About the dynamics of the evection resonance

¹ Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE), Observatoire de Paris, UMR 8028, Avenue Denfert-Rochereau, 75014 Paris, France e-mail: frouard@imcce.fr
² Université de Lille 1, LAL-IMCCE, UMR 8028, 59000 Lille, France e-mail: [Marc.Fouchard;Alain.Vienne]@univ-lille1.fr

Received: 31 July 2009
Accepted: 10 November 2009

Abstract

Context. The evection resonance appears to be the outermost region of stability for prograde satellite orbiting a planet, the critical argument of the resonance indeed being found librating in regions surrounded only by chaotic orbits. The dynamics of the resonance itself is thus of great interest for the stability of satellites, but its analysis by means of an analytical model is not straightforward because of the high perturbations acting on the dynamical region of interest.

Aims. It is thus important to show the results and the limits inherent in analytical models. We use numerical methods to test the validity of the models and analyze the dynamics of the resonance.

Methods. We use an analytical method based on a classical averaged expansion of the disturbing function valid for all eccentricities as well as numerical integrations of the motion and surfaces of section.

Results. By comparing analytical and numerical methods, we show that aspects of the true resonant dynamic can be represented by our analytical model in a more accurate way than previous approximations, and with the help of the surfaces of section we present the exact location and dynamics of the resonance. We also show the additional region of libration of the resonance that can be found much closer to the planet due to its oblateness.