Astronomy and Astrophysics – Astrophysics – Earth and Planetary Astrophysics
Scientific paper
2009-02-03
Celest.Mech.Dyn.Astron.103:267-279, 2009
Astronomy and Astrophysics
Astrophysics
Earth and Planetary Astrophysics
15 pages, 3 figures, accepted for publication in Celestial Mechanics and Dynamical Astronomy (January 28, 2009)
Scientific paper
10.1007/s10569-009-9191-8
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.
Bois Eric
Gayon Julie
Scholl Hans
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