Periodic orbits of planets in binary systems

Abstract

Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of periodic orbits for planetary systems. The study is restricted to coplanar motion. Staring from known results of two-planet systems around single stars, we perform continuation of solutions with respect to the mass and approach periodic orbits of single planets in two-star systems. Also, families of periodic solutions can be computed for fixed masses of the primaries. When they are linearly stable, we can conclude about the existence of phase space domains of long-term orbital stability.