Could the 55 Cnc Planetary System Really Be in the 3:1 Mean Motion Resonance?

Abstract

We integrate the orbital solutions of the planets orbiting 55 Cnc. In the simulations, we find that not only three resonant arguments θ1 = λ1 −3λ2 +2˜ω1, θ2 = λ1 − 3λ2 + 2˜ω2 and θ3 = λ1 − 3λ2 + (˜ω1 + ˜ω2) librate respectively, but the relative apsidal longitudes ∆ω also librates about 250 ◦ for millions of years. The results imply the existence of the 3:1 resonance and the apsidal resonance for the studied system. We emphasize that the mean motion resonance and apsidal locking can act as two important mechanisms of stabilizing the system. In addition, we further investigate the secular dynamics of this system by comparing the numerical results with those given by Laplace-Lagrange secular theory. Subject headings: methods:N-body simulations — celestial mechanics — planetary