标题： 月球卫星轨道全解析传播器的封闭形式 显示英文标题

标题： Fully analytical propagator for lunar satellite orbits in closed form

摘要： 我们提出了一种完全解析的传播器，用于月球人造卫星在月球引力和第三体模型中的轨道，该模型足够精确，适用于广泛的实际应用。 引力模型包括十二个最重要的月球重力谐波，以及地球的四极潮汐项，并且对地月中心星历有精确表示，其精度与半解析传播器SELENA [6]相当，后者适用于从300到3000公里高度的卫星轨道。 使用目前讨论的解析理论公式，可以轻松包含更完整引力模型的额外项。 该理论基于利用封闭形式的哈密顿正则形式，导出运动方程定常部分的近似解析解。 总共，我们有两种类型的元素变换：从瞬时轨道元素到平均轨道元素（如[6]），以及从平均轨道元素到真轨道元素。 在真轨道元素问题中的解是平凡的，通过上述变换的逆变换，它允许在给定瞬时轨道元素在时间$t_0$的初始条件的情况下，无需任何中间数值传播即可解析地恢复卫星在任意时刻 t 的位置和速度。 传播器模型在数十年的时间跨度内有效，并且对于所有导致卫星不坠落到月球表面的初始条件都适用，除了在一组与卫星的定常频率和地月中心轨道的定常频率之间的整数比值相对应的定常共振附近的识别出的薄区域之外。 提供了实现我们传播器的开源Python和符号计算例程，可在仓库[14]中获取。 报告了与笛卡尔坐标系下的全数值轨道传播相比的精度测试结果。 显示英文摘要

摘要： We present a fully analytical propagator for the orbits of lunar artificial satellites in a lunar gravity and third-body model sufficiently precise for a wide range of practical applications. The gravity model includes the twelve most important lunar gravity harmonics as well as the Earth's quadrupole tidal terms with a precise representation of the Earth's lunicentric ephemeris, and it gives an accuracy comparable to the way more extended semi-analytical propagator SELENA [6] for satellite orbits at altitudes from 300 to 3000 km. Extra terms of a more complete gravity model are straightforward to include using the formulas of the presently discussed analytical theory. The theory is based on deriving an approximate analytical solution of the secular part of the equations of motion using a Hamiltonian normal form in closed form. In total, we have two types of element transformations: from osculating to mean elements (as in [6]), and from mean to proper elements. The solution of the problem in proper elements is trivial, and, through the inverses of the above transformations, it allows to recover the position and velocity of a satellite analytically at any time t given initial conditions of the osculating elements at time $t_0$ without any intermediate numerical propagation. The propagator model is valid in time spans of several decades, and for every initial condition leading to no-fall on the Moon's surface, except for identified thin zones around a set of secular resonances corresponding to commensurabilities between the satellite's secular frequencies and the secular frequencies of the lunicentric Earth's orbit. Open software python and symbolic routines implementing our propagator are provided in the repository [14]. Precision tests with respect to fully numerical orbital propagation in Cartesian coordinates are reported.