环火卫星运动的坐标系附加摄动及相应坐标系的选择

The Coordinate Additional Perturbations to Mars Orbiters and the Choice of Corresponding Coordinate System

与处理地球卫星相关问题类似,在研究和处理环火卫星(尤其是低轨卫星)的轨道问题时,宜采用火心历元平赤道坐标系,即火心天球坐标系,其xy坐标面和x轴方向就是相应的平赤道面和平春分点方向.与地球的岁差章动现象类似,在该坐标系中,火星赤道面在空间的摆动同样会引起坐标系附加摄动.采用类似对地球岁差章动的处理方法,在一定精度前提下,基于IAU2000火星定向模型,处理了火星赤道面摆动中的岁差效应,并在此基础上,研究岁差对环火卫星轨道的影响,给出了相应的火星非球形引力位的变化及其导致的卫星轨道的坐标系附加摄动解,其表达形式简单,引用方便.与高精度数值解的比对表明,该分析解能够满足通常的精度要求.因此,在处理环火卫星(即使是低轨卫星)轨道及其相关问题时,可以采用统一坐标系:火心天球坐标系.而不必像当初处理地球卫星那样,为了避免计算坐标系附加摄动而引进一种混合型赤道坐标系,即采用瞬时真赤道面和历元平春分点方向作为其xy坐标面和x轴方向.在统一坐标系的选择下,实际工作中就不会存在坐标系转换的麻烦.

Similar to the study of the related problems of Earth satellites, in the research of the motion of Mars orbiter especially for low orbit satellites, it is more appropriate to choose an epoch Mars-centered and Mars-equator reference system, which indeed is called the Mars-centered celestial coordinate system. In this system, the xy plane and the direction of the x axis correspond to the mean equator and mean equinox. Similar to the precession and nutation on the Earth, the wiggling of instantaneous Mars equator causes the coordinate additional perturbations in this Mars coordinate system. The paper quotes a method which is similar to the one used in dealing with the coordinate additional perturbations of Earth. According to this method, based on the IAU2000 Mars orientation model and under the precondition of a certain accuracy, we are able to figure out the precession part of the change of Mars gravitation. This lays the foundation for further study of its influence on the Mars orbiter＇s orbit of precession and the solution of the corresponding coordinate additional perturbations. The obtained analytical solution is easy to use. Compared with the numerical solution with higher accuracy, the result shows that the accuracy of this analytical solution could satisfy general requirements in use. Therefore, our result verifies that a unified coordinate system, the Mars-centered celestial system in which J2000.0 is chosen as its current initial epoch, could be applied to deal with the relative problems of Mars orbiters, especially for low orbit satellites. It is different from the method we previously used in dealing with the corresponding problems of Earth satellites, where we adopted the instantaneous equator and epoch （J1950.0） mean equinox as xy plane and the direction of x axis. In contrast, the coordinate transformation brings heavy workload and certain inconvenience in relative former works in which the prior system is used. If adopting the unified coordinate system, the transformation could be simply avoided and the computation load could be decreased significantly.