Celestial Mechanics and Dynamical Astronomy

, Volume 52, Issue 2, pp 107–146 | Cite as

Second-species solutions in the circular and elliptic restricted three-body problem

I. Existence and asymptotic approximation
  • Gerard Gomez
  • Merce Olle
Article
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Accepted:

Abstract

An analytical proof of the existence of some kinds of periodic orbits of second species of Poincaré, both in the Circular and Elliptic Restricted three-body problem, is given for small values of the mass parameter. The proof uses the asymptotic approximations for the solutions and the matching theory developed by Breakwell and Perko. In the paper their results are extended to the Elliptic problem and applied to prove the existence of second-species solutions generated by rectilinear ellipses in the Circular problem and nearly-rectilinear ones in the Elliptic case.

Key words

Elliptic problem circular problem restricted problem second-species solutions asymptotic approximations 
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Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Gerard Gomez
    • 1
  • Merce Olle
    • 2
  1. 1.Departament de Matemática Aplicada i AnálisiUniversitat de BarcelonaBarcelonaSpain
  2. 2.Departament de Matemática AplicadaUniversitat Politècnica de CatalunyaBarcelonaSpain

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