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New stacked central configurations for the planar 5-body problem

Celestial Mechanics and Dynamical Astronomy volume 110, pages 43–52 (2011)Cite this article

Abstract

A stacked central configuration in the n-body problem is one that has a proper subset of the n-bodies forming a central configuration. In this paper we study the case where three bodies with masses m 1, m 2, m 3 (bodies 1, 2, 3) form an equilateral central configuration, and the other two with masses m 4, m 5 are symmetric with respect to the mediatrix of the segment joining 1 and 2, and they are above the triangle generated by {1, 2, 3}. We show the existence and non-existence of this kind of stacked central configurations for the planar 5-body problem.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Catalonia, Spain

    Jaume Llibre

  2. Instituto de Ciências Exatas, Universidade Federal de Itajubá, Av. BPS 1303, Pinheirinho, CEP 37.500-903, Itajubá, MG, Brazil

    Luis Fernando Mello

  3. Departamento de Matemáticas, UAM-Iztapalapa, A.P. 55534, 09340, Iztapalapa, Mexico, D.F., Mexico

    Ernesto Perez-Chavela

Authors
  1. Jaume Llibre
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  2. Luis Fernando Mello
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  3. Ernesto Perez-Chavela
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Correspondence to Jaume Llibre.

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Llibre, J., Mello, L.F. & Perez-Chavela, E. New stacked central configurations for the planar 5-body problem. Celest Mech Dyn Astr 110, 43–52 (2011). https://doi.org/10.1007/s10569-011-9342-6

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  • DOI: https://doi.org/10.1007/s10569-011-9342-6

Keywords

  • Planar central configurations
  • n-body problem
  • Stacked central configurations
  • 5-body problem