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Spiral Structures and Chaotic Scattering of Coorbital Satellites

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Abstract

The fractal nature of the transitions between two sets of orbits separated by heteroclinic or homoclinic orbits is well known. We analyze in detail this phenomenon in Hill's problem where one set of orbits corresponds to coorbital satellites exchanging semi-major axis after close encounter (horse-shoe orbits) and the other corresponds to orbits which do not exchange semi-major axis (passing-by orbits). With the help of a normalized approximation of the vicinity of unstable periodic orbits, we show that the fractal structure is intimately tied to a special spiral structure of the Poincaré maps. We show that each basin is composed of a few ‘well behaved’ areas and of an infinity of intertwined tongues and subtongues winding around them. This behaviour is generic and is likely to be present in large classes of chaotic scattering problems.

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Authors and Affiliations

  1. Département de Mathématique, University of Namur, 8, Rempart de la Vierge, B-5000, Namur, Belgium

    Jacques Henrard

  2. Departamento de Matemática A., University of Alicante, P.O. Box 99, E-03080, Alicante, Spain

    Juan F. Navarro

Authors
  1. Jacques Henrard
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  2. Juan F. Navarro
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Henrard, J., Navarro, J.F. Spiral Structures and Chaotic Scattering of Coorbital Satellites. Celestial Mechanics and Dynamical Astronomy 79, 297–314 (2001). https://doi.org/10.1023/A:1017536931038

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  • DOI: https://doi.org/10.1023/A:1017536931038

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