Celestial Mechanics and Dynamical Astronomy

, Volume 93, Issue 1–4, pp 87–100 | Cite as

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



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 → − ∞.


Hill’s problem numerical integration periodic orbits second species families 


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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Observatoire de la Côte d’AzurC.N.R.S.Nice Cedex 4France

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