球谐函数变换快速计算扰动引力

Pole Transform of Spherical Harmonic Function to Quickly Calculate Gravity the Disturbance on Earth-Orbiting Satellites

在球谐函数变换基础上,利用新极下轨道的特殊性,在新坐标下引入Clenshaw求和计算轨道扰动引力。从理论上对比分析了传统方法、球谐函数变换方法和改进方法的计算速度和存储模型需要的物理空间。模拟试验分别采用3种方法计算了一段轨道的扰动引力,试验结果表明,改进的球谐函数变换方法比传统球谐函数变换方法计算速度可提高100倍,数据存储量仅占传统方法的3%。

The spherical harmonics transform is a method to improve the calculation speed of the earth＇s gravity disturbsance on orbiting satellites. Based on the particularity of the traj- ectory for pole transformation, the Clenshaw sun method is introduced to calculate the gravi- ty disturbance on the new coordinates. Then, a comparative analysis focuses on the calcula- tion speed and physical space needs using three methods~ the traditional, pole transform, and improved pole transform methods. A simulation using the three methods is used to cal- culate the gravity disturbance on one period of the orbit. Test results show that the improved pole transformation of spherical harmonic functions is 100 times the calculation speed of the traditional pole transformation method. Furthermore, the data storage capacity required by the new method is only three percent of the traditional method.