Secular Perturbations near Mean Motion Resonances

Abstract

In this work we attempt to make progress into assessing the importance of secular interactions between planetary satellites. In recent years, discrepancies have been observed in the expected positions of small planetary satellites (Bosh & Rivkin, 1996; Roddier et al., 1998). The existing ephemerides-producing algorithms for these objects assume fixed, elliptical and inclined orbits whose rate of precession is determined by oblateness alone. Even though the masses of these satellites are quite small relative to the planet (∼ 10−9 – 10−10) their small mutual separations and the existence of much larger satellites further out leaves open the possibility that in some cases at least the fixed-orbit assumption is only a crude approximation to reality. Two important dynamical mechanisms through which these orbits may evolve are resonant or secular interactions. In order to explore the possibility of the latter we have set up a simple planar system where an satellite in a circular orbit around a spherical planet is perturbing a massless particle which moves in proximity to various mean motion resonances. We aim to examine the effect of the resonance on the particle’s reference orbit by measuring the secular frequency. The effects of oblateness have not been taken into account as they are adequately modeled by orbit-fitting theories and can thus be readily subtracted.