Periodic Motion and Stability of Gravitational Planar Triple Systems

摘要

The stability of gravitational triple systems is a well known problem in celestial mechanics. The basic model used is the general three body problem. Many criteria estimated from the integrals of motion and zero velocity curves or from purely numerical simulations have been given in literature. In this paper we propose a different approach for the study of stability of triple systems based on the numerical computation of manifolds of periodic orbits and their linear stability. Such an approach has been used for the study of two-planet exosolar systems but here, applying the method of continuation with respect to the masses, we refer to systems where all bodies can have similar mass values. In the present work we apply the proposed approach by starting from the circular family of periodic orbits, which is known to exist for the planetary type problem, and we restrict our computations to the case of two equal masses. By considering that the system has a hierarchical structure, the constructed manifold of periodic solutions can be projected on a plane defined by the relative distance and the relative mass of the system. On such a plane a stability map can be constructed showing the stability limits on the manifold of periodic orbits.