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Celestial Mechanics and Dynamical Astronomy

, Volume 109, Issue 1, pp 27–43 | Cite as

On the central configurations of the planar 1 + 3 body problem

  • Montserrat Corbera
  • Josep Maria Cors
  • Jaume Llibre
Original Article

Abstract

We consider the Newtonian four-body problem in the plane with a dominat mass M. We study the planar central configurations of this problem when the remaining masses are infinitesimal. We obtain two different classes of central configurations depending on the mutual distances between the infinitesimal masses. Both classes exhibit symmetric and non-symmetric configurations. And when two infinitesimal masses are equal, with the help of extended precision arithmetics, we provide evidence that the number of central configurations varies from five to seven.

Keywords

1 + 3 body problem Central configurations Coorbital satellites 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Montserrat Corbera
    • 1
  • Josep Maria Cors
    • 2
  • Jaume Llibre
    • 3
  1. 1.Departament de Tecnologies Digitals i de la InformacióUniversitat de VicVic, BarcelonaSpain
  2. 2.Matemàtica Aplicada IIIUniversitat Politècnica de CatalunyaManresa, BarcelonaSpain
  3. 3.Departament de MatemàtiquesUniversitat Autònoma de Barcelona, BellaterraBarcelonaSpain

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