针对卫星轨道数值积分、变分方程解算等问题,研究了Gauss-Jackson积分器的原理和计算流程,提出了移位重排方式来优化其存储方式的方法,采用开普勒轨道、庞加莱轨道根数、状态转移矩阵等多种参数评估其性能,并与Runge-Kutta、Adams-Cowell等数值积分器进行了比较。计算结果表明,由于对启动点引入中值改正,Gauss-Jackson数值积分器的计算精度高、速度快,可为卫星轨道数值积分和变分方程求解等问题提供稳定、高效的算法。 For the problems of numerical integration of satellite orbit and variational equation solving, the principle and calculation flow of Gauss-Jackson integrator are studied, and the method of shift rearrangement is proposed to optimize its storage method. Kepler orbit, Levin orbit number, state transition matrix and other parameters to evaluate its performance, and with Runge-Kutta, Adams-Cowell and other numerical integrators were compared. The calculation results show that the Gauss-Jackson numerical integrator can provide stable and efficient algorithms for numerical integration and variational equation solving of satellite orbit due to the high accuracy and speed of Gauss-Jackson numerical integrator.