Abstract
We integrate the orbital solutions of the planets orbiting 55 Cancri. In the simulations, we find that not only do the three resonant arguments θ1 = λ1 - 3λ2 + 21, θ2 = λ1 - 3λ2 + 22, and θ3 = λ1 - 3λ2 + (1 + 2) librate, respectively, but the relative apsidal longitude Δω 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 for 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.
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