卫星的运动学方程及其等时逐点轨迹

Kinematic equation of satellite and its isochronous point by point trajectory

文章根据卫星在极坐标系中的椭圆轨道方程和角动量守恒式,积分求得卫星的隐函数形式的运动学方程,并作出偏心率e=0.6时卫星的等时逐点轨迹图,以及卫星的极坐标r、θ随时间t的变化曲线图,指出在椭圆轨道与(右)正焦弦的交点处r随t变化最为迅速,即卫星的径向速度最大.文章所求得的运动学方程实际上是开普勒方程的另一种表达,但其推理过程更便于理解.文章所给较详细的积分过程及相关结论或可为相关内容的教与学提供参考.

According to the elliptic orbit equation and angular momentum conservation formula of satellite in polar coordinate system,the kinematic equation in the form of implicit function of the satellite is obtained by integration,and the isochronous point by point trajectory diagram,the change curve diagrams of polar coordinates r andθwith time t of the satellite with eccentricity e=0.6 are made.It is pointed out that r changes most rapidly with t at the intersection of the elliptical orbit and the right rectum,that is,the radial velocity of the satellite is the largest.The kinematic equation obtained in this paper is actually another expression of Kepler’s equation,but its reasoning process is easier to understand.The detailed integration process and relevant conclusions given in this paper may provide reference for the teaching and learning of relevant contents.