DRO计算及其在地月系中的摄动力研究

针对远距逆行轨道（DRO）的航天工程应用问题，研究了DRO的计算方法以及轨道特性，分析了DRO在实际力环境中的主要摄动因素，为DRO的精确建模和标称轨道设计奠定一定的理论基础。首先，利用仿真算例验证流函数法在计算DRO周期轨道族中的有效性。然后，利用该方法，通过改变雅可比常数，延拓计算DRO周期轨道族，获得不同共振比的DRO，仿真结果表明整数共振比的DRO在地月惯性坐标系中的轨迹是封闭的曲线，而共振比非整数的DRO则不封闭。最后，通过轨道外推分析影响DRO稳定性的主要摄动因素，仿真结果表明太阳引力和月球轨道偏心率是影响DRO稳定性的主要摄动因素。在动力学模型中，使用标准星历表示行星的运动状态，当积分时间多于10天时模型误差为km量级，因此在地月系这样大尺度的空间范围内，可以使用星历模型近似的分析DRO在真实力环境中的运动状态，为任务轨道设计提供依据。 

DRO computation and its perturbative force in the Earth-Moon system

For the aerospace engineering application of Distant Retrograde Orbit (DRO), a calculation method and orbit characteristics are studied, and the main perturbation factors of DRO in actual force environment are analyzed to provide a theoretical foundation for DRO's precise modeling and nominal orbit design. Firstly, the effectiveness of the stream function method in calculating the DRO periodic orbit family is verified by simulation examples. Secondly, the DRO periodic orbit family is calculated by adjusting the Jacobi constant, and the DRO orbits with different resonance ratios are obtained. The simulation results show that the trajectory of DRO with an integer resonance ratio in the Earth-Moon inertial coordinate system is a closed curve, while DRO orbits with non-integer resonance ratio are not closed. Finally, the main perturbation factors affecting DRO stability are analyzed by orbit extrapolation. The simulation results show that solar gravitation and lunar orbit eccentricity are the main perturbation factors that affect stability of DRO. In the dynamic model, the standard ephemeris is used to represent the motion state of the planet. When the integration time reaches more than 10 days, the model error is about kilometer-scale. Therefore, in the large spatial scale of the Earth-Moon system, the ephemeris model can be used to analyze the motion state of the DRO approximately in the real force environment, which could provide a basis for mission orbit design.