A family of periodic solutions of the planar threebody problem, and their stability
Abstract
We describe a oneparameter family of periodic orbits in the planar problem of three bodies with equal masses. This family begins with Schubart's (1956) rectilinear orbit and ends in retrograde revolution, i.e. a hierarchy of two binaries rotating in opposite directions. The firstorder stability of the orbits in the plane is also computed. Orbits of the retrograde revolution type are stable; more unexpectedly, orbits of the ‘interplay’ type at the other end of the family are also stable. This indicates the possible existence of triple stars with a motion entirely different from the usual hierarchical arrangement.
 Publication:

Celestial Mechanics
 Pub Date:
 May 1976
 DOI:
 10.1007/BF01228647
 Bibcode:
 1976CeMec..13..267H
 Keywords:

 Orbital Mechanics;
 Periodic Functions;
 Stellar Motions;
 Three Body Problem;
 Angular Momentum;
 Motion Stability;
 Orbit Perturbation;
 Triple Stars;
 Astronomy