椭圆三体问题下月球L2低能逃逸轨道设计

针对圆形限制性三体问题下求解月球探测器逃逸轨道时，不能充分利用月球椭圆公转动力学特性节约逃逸能量的问题，对动力学模型进行拓展，在椭圆三体问题下建立月球探测器轨道动力学方程与能量表达式。首先通过理论推导，求解了探测器逃逸所需的发射能量与逃逸过程中的轨道能量随月地椭圆相对运动状态的数学表达式，对其进行分析发现，同一环月轨道上出发的逃逸探测器所需发射能量与地月距离呈正相关，而逃逸过程中探测器轨道能量变化与地月相向运动速度呈正相关，从而得出在月球接近其近地点过程中发射逃逸探测器可以最大限度节约发射能量的结论。在此基础上，引入庞加莱截面法设计探测器最低能量逃逸轨道。通过寻找使逃逸轨道所在不变流形的庞加莱截面收缩为一点的发射位置与能量，求解不同地月相位下的逃逸轨道能量需求，进而迭代求解能量最优逃逸轨道。最终，通过对比仿真结果得到，月球真近角为283°时发射逃逸探测器将最节约能量，与理论推导的结果相吻合。相对于圆形限制性三体问题下推导的最低逃逸能量，采用椭圆三体模型设计的低能量逃逸轨道可以节约8%左右的发射能量，对于深空探测等任务来说具有明显优势。

Designing of the Optimal Energy Escaping Orbit from Moon L2 Point in Elliptical Three-body Problem

To solve the problem that it is hard to save energy by making full use of the elliptical orbit dynamics of the Earth-Moon system in the escaping orbit design of a moon probe under a circular restricted three-body environment, a dynamic model is extended to an elliptical three-body model for which the dynamic equation and the orbit energy is given. The relationship between the orbit energy of the probe and the Moon's phase is constructed by deriving the variation of the orbit energy during the escaping process. It is found that from the same original cislunar orbit, the launching energy will change mainly with the distance between the Earth and the Moon while the energy variation during the escaping process is closely related with the Earth-Moon relative speed. Then it is concluded that the optimal escaping orbit exists when the Moon comes close to its perigee. To design the optimal escaping orbit the Poincare section method is introduced. By solving the relationship between the Moon's phase and the corresponding energy need for escaping, the optimal solution is given with iteration. From the simulation it is found that when the Moon's true anomaly reaches 283°, up to 8% of energy can be saved with the elliptical three body model as compared with the circular restricted three-body model, which is in good agreement with the theoretical results, and the advantage is obvious.