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Families of Asymmetric Periodic Orbits in Hill’s Problem of Three Bodies

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Abstract

We present five families of periodic solutions of Hill’s problem which are asymmetric with respect to the horizontal ξ axis. In one of these families, the orbits are symmetric with respect to the vertical η axis; in the four others, the orbits are without any symmetry. Each family consists of two branches, which are mirror images of each other with respect to the ξ axis. These two branches are joined at a maximum of Γ, where the family of asymmetric periodic solutions intersects a family of symmetric (with respect to the ξ axis) periodic solutions. Both branches can be continued into second species families for Γ → − ∞.

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References

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Authors and Affiliations

  1. Observatoire de la Côte d’Azur, C.N.R.S., B.P. 4229, 06304, Nice Cedex 4, France

    Michel Hénon

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  1. Michel Hénon
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Correspondence to Michel Hénon.

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Hénon, M. Families of Asymmetric Periodic Orbits in Hill’s Problem of Three Bodies. Celestial Mech Dyn Astr 93, 87–100 (2005). https://doi.org/10.1007/s10569-005-3641-8

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  • DOI: https://doi.org/10.1007/s10569-005-3641-8

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