Dynamics of planets in retrograde mean motion resonance

作者：Gayon Julie^*; Bois Eric; Scholl Hans

来源：Celestial Mechanics and Dynamical Astronomy, 2009, 103(3): 267-279.

DOI：10.1007/s10569-009-9191-8

• Hamiltonian systems
• Planetary systems
• Resonance
• Periodic orbits
• Retrograde planets
• Resonant average
• Hamiltonian

In a previous paper (Gayon and 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.

• 出版日期2009-3