行星运动轨迹的不同推导方法

The Different Methods to Deduct the Equation of the Planet Orbit

本文简略叙述前人的两种方法，即用变分法推导和求解质点运动微分方程，此外，作者用新途径──微分几何方法求解矢量式运动微分方程，从而得到行星轨迹曲线的曲率公式，并将此公式与前人所求公式作一个比较。同时运用此公式，求出地球同步卫星离地面的高度及第一宇宙速度。

This paper gives a brief account of 2 methods to deduct and solve thedifferential equation of the particle motion by variational deduction. The author also usesanew method, differential qcometry, to solve the differential vector equation of motionand, from this,the formula for the currature of the planet orbit is deducted and a com-parison between above mentioned formula and the one deducted before is made.By using the formula the author also deducted the height of the svnchronous satelliteand the first universal speed to show the practical value ofthe formula.