卫星相对运动的新解法

A New Approach to Relative Motion Between Two Satellites

卫星相对运动的研究在航天飞行中有着较为广泛的应用价值。Ｃ－ Ｗ的解对于计算两星近距离的相对运动是很有效的， 但是， 当两星距离变大时其误差就不断地放大。文章采用一种新解法： 首先建立相对运动的解析关系； 然后利用椭圆运动的结果导出三维的近似分析解。它可以精确到偏心率和倾角差的一阶项， 而且不再包括长期误差。理论分析和数值检验的结果表明， 整个新的解的精度大大高于Ｃ－ Ｗ 解的精度。

A study of the relative motion of satellites is widely applied in the area of spaceflight.The earliest way to solve this problem is to establish the relative motion equation and to have its linear approximate solution.That is the well kmown C W method which is very efficient and accurate as two bodies are closer,but the error would grow up rapidly as time goes on.The reason of error grown is the omitting an acceleration term,which causes the solution including a linear term with time,when linearizing the motion equation.An approximate analytical solution for three dimension is derived by establishing an analytical relation of relative motion and then using the exact results of elliptical motion.The solution is accurate to first order in the eccentricity and inclination difference and including no long term errors.The numerical testing is also presented in comparing with the exact solution and the result shows that the new solution is much more accurate than C W solution.