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Chaotic scattering in the restricted three-body problem I. The Copenhagen problem

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Abstract

We consider the scattering motion of the planar restricted three-body problem with two equal masses on a circular orbit. Using the methods of chaotic scattering we present results on the structure of scattering functions. Their connection with primitive periodic orbits and the underlying chaotic saddle are studied. Numerical evidence is presented which suggests that in some intervals of the Jacobi integral the system is hyperbolic. The Smale horseshoe found there is built from a countable infinite number of primitive periodic orbits, where the parabolic orbits play a fundamental role.

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Author notes

  1. L. Benet

    Present address: Lab. Cuernavaca, Instituto de Física, National University of México (UNÁM), A. P. 139-B, MEX-62191, Cuernavaca, Mexico

Authors and Affiliations

  1. Institut für theoretische Physik, Universität Basel, Klingelbergstr 82, CH-4056, Basel, Switzerland

    L. Benet & D. Trautmann

  2. Lab. Cuernavaca, Instituto de Física, National University of México (UNÁM), A. P. 139-B, MEX-62191, Cuernavaca, Mexico

    T.H. Seligman

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  1. L. Benet
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  2. D. Trautmann
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  3. T.H. Seligman
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Benet, L., Trautmann, D. & Seligman, T. Chaotic scattering in the restricted three-body problem I. The Copenhagen problem. Celestial Mech Dyn Astr 66, 203–228 (1996). https://doi.org/10.1007/BF00054965

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