三体问题理论解和月球引力助推研究

N-body problem is an unsolved theoretical problem in the orbital mechanics. The problem was first proposed by Newton in 1687 in his well-known Principle of Mathematics. Based on historical contributions of the well-known scientists, theoretical research of N-body problem focuses on two directions: searching for the series solution and solving the singularity problem. Based on applicant’s contribution to the analytical solution of the multi-body perturbation of satellite orbital disturbing problem, this research attempts to use the similarities of the 3-body problem and the two-body disturbing theory, taking the solar system Earth-Moon planetary orbits as precision estimation and series truncation references to derive the 3-body problem solution. The theoretical derivation will be computed by software design via symbolic mathematical operation. The first three order solutions are obtained during the pre-researching. Then using the general 3-body problem solution to replace the restricted three body theory for studying the lunar gravity assist problem, to enable the progress of the deep space mission orbit design from the numerical searching to the theoretical optimization; using lunar gravity assist to saving energy needs for the space missions and orbit design.

N体问题是世界上尚未解决的由牛顿1687年在《原理》中提出的轨道理论难题。由于众多历史名人的贡献，N体问题理论研究主要集中在寻求级数解和解决奇点问题两个方向。基于申请者推导的二体问题的日月行星多体摄动解析解理论，本研究试图通过利用三体问题和二体摄动问题的局部共性，依据太阳系地月轨道参数作为精度估计级数截断的参照，推导一般三体问题的级数理论解。整个理论推导将通过数学符号运算软件设计计算完成，前期研究已经获得前三阶的理论解。并以三体问题一般性理论取代限制性三体理论，研究月球引力助推问题的解析表达，达到深空探测轨道设计从数值搜索优化向理论优化的进步，研究利用月球引力助推节约推动能量，开展对月和对地外行星探测优化轨道设计的研究。

N体问题理论研究主要集中在寻求级数解和解决奇点问题两个方向。本项目依据前期二体问题的日月行星多体摄动解析解理论，通过利用三体问题和二体摄动问题的局部共性，基于太阳系N体问题限定于推导三体问题的理论解。针对卫星轨道理论中的奇点问题，考虑圆轨道、圆赤道轨道和赤道轨道三种奇点情况，推导了一种新的拉格朗日/高斯无奇点卫星运动方程，并探讨了方程的连续性。研究月球引力助推问题的解析表达，对引力助推轨道设计及月球借力的可行性做了系统的研究和分析；在此基础上，完成和实现了月球借力金星探测轨道的方案设计和算法分析。对行星逆行的机制及行星碰撞后的轨道进行了扩展研究。