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Paper: The 3:1 Resonance in the 55 Cancri
Volume: 316, Order and Chaos in Stellar and Planetary Systems
Page: 155
Authors: Zhou, L.Y.; Lehto, H.J.; Zheng, J.Q.
Abstract: Twenty eight extra-solar planets are located in 13 “multiple planet systems”, and some of them are in mean motion resonances (MMR). Recently, the inner two planets around the 55 Cnc, with masses m1 = 0.83 MJupiter, m2 = 0.20 MJupiter and semimajor axes a1 = 0.115, a2 = 0.241 AU (Fischer et al. 2003), were found to be in a possible 3:1 MMR (Ji et al. 2003). The three resonant angles θ1 = λ1 - 3λ2 + 2ω1, θ2 = λ1 - 3λ2 + 2ω2, and θ3 = λ1 - 3λ2 + ω1 + ω2 may librate around certain values, and the difference between the two periastrons Δω = ω1 - ω2 may also be locked to a definite value. Our numerical integrations imply a complex orbital motion. Via a new expansion of the Hamiltonian of the planar three-body problem, we analyze the dynamics of this system.
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