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Periodic elliptic motions in a planar restricted (N+1)-body problem

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Abstract

LetN≧2 mass points (primaries) move on a collinear solution of relative equilibrium of theN-body problem; i.e. suitably fixed on a uniformly rotating straight line. Consider the motion of a massless particle in the gravitational field of these primaries with arbitrarily given masses. An existence proof for periodic solutions (i.e. closed trajectories in a rotating coordinate system) will be given, in which the particle performs nearly keplerian elliptic motions about (and close to) any one of the primaries.

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Authors and Affiliations

  1. Dept. of Mathematics, Vanderbilt University, Nashville, Tenn., U.S.A.

    R. F. Arenstorf

  2. Dept. of Mathematics, Morehouse College, Atlanta, Ga., U.S.A.

    R. E. Bozeman

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  1. R. F. Arenstorf
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  2. R. E. Bozeman
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Arenstorf, R.F., Bozeman, R.E. Periodic elliptic motions in a planar restricted (N+1)-body problem. Celestial Mechanics 16, 179–189 (1977). https://doi.org/10.1007/BF01228599

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  • DOI: https://doi.org/10.1007/BF01228599

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