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A two-parameter survey of periodic orbits in the restricted problem of three bodies

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Abstract

Within the context of the restricted problem of three bodies, we wish to show the effects, caused by varying the mass ratio of the primaries and the eccentricity of their orbits, upon periodic orbits of the infinitesimal mass that are numerical continuations of circular orbits in the ordinary problem of two bodies. A recursive-power-series technique is used to integrate numerically the equations of motion as well as the first variational equations to generate a two-parameter family of periodic orbits and to identify the linear stability characteristics thereof. Seven such families (comprised of a total of more than 2000 orbits) with equally spaced mass ratios from 0.0 to 1.0 and eccentricities of the orbits of the primaries in a range 0.0 to 0.6 are investigated. Stable orbits are associated with large distances of the infinitesimal mass from the perturbing primary, with nearly circular motion of the primaries, and, to a slightly lesser extent, with small mass ratios of the primaries.

Conversely, unstable orbits for the infinitesimal mass are associated with small distances from the perturbing primary, with highly elliptic orbits of the primaries, and with large mass ratios.

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Authors and Affiliations

  1. Dept. of Astronomy, University of Texas, Austin, Tex., USA

    Peter J. Shelus

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  1. Peter J. Shelus
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Shelus, P.J. A two-parameter survey of periodic orbits in the restricted problem of three bodies. Celestial Mechanics 5, 483–489 (1972). https://doi.org/10.1007/BF01464774

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  • DOI: https://doi.org/10.1007/BF01464774

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