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Detection of close encounters and resonances in three-body problems through Levi-Civita regularization

Authors

  • E. Lega,

    Corresponding author
    1. Université de Nice Sophia Antipolis, CNRS UMR 6202, Observatoire de la Côte d’Azur, Bv. de l’Observatoire, BP 4229, 06304 Nice cedex 4, France
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  • M. Guzzo,

    Corresponding author
    1. Università degli Studi di Padova, Dipartimento di Matematica Pura ed Applicata via Trieste 63, 35121 Padova, Italy
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  • C. Froeschlé

    Corresponding author
    1. Université de Nice Sophia Antipolis, CNRS UMR 6202, Observatoire de la Côte d’Azur, Bv. de l’Observatoire, BP 4229, 06304 Nice cedex 4, France
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E-mail: elena@oca.eu (EL); guzzo@math.unipd.it (MG); claude@oca.eu (CF)

ABSTRACT

The detection and identification of resonances is a key ingredient in the studies of stability of dynamical systems, with important applications for our Solar as well as for extrasolar systems. In this paper we study the detection of resonances and close encounters in the three-body problem using the fast Lyapunov indicator method. In order to investigate the close encounters, we needed to adapt the method to the model and its singularities. Our technical improvement lies in computation of the solutions of the singular variational equations by measuring the divergence of close initial conditions. We have used the Levi-Civita regularization for the integration of the equations of motion. As an application of the method, we show that it provides a correct detection of the tube manifolds related to the Lagrangian point L1 of the Sun–Jupiter system.

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