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Symmetry of planar four-body convex central configurations. (English) Zbl 1138.70006

Summary: We study the relationship between the masses and 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 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.

MSC:

70F10 \(n\)-body problems

Keywords:

equal masses
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