Periodic Orbits in the 3:2 Orbital Resonance and Their Stability

Periodic orbits in the external 3:2 orbital resonance are investigated in the context of the planar, elliptic restricted three-body problem. Differential continuation is employed to determine the location of such orbits. Their stability and periods of libration around them are also computed. Stable, nearly circular orbits for hypothetical small bodies are found in extrasolar planetary systems having a giant planet on a very eccentric orbit. These orbits cross the orbit of the giant planet, but the 3:2 orbital resonance keeps them safely apart in a configuration analogous to that of Neptune and Pluto.