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Families of periodic orbits in the planar three-body problem

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Abstract

A periodic orbit of the restricted circular three-body problem, selected arbitrarily, is used to generate a family of periodic motions in the general three-body problem in a rotating frame of reference, by varying the massm 3 of the third body. This family is continued numerically up to a maximum value of the mass of the originally small body, which corresponds to a mass ratiom 1:m 2:m 3≃5:5:3. From that point on the family continues for decreasing massesm 3 until this mass becomes again equal to zero. It turns out that this final orbit of the family is a periodic orbit of the elliptic restricted three body problem. These results indicate clearly that families of periodic motions of the three-body problem exist for fixed values of the three masses, since this continuation can be applied to all members of a family of periodic orbits of the restricted three-body problem. It is also indicated that the periodic orbits of the circular restricted problem can be linked with the periodic orbits of the elliptic three-body problem through periodic orbits of the general three-body problem.

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Authors and Affiliations

  1. University of Thessaloniki, Thessaloniki, Greece

    John D. Hadjidemetriou & Th. Christides

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  1. John D. Hadjidemetriou
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  2. Th. Christides
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Hadjidemetriou, J.D., Christides, T. Families of periodic orbits in the planar three-body problem. Celestial Mechanics 12, 175–187 (1975). https://doi.org/10.1007/BF01230210

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  • DOI: https://doi.org/10.1007/BF01230210

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