Apsidal corotation in mean motion resonance: the 55 Cancri system as an example

The inner two planets around 55 Cancri were found to be trapped in a 3 : 1 mean motion resonance (MMR). In this paper, we study the dynamics of this extrasolar 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 apsidal corotation, are found. Owing 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 apsidal corotation in this MMR and its influence on the stability of the system.