HD 82943行星系統的2:1共振與穩定性

It is mainly explored the secular dynamical evolution of the HD 82943 system, with two resonant giant planets, by simulating various planetary configurations through direct integrations, in the meantime, and also studied their orbital motions in phase space. In numerical integrations for 10^7 yr, it showed that those stable orbits are connected with the 2:1 resonance. Typically, there exists the libration of the two resonant arguments of θ1 and (or) θ2 on the same timescale. Hence, the variations of both semi-major axes of the planets can be greatly restricted to behave in regular modes, due to the confinement of the libration of the related angles. Moreover, by means of the analytical model for the semi-major axis which contains the effects of the eccentricity of the outer planet e2, it is again discussed the motion of the phase space of the inner planet dependence on various e2 and the relative apsidal longitudes θ, and showed that the 2:1 orbital resonance can be easily preserved when θ=0° for the relatively smaller e2, additionally, a moderate e2 results in deep locking into the resonance for two planets of this system. And the results by the analytical model is well consistent with the numerical outcomes, which both reveal the 2:1 resonant architecture.