The Existence of Families of Periodic Orbits in the Threedimensional General Nbody Problem
Abstract
Summary. It is proved that monoparametric families of periodic orbits of the threedimensional general Nbody problem (NG), for fixed values of all masses, exist in a suitably defined rotating frame of reference whose xzplane always contains two of the bodies P1 and P2. These orbits are obtained as a continuation of N  2 symmetric periodic orbits of the threedimensional circular restricted threebody problem (3R) whose periods are in integer dependence, by increasing the masses of the N  2 mass less bodies Pa PN. Some numerical examples are given. Key words: general Nbody problem  three dimensions  families of periodic orbits
 Publication:

Astronomy and Astrophysics
 Pub Date:
 November 1978
 Bibcode:
 1978A&A....70..473M