Celestial Mechanics and Dynamical Astronomy

, Volume 121, Issue 2, pp 191–210 | Cite as

Transport orbits in an equilateral restricted four-body problem

Original Article


In this paper we consider a restricted equilateral four-body problem where a particle of negligible mass is moving under the Newtonian gravitational attraction of three masses (called primaries) which move on circular orbits around their center of masses such that their configuration is always an equilateral triangle (Lagrangian configuration). We consider the case of two bodies of equal masses, which in adimensional units is the parameter of the problem. We study numerically the existence of families of unstable periodic orbits, whose invariant stable and unstable manifolds are responsible for the existence of homoclinic and heteroclinic connections, as well as of transit orbits traveling from and to different regions. We explore, for three different values of the mass parameter, what kind of transits and energy levels exist for which there are orbits with prescribed itineraries visiting the neighborhood of different primaries.


Lagrangian configuration Four-body problem Invariant manifolds  Transfer orbits Homoclinic and heteroclinic connections 



M. Alvarez-Ramírez is supported by the project grant Red de cuerpos académicos Ecuaciones Diferenciales. Proyecto sistemas dinámicos y estabilización. PROMEP 2011–SEP Mexico. E. Barrabés is supported by the Grants MTM2010-16425, MTM2013-41168, and 2014 SGR 1145.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Departamento de MatemáticasUAM–IztapalapaMexicoMexico
  2. 2.Departament d’Informàtica, Matemàtica Aplicada i Estadística Campus Montilivi, Universitat de GironaGironaSpain

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