关键词: 航天器, 相对运动, 数学模型, 误差分析, 方法

Abstract: 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.