Celestial Mechanics and Dynamical Astronomy

, Volume 84, Issue 4, pp 387–407 | Cite as

Spatial p-q Resonant Orbits of the RTBP

  • Esther Barrabés
  • Gerard Gómez


The purpose of this paper is to extend the study of the so called p-q resonant orbits of the planar restricted three-body problem to the spatial case. The p-q resonant orbits are solutions of the restricted three-body problem which have consecutive close encounters with the smaller primary. If E, M and P denote the larger primary, the smaller one and the infinitesimal body, respectively, then p and q are the number of revolutions that P gives around M and M around E, respectively, between two consecutive close approaches. For fixed values of p and q and suitable initial conditions on a sphere of radius μα around the smaller primary, we will derive expressions for the final position and velocity on this sphere for the orbits under consideration.

restricted three-body problem close encounters resonance 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Esther Barrabés
    • 1
  • Gerard Gómez
    • 2
  1. 1.Departament d'Informàtica i Matemàtica AplicadaUniversitat de GironaGironaSpain
  2. 2.IEEC & Departament de Matemàtica Aplicada i AnàlisiUniversitat de BarcelonaBarcelonaSpain

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