相邻两航天器相对运动近似方程的解析解及比动能方程

ANALYTICAL SOLUTION OF MOTION EQUATIONS AND EQUATION OF SPECIFIC KINETIC ENERGY FOR RELATIVE MOTION OF TWO NEAR SPACECRAFTS

在地心引力场中,当目标航天器沿近圆轨道作无动力运动时,与目标航天器相邻的受控航天器相对于目标航天器的运动可以近似地用Hill方程描述。文章给出了受控航天器对目标航天器运动的推力加速度随时间线性变化时Hill方程的解析解。并根据Hill方程导出了受控航天器相对目标航天器运动的比动能方程。还讨论了比动能方程在上述两航天器轨道相遇和轨道交会问题中的应用。

When a objective spacecraft (OS) moves along near circular orbit in unpowered flight, the relative motion of controlled spacecraft (CS) relatively to the OS is described approximately by the Hill equations on condition that the CS is near to the OS. The Hill equations are solved on the assumption that the thrust acceleration of the CS is the linear function of time.The equation of specitic kinetic energy (ESKE) for the relative motion of the two near spacecrafts is deduced from the Hill equations. The applications of ESKE to orbit meet and orbit rendezvous are discussed.