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

Abstract

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 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barrabés, E.: 2001, 'Òrbites de segona espcie del problema espacial de 3 cossos', PhD Thesis, Universitat Autònoma de Barcelona.Google Scholar
  2. Font, J., Nunes, A. and Simó, C.: 2001, 'Successive quasi-collisions in the planar circular RTBP', Nonlinearity (to appear).Google Scholar
  3. Perko, L.: 1996, Differential Equations and Dynamical Systems, 2nd edn, Springer-Verlag, New York.Google Scholar
  4. Szebehely, V.: 1967, Theory of Orbits. The Restricted Problem of Three Bodies, Academic Press.Google Scholar
  5. Yen, C.: 1985, 'Ballistic mercury orbiter mission via Venus and Mercury gravity assists', AAS/AIAA Astrodynamics Specialist Conference, Paper AAS 85uu346.Google Scholar

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

Personalised recommendations