Differential Apsidal Precession in Mean Motion Resonant Planetary Systems

In this poster, we consider first order, coplanar mean motion resonances (MMRs) between two planets orbiting a central primary. The corresponding resonance angles are a linear combination of the two planets’ mean longitudes and their longitudes of perihelion. In real exoplanet systems, MMR planet pairs can be perturbed by various physical effects, such as secular precession from giant planetary companions or nodal precession due to an oblate star. For the case of a massive perturber on a circular orbit, differential apsidal precession between the two planets “splits” their resonant angles. To study this effect, we parametrize the effective differential precession rate and then investigate the effects of resonance splitting through time-dependent integrations of the interaction Hamiltonian. We begin with the test particle treatment of the problem and then present our results for comparable mass planets.