The apsidal corotation in mean motion resonance: the 55 Cancri as an example

Abstract

The inner two planets around the 55 Cancri were found to be trapped in the 3:1 mean motion resonance. In this paper, we study the dynamics of this extra-solar planetary system. Our numerical investigation confirms the existence of the 3:1 resonance and implies a complex orbital motion. Different stable motion types, with and without the apsidal corotation, are found. Due to the high eccentricities in this system, we apply a semi-analytical method based on a new expansion of the Hamiltonian of the planar three-body problem in the discussion. We analyse the occurrence of the apsidal corotation in this mean motion resonance and its influence on the stability of the system.

8 pages, 9 figures. Revised version for submitting to MNRAS

References in corpus (5)

• Extrasolar Planets in Mean-Motion Resonance: Apses Alignment and Asymmetric Stationary Solutions
• On the migration of a system of protoplanets
• Possible Commensurabilities Among Pairs of Extrasolar Planets
• Could the 55 Cancri Planetary System Really Be in the 3:1 Mean Motion Resonance?
• Dynamical Evolution of Planets in Disks

Cited by in corpus (9)

• Planetary Migration and Extrasolar Planets in the 2/1 Mean-Motion Resonance
• The 55 Cancri Planetary System: Fully Self-Consistent N-body Constraints and a Dynamical Analysis
• Stability Limits in Resonant Planetary Systems
• On the Stability of Test Particles in Extrasolar Multiple Planet Systems
• Simulations for Terrestrial Planets Formation
• The Dynamical Architecture and Habitable Zones of the Quintuplet Planetary System 55 Cancri
• Formation and transformation of the 3:1 mean-motion resonance in 55 Cancri System
• Secular evolution of resonant small bodies: semi-analytical approach for arbitrary eccentricities in the coplanar case
• Continuation of periodic orbits in two-planet resonant systems