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Symmetry, bifurcation and stacking of the central configurations of the planar \(1+4\) body problem

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Abstract

In this work we are interested in the central configurations of the planar \(1+4\) body problem where the satellites have different infinitesimal masses and two of them are diametrically opposite in a circle. We can think of this problem as a stacked central configuration too. We show that the configurations are necessarily symmetric and the other satellites have the same mass. Moreover we prove that the number of central configurations in this case is in general one, two or three and, in the special case where the satellites diametrically opposite have the same mass, we prove that the number of central configurations is one or two and give the exact value of the ratio of the masses that provides this bifurcation.

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  1. Núcleo de Formação Docente, Universidade Federal de Pernambuco, Caruaru, PE, CEP 55002-970, Brazil

    Allyson Oliveira

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  1. Allyson Oliveira
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Correspondence to Allyson Oliveira.

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Oliveira, A. Symmetry, bifurcation and stacking of the central configurations of the planar \(1+4\) body problem. Celest Mech Dyn Astr 116, 11–20 (2013). https://doi.org/10.1007/s10569-013-9472-0

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  • DOI: https://doi.org/10.1007/s10569-013-9472-0

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