Could the 55 Cancri Planetary System Really Be in the 3[rcolon]1 Mean Motion Resonance?

We integrate the orbital solutions of the planets orbiting 55 Cnc. In thesimulations, we find that not only three resonant arguments$\theta_{1}=\lambda_{1}-3\lambda_{2}+2\tilde\omega_{1}$,$\theta_{2}=\lambda_{1}-3\lambda_{2}+2\tilde\omega_{2}$ and$\theta_{3}=\lambda_{1}-3\lambda_{2}+(\tilde\omega_{1}+\tilde\omega_{2})$librate respectively, but the relative apsidal longitudes $\Delta\omega$ alsolibrates about $250^{\circ}$ for millions of years. The results imply theexistence of the 3:1 resonance and the apsidal resonance for the studiedsystem. We emphasize that the mean motion resonance and apsidal locking can actas two important mechanisms of stabilizing the system. In addition, we furtherinvestigate the secular dynamics of this system by comparing the numericalresults with those given by Laplace-Lagrange secular theory.Comment: 12 Pages, 4 figures, Published by ApJ Letters, 585, 2003 March 10 (Figures now included to match the publication