symmetries. For all masses sufficiently close to the equal masses case we give an exact count of configurations in the planar case for n = 4, 5, 6, 7 and in the spatial case for n = 4, 5, 6.