Abstract
According to statistics of planetary period ratios in multi-planet extrasolar systems, evident excesses appear just over the exact integral ratios 2:1 and 3:2, while deficits exist on the near left side. There are various dynamical explanations for the phenomenon. For three observed planets in Kepler-9 system, the period ratio of the planet b and c approximately equals to 2.03, which cause this planet pair as a typical sample close to the 2:1 resonance. For two situations where secular interactions are considered only and resonance perturbations are added in, we applied Hamiltonian functions with second-order eccentricity terms to provide positions of current orbital configurations located in the level curves of energy as well as surfaces of section, then discussed the probable near resonance configurations of the two planets.
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