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Periodic solutions of the third sort for restricted problem of three bodies and their stability

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Abstract

In this paper periodic solutions of the third sort for restricted problem of three bodies in the three-dimensional space are derived numerically by starting from generating solutions obtained by one of the authors (1969) and by increasing the mass-ratio of the two primaries stepwise from zero to about 1000 for 2∶1, 3∶2 and 6∶1 cases of commensurable mean motions. Periodic solutions both for circular and elliptic orbits of the primaries are obtained.

The stability of the periodic solutions for the 2∶1 circular case is discussed and it is found that none of them is linearly stable.

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Authors and Affiliations

  1. Tokyo Astronomical Observatory, Mitaka, Tokyo, Japan

    Yoshihide Kozai & Hiroshi Kinoshita

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  1. Yoshihide Kozai
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  2. Hiroshi Kinoshita
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Kozai, Y., Kinoshita, H. Periodic solutions of the third sort for restricted problem of three bodies and their stability. Celestial Mechanics 7, 156–176 (1973). https://doi.org/10.1007/BF01229945

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  • DOI: https://doi.org/10.1007/BF01229945

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