行星会合指数与行星系质心的日心经度模型构建及数值模拟

Modeling of the planet juncture index and heliocentric longitude of the centroid of planetary systems and numerical simulation

本文根据太阳系各行星运动参数构建了行星系日心经度运动学方程,利用行星系质心日心经度的变化规律探讨太阳绕太阳系质心运动的周期性规律.通过对行星系质心日心经度运动学方程进行数值模拟发现,太阳绕太阳系质心运动存在明显的11.5年的周期;同时对行星系日心经度运动学方程和行星会合指数运动学方程进行数值模拟,获得了太阳质心与太阳系质心相互运动的轨迹,数值模拟结果显示太阳与太阳系质心的相互运动轨迹具有11.5年的周期;同时,通过对1000年来太阳系质心与太阳本体位置关系的统计,发现太阳在绕太阳系质心运动过程中,太阳系质心位于太阳本体内的时间约占全程时间的三分之一.

In this article, the kinematic equation of the heliocentric longitude was created based on the orbital elements of the planets in the solar system, which can be used to investigate the periodic movement of the sun around the mass center of the solar system. The sidereal period of the Sun around the centroid of solar system was obtained as 11.5 years by the way of numerical simulation. Both of the kinematic equation of the heliocentric longitude and the kinematic equation of the planet juncture index were studied by simulation. Then, both of the trajectory of the Sun around the solar system barycenter and the cycle of 11.5 years were also obtained by numerical simulation. On analysis of the date of the positions between the Sun and the solar system barycenter for 1000 years, we found that about one-third of the time of the centroid of solar system was in the body of the Sun during the track.