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.

15 pages, 3 figures, accepted for publication in Celestial Mechanics and Dynamical Astronomy (January 28, 2009)

References in corpus (8)

• Formation of Hot Planets by a combination of planet scattering, tidal circularization, and Kozai mechanism
• Secular Evolution of Hierarchical Planetary Systems
• Modeling the 3--D Secular Planetary Three-Body Problem. Discussion on the outer $\upsilon$ Andromedae Planetary System
• The Apsidal Antialignment of the HD 82943 System
• The Secular Evolution and Dynamical Architecture of the Neptunian Triplet Planetary System HD 69830
• Are retrograde resonances possible in multi-planet systems?
• Conditions of Dynamical Stability for the HD 160691 Planetary System
• Retrograde resonances in compact multi-planetary systems: a feasible stabilizing mechanism

Cited by in corpus (8)

• The Planet Nine Hypothesis
• Retrograde resonance in the planar three-body problem
• Stability of prograde and retrograde planets in circular binary systems
• Transit Timing Variations for Inclined and Retrograde Exoplanetary Systems
• On fitting planetary systems in counter-revolving configurations
• Dynamic portrait of the retrograde 1:1 mean motion resonance
• Kozai-Lidov Mechanism inside Retrograde Mean Motion Resonances
• Secular resonances between bodies on close orbits II: prograde and retrograde orbits for irregular satellites