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

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

2003-01-31

arxiv.org/abs/astro-ph/0301636v2

Astrophys.J. 585 (2003) L139-L142

Astronomy and Astrophysics

Astrophysics

12 Pages, 4 figures, Published by ApJ Letters, 585, 2003 March 10 (Figures now included to match the publication)

Scientific paper

10.1086/374391

We integrate the orbital solutions of the planets orbiting 55 Cnc. In the simulations, 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 $\Delta\omega$ also librates about $250^{\circ}$ 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.

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