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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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