对有心力场中的行星轨迹问题，通过建立以复数矢量为变量的方程进行求解．在求解过程中不仅得到了行星运动的一般性规律，还推导出行星的速度公式和哈密顿定理，同时发现行星轨道的第二焦点位置及基于拉普拉斯-隆格-楞次矢量的轨迹方程，并由此求出不同方向发射卫星的轨迹包络线．

For the problem of planetary trajectory in a centered force field, it is solved by establishing equations with complex vectors as variables. In the process of solving, not only the general law of planetary motion is obtained, but also the speed formula of the planet and Hamilton's theorem are derived, and the second focus position of the planetary orbit and the trajectory based on the Laplace-Runge-Lenz vector are found, and thus the trajectory envelopes of satellites launched in different directions are obtained.