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The existence of families of periodic orbits in theN-body problem

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Abstract

It is proved that monoparametric families of periodic orbits of theN-body problem in the plane, for fixed values of all masses, exist in a rotating frame of reference whosex axis contains always two of the bodiesP 1 andP 2. A periodic motion of theN-body problem is obtained as a continuation ofN−2 symmetric periodic orbits of the circular restricted three-body problem whose periods are in integer dependence, by increasing the masses of the originallyN−2 massless bodiesP 3, ...,P k. The analytic continuation, for sufficiently small values of theN−2 bodiesP 3 ...P k and finite values for the masses ofP 1 andP 2 has been proved by the continuation method and the solution itself has been found explicitly to a linear approximation in the small masses. Also, the possible application of the above periodic orbits to the study of the Solar system and of stellar systems is mentioned.

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  1. University of Thessaloniki, Thessaloniki, Greece

    John D. Hadjidemetriou

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  1. John D. Hadjidemetriou
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Hadjidemetriou, J.D. The existence of families of periodic orbits in theN-body problem. Celestial Mechanics 16, 61–76 (1977). https://doi.org/10.1007/BF01235730

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