Dynamics of planets in retrograde mean motion resonance
Abstract
In a previous paper (Gayon & Bois 2008a), we have shown the general efficiency of retrograde resonances for stabilizing compact planetary systems. Such retrograde resonances can be found when two-planets of a three-body planetary system are both in mean motion resonance and revolve in opposite directions. For a particular two-planet system, we have also obtained a new orbital fit involving such a counter-revolving configuration and consistent with the observational data. In the present paper, we analytically investigate the three-body problem in this particular case of retrograde resonances. We therefore define a new set of canonical variables allowing to express correctly the resonance angles and obtain the Hamiltonian of a system harboring planets revolving in opposite directions. The acquiring of an analytical "rail" may notably contribute to a deeper understanding of our numerical investigation and provides the major structures related to the stability properties. A comparison between our analytical and numerical results is also carried out.
Keywords
Cite
@article{arxiv.0902.0428,
title = {Dynamics of planets in retrograde mean motion resonance},
author = {Julie Gayon and Eric Bois and Hans Scholl},
journal= {arXiv preprint arXiv:0902.0428},
year = {2009}
}
Comments
15 pages, 3 figures, accepted for publication in Celestial Mechanics and Dynamical Astronomy (January 28, 2009)