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

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

Abstract

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 .