Periodic Solutions of CircularElliptic Type in the Planar NBody Problem
Abstract
Letn≥2 mass points with arbitrary masses move circularly on a rotating straightline centralconfiguration; i.e. on a particular solution of relative equilibrium of thenbody problem. Replacing one of the mass points by a close pair of mass points (with mass conservation) we show that the resultingNbody problem (N=n+1) has solutions, which are periodic in a rotating coordinate system and describe precessing nearlyelliptic motion of the binary and nearlycircular collinear motion of its center of mass and the other bodies; assuming that also the mass ratio of the binary is small.
 Publication:

Celestial Mechanics
 Pub Date:
 May 1978
 DOI:
 10.1007/BF01228956
 Bibcode:
 1978CeMec..17..331A
 Keywords:

 Circular Orbits;
 Equations Of Motion;
 Many Body Problem;
 Orbit Perturbation;
 Determinants;
 Ellipses;
 Periodic Functions;
 Transformations (Mathematics);
 Astronomy