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

Abstract

AbstractWe present a computer assisted proof of the full listing of central configurations for spatialn-body problem for$$n=5$$n=5and 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$$n=4,5,6,7$$n=4,5,6,7and in the spatial case for$$n=4,5,6$$n=4,5,6.