Mean motion resonances at high eccentricities: the 2:1 and the 3:2 interior resonances

Mean motion resonances [MMRs] play an important role in the formation and evolution of planetary systems and have significantly influenced the orbital properties and distribution of planets and minor planets in the solar system as well as exo-planetary systems. Most previous theoretical analyses have focused on the low-to-moderate eccentricity regime, but with new discoveries of high eccentricity resonant minor planets and even exoplanets, there is increasing motivation to examine MMRs in the high eccentricity regime. Here we report on a study of the high eccentricity regime of MMRs in the circular planar restricted three-body problem. Non-perturbative numerical analyses of the 2:1 and the 3:2 interior resonances are carried out for a wide range of secondary-to-primary mass ratio, and for a wide range of eccentricity of the test particle. The surface-of-section technique is used to study the phase space structure near resonances. We identify transitions in phase space at certain critical eccentricities related to the geometry of resonant orbits; new stable libration zones appear at high eccentricity at libration centers shifted from those at low eccentricities. We present novel results on the mass and eccentricity dependence of the resonance libration centers and their widths in semi-major axis. Our results show that MMRs have sizable libration zones at high eccentricities, comparable to those at lower eccentricities.