中文摘要：

引力位及其一、二阶导数的计算在卫星精密定轨和重力场解算等研究中有着广泛的应用.本文综合已有方法,选择了其中的3种计算方法进行比较研究,即传统Legendre方法,Cunningham直角坐标递推方法,Zhang方法.首先对3种方法重新推导整理,给出较为准确的计算公式,并采用最新月球探测器GRAIL得到的660阶次重力场模型GRGM660PRIM,从计算效率和精度角度对3种方法进行了分析比较,结果表明Zhang方法在效率和精度方面有较高优势.本文结论可为月球卫星精密定轨和重力场解算等相关研究提供重要参考.

英文摘要：

Gravitational potential and its derivatives are widely used in fields such as POD（Precise Orbit Determination）and gravity field recovery.Based on known methods,this work compares three different calculational methods for gravitational potential and its derivatives：the traditional Legendre method,the Cunningham recursion method and Zhang method.First,the three methods are re-derived and examined.Then,using the newest lunar gravity model—GRGM660PRIM,up to 660 degrees and orders,from GRAIL（Gravity Recovery and Interior Laboratory）mission,the efficiency and precision of the three methods are studied.The results show Zhang method has advantages in both efficiency and precision.The conclusion can supply important reference for lunar satellite POD and gravity field recovery.