火星非球形引力位田谐项联合摄动分析解

火星非球形引力场模型与地球有明显差别,其非球形引力位中的田谐项系数基本都要比地球的相应值大一个量级,尤其是J_2,2项（赤道椭率项）的大小接近它的动力学扁率项J₂.对于低轨探测器,若要使轨道外推1 d弧段的精度达到500 m(相当于标准单位10^-4量级),在构造环火探测器的轨道分析解时,田谐项与J₂项以及田谐项与田谐项之间的联合摄动不容忽视.根据摄动量级分析和构造的摄动分析解证实,上述联合摄动对轨道沿迹方向的影响可超过10^-4,并给出了数值验证.结果表明,与地球低轨卫星不同,在类似的问题中,构造环火卫星摄动分析解时,必须考虑这些联合摄动项的影响.

Analytical Solutions of Coupled Perturbation of Tesseral Harmonic Terms of Mars Orbiters under Nonspherical Gravitational Potential

The nonspherical gravitational potential of the Mars is significantly different from that of the Earth.The absolute value of the Mars’s most tesseral harmonic coefficients are nearly ten times larger than the corresponding terms of the latter.Especially, the absolute value of the Mars’s second degree and order tesseral harmonic coefficient J_2,2 is nearly 40 times as large as that of the Earth,and approaches one-tenth of its second zonal harmonic coefficient J₂.Because of these differences,the coupled terms of J₂ and the tesseral harmonics,and even those of the tesseral harmonics themselves all neglected for Earth satellites should be considered in the analytical perturbation solutions,which are used to predict the Mars’s low-orbit orbiters and the prediction errors must be limited within 500 meters in a time span of one Mars day.In this paper,the analytical solutions of the coupled terms are presented.With the numerical method,it is proved that the coupled terms are effective to influence the analytical solutions up to more than 500 meters along track,which is emphasized by the analysis.The conclusion is that the solutions of Earth satellites cannot be simply used without modification when dealing with the analytical solutions of Mars’ orbiters,and the coupled terms discussed in this paper should be considered.