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Global Bifurcations of Periodic Solutions of the Restricted Three Body Problem

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Abstract

We describe global bifurcations from the libration points of non-stationary periodic solutions of the restricted three body problem. We show that the only admissible continua of non-stationary periodic solutions of the planar restricted three body problem, bifurcating from the libration points, can be the short-period families bifurcating from the Lagrange equilibria L μ4 , L μ5 . We classify admissible continua and show that there are possible exactly six admissible continua of non-stationary periodic solutions of the planar restricted three body problem. We also characterize admissible continua of non-stationary periodic solutions of the spatial restricted three body problem. Moreover, we combine our results with the Déprit and Henrard conjectures (see [8]), concerning families of periodic solutions of the planar restricted three body problem, and show that they can be formulated in a stronger way. As the main tool we use degree theory for SO(2)-equivariant gradient maps defined by the second author in [25].

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Authors and Affiliations

  1. Institute of Astronomy, University of Zielona Góra, Podgórna 50, 65-246, Zielona Góra, Poland

    A. J. Maciejewski

  2. Faculty of Mathematics and Computer Science, Nicolaus, Copernicus University, PL-87-100, Toruń, ul. Chopina 12/18, Poland

    S. M. Rybicki

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  1. A. J. Maciejewski
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  2. S. M. Rybicki
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Maciejewski, A.J., Rybicki, S.M. Global Bifurcations of Periodic Solutions of the Restricted Three Body Problem. Celestial Mechanics and Dynamical Astronomy 88, 293–324 (2004). https://doi.org/10.1023/B:CELE.0000017193.10060.ac

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