EDP Sciences
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Volume 432, Number 3, March IV 2005
Page(s) 1115 - 1129
Section Celestial mechanics and astrometry
DOI http://dx.doi.org/10.1051/0004-6361:20041483

A&A 432, 1115-1129 (2005)
DOI: 10.1051/0004-6361:20041483

Families of periodic horseshoe orbits in the restricted three-body problem

E. Barrabés1 and S. Mikkola2

1  Dept. Informàtica i Matemàtica Aplicada, Universitat de Girona, Avd. LLuís Santaló s/n 17071 Girona, Spain
    e-mail: barrabes@ima.udg.es
2  Tuorla Observatory, University of Turku, 21500, Piikkiö, Finland
    e-mail: mikkola@utu.fi

(Received 17 June 2004 / Accepted 15 November 2004)

We compute families of symmetric periodic horseshoe orbits in the restricted three-body problem. Both the planar and three-dimensional cases are considered and several families are found. We describe how these families are organized as well as the behavior along and among the families of parameters such as the Jacobi constant or the eccentricity. We also determine the stability properties of individual orbits along the families. Interestingly, we find stable horseshoe-shaped orbit up to the quite high inclination of $17^\circ$.

Key words: celestial mechanics

© ESO 2005