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

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 trajectory for pole transformation,the Clenshaw sun method is introduced to calculate the gravity disturbance on the new coordinates.Then,a comparative analysis focuses on the calculation 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 calculate 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.