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On relative periodic solutions of the planar general three-body problem

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Abstract

We describe two relatively simple reductions to order 6 for the planar general three-body problem. We also show that this reduction leads to the distinction between two types of periodic solutions: absolute or relative periodic solutions. An algorithm for obtaining relative periodic solutions using heliocentric coordinates is then described. It is concluded from the periodicity conditions that relative periodic solutions must form families with a single parameter. Finally, two such families have been obtained numerically and are described in some detail.

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  1. R. Broucke (Visiting Associate Professor)

    Present address: University of Texas, Texas, USA

Authors and Affiliations

  1. Jet Propulsion Laboratory, Pasadena, Calif., USA

    R. Broucke (Visiting Associate Professor)

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  1. R. Broucke
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Broucke, R. On relative periodic solutions of the planar general three-body problem. Celestial Mechanics 12, 439–462 (1975). https://doi.org/10.1007/BF01595390

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  • DOI: https://doi.org/10.1007/BF01595390

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