  We study the relationship between the masses and the geometric properties of
central configurations. We prove that in the planar four-body problem, a convex
central configuration is symmetric with respect to one diagonal if and only if
the masses of the two particles on the other diagonal are equal. If these two
masses are unequal, then the less massive one is closer to the former diagonal.
Finally, we extend these results to the case of non-planar central
configurations of five particles.
