Resonant quasi-periodic near-rectilinear Halo orbits in the Elliptic-Circular Earth-Moon-Sun Problem

Motivated by the near-future re-exploration of the cislunar space, this paper investigates dynamical substitutes of the Earth-Moon’s resonant Near-Rectilinear Halo Orbits (NRHOs) under the Elliptic-Circular Restricted Four-Body Problem formulation of the Earth-Moon-Sun system. This model considers that the Earth and Moon move in elliptical orbits about each other and that a third body, the Sun, moves in a circular orbit about the Earth-Moon barycenter. By making use of this higher-fidelity dynamical model, we are able to incorporate the Sun’s influence and the Moon’s eccentricity, two of the most significant perturbations of the cislunar environment. As a result of these perturbations, resonant periodic NRHOs of the Earth-Moon Circular Restricted Three-Body Problem (CR3BP) are hereby replaced by two-dimensional quasi-periodic tori that better represent the dynamical evolution of satellites near the vicinity of the Moon. We present the steps and algorithms needed to compute these dynamical structures in the Elliptic-Circular model and subsequently assess their utility for spacecraft missions. We focus on the planned orbit for the NASA-led Lunar Gateway mission, a 9:2 synodic resonant L₂ southern NRHO, as well as on the 4:1 synodic and 4:1 sidereal resonances, due to the proximity to the nominal orbit and their advantageous dynamical properties. We verify that the dynamical equivalents of these orbits preserve key dynamical attributes such as eclipse avoidance and near-linear stability. Furthermore, we find that the higher dimensionality of quasi-periodic solutions offers interesting alternatives to mission designers in terms of phasing maneuvers and low-altitude scientific observations.     

嫦娥五号月面上升和下降段实时轨道确定

针对月球探测中月面上升和下降段的实时轨道确定问题,提出基于三向测量的实时自适应当前统计方法。首先,通过自适应当前统计模型描述探测器月面上升下降过程,其次,综合利用三向数据进行测量更新,最后,通过UKF滤波算法完成实时轨道确定。由于自适应当前统计模型具有良好的适应性,该方法能对探测器月面上升和下降段进行有效定位,通过嫦娥五号探测器实际上升和下降过程数据进行测试,结果表明,文章提出的基于三向测量的实时自适应当前统计方法比传统的几何定位方法具有更好的抗差性,对深空目标探测具有一定的工程应用价值。     

月地转移轨道快速设计方法

月地转移轨道设计一般分为初步轨道设计和精确轨道设计.其中,初步轨道设计的准确性是确保后续精确轨道设计收敛的关键.提出了一种基于Lambert算法的月地转移轨道快速设计方法.以出月球影响球的时刻、位置和速度为中间变量,将轨道分为地心段和月心段分别进行计算.将探测器飞出月球影响球至指定再入点的地心段轨道简化为一个Lambert问题进行求解,提出了通过牛顿迭代法求解月地转移轨道Lambert问题的方法,避免了Lambert问题求解时大量的超几何函数和级数计算,提高了计算效率.在月心段轨道的快速计算中,提出了根据探测器出影响球速度矢量、月球停泊轨道倾角和近月点高度计算月心双曲线轨道根数的新方法.通过迭代计算,使得两段轨道在月球影响球处的位置和速度连续,从而获得一条完整的满足两端约束的双二体月地转移轨道.该方法计算速度快,精度相对较高.计算结果可以作为后续精确轨道设计的初值.      

Design and analysis of an extended mission of CE-2: From lunar orbit to Sun–Earth L2 region

Chang’E-2 (CE-2) has firstly successfully achieved the exploring mission from lunar orbit to Sun–Earth L2 region. In this paper, we discuss the design problem of transfer trajectory and at the same time analyze the visible segment of Tracking, Telemetry & Control (TT&C) system for this mission. Firstly, the four-body problem of Sun–Earth–Moon and Spacecraft can be decoupled in two different three-body problems (Sun–Earth + Moon Restricted Three-Body Problems (RTBPs) and Earth–Moon ephemeris model). Then, the transfer trajectory segments in different model are computed, respectively, and patched by Poincaré sections. The full-flight trajectory including transfer trajectory from lunar orbit to Sun–Earth L2 region and target Lissajous orbit is obtained by the differential correction method. Finally, the visibility of TT&C system at the key time is analyzed. Actual execution of CE-2 extended mission shows that the trajectory design of CE-2 mission is feasible.     

月球探测器转移轨道的特性分析

主要分析了月球探测器由近地点出发，在假定末端条件不变的情况下，其转移轨道的特性参数对初始条件和变轨所需的速度脉冲等的影响；考虑的特性参数的变化包括转移轨道倾角的变化，近地点高度的变化和转移时间的不同．     

环月降轨实现月面着陆的控制策略

针对探测器实现月面着陆的问题，对环月降轨轨道控制策略进行了研究。根据环月降轨的控制方程，将环月降轨单脉冲控制变量的不同组合与月面着陆目标参数建立了3种关系；建立了定时定点月面着陆、定点月面着陆和目标纬度区域月面着陆3种环月降轨控制策略，并给出了控制策略求解算法和步骤。针对定点月面着陆，单脉冲对半长轴和近月点高度进行组合控制，分析了环月降轨控制解空间。针对标称环月轨道/-偏差环月轨道/+偏差环月轨道，分别进行了定时定点/定点/目标纬度区域3种月面着陆的控制计算，验证了环月降轨控制策略。可应用于月球着陆、月球采样返回及载人登月等实施月面定时定点着陆任务的轨道控制。      

Phasing with near rectilinear Halo orbits: Design and comparison

In the next future, space agencies are planning to return to the Moon. The objective is to assemble an orbiting space station, called Gateway, on a Near Rectilinear Halo Orbit around the Moon as a base for future Moon and deep space missions. Within this framework, multiple side missions will be planned to sustain the Gateway (Artemis mission). The proposed work is thought in framework of the preliminary design of future cargo missions, in particular on the design of an efficient phasing trajectory, under the Circular Restricted Three body problem hypotheses, to bring a cargo vehicle from the end of the Earth-Moon transfer to the beginning of the proximity operations such as rendezvous and docking with the space station. The work aims covering the lack of literature in phasing trajectories with the NRHO by proposing three different strategies to connect the Earth-Moon transfer trajectory with the proximity operations. The three strategies are classified based on the choice of the parking orbits or the choice of the manifolds. Two strategies use butterfly and Halo orbits to park the vehicle before transferring to the target orbit. The third strategy, instead, uses manifolds to allow a direct phasing. In the paper, the three innovative strategies are designed and compare in a specific scenario.     

Navigating BepiColombo during the weak-stability capture at Mercury

BepiColombo is scheduled for launch in August 2013 and to arrive after a nearly six-year long transfer at Mercury in June 2019. The trajectory has a number of challenging elements: a launch with Soyuz/Fregat into a geostationary transfer orbit, followed by a lunar flyby, long low-thrust arcs and five more planetary flybys (one at the Earth, two at Venus and two at Mercury). At arrival the low thrust arcs reduce the approach velocity so much that BepiColombo passes by the Sun–Mercury Lagrange points L₁ and L₂ and gets weakly captured in a highly eccentric orbit around Mercury in case the orbit insertion manoeuvre would fail.This paper describes the navigation strategy during the final phase. Five trajectory correction manouevres during the last 65 days requiring up to 20 m/s (3σ) are proposed. With this strategy it is possible to navigate BepiColombo safely through the weak-stability boundary of Mercury and to reach the target periherm with a precision of 11 km.     

月球极轨探测器轨道方案设计

首先介绍了一种当前技术较为先进的奔月转移轨道方案－定相环形轨移轨道，指出了其优缺点及可行的轨道修正方案，然后确定了对月观测型探测器轨道设计原则，并采用定相环形奔月转移轨道，从总体方案的角度给出了一个月球探测器轨道设计方案，提出了具体的设计与分析方法，最后以某月球探测器为例进行了计算，给出了设计结果。     

有限推力变轨的月球探测器发射轨道设计

月球探测器的发射是一个多体问题,也是严格的轨道交会问题。发射轨道方案从理论上有很多种形式,但在工程应用中,受到火箭能力、发射场和测控条件等多种因素制约,方案选择限制非常严格。利用现有火箭,采用有限推力从停泊轨道转移发射是最常用的一种发射方式。本文以某典型火箭为例,对采用有限推力变轨方案的奔月轨道设计流程、发射方案、轨道设计方法、精度分析、发射窗口设计进行了详细分析和研究。     

环月轨道交会的载人登月任务轨道与窗口规划

针对环月轨道(Low Lunar Orbit,LLO)共面交会支持的"人货分离"载人登月任务,提出了一种任务窗口与轨道一体化规划方法。分析了基于LLO共面交会的"人货分离"载人登月任务的基本流程和工程约束;针对任务各阶段窗口与轨道求解问题,提出了以动力下降时刻为迭代初值的窗口规划策略,并建立了高精度模型下的环月轨道、双二体模型下的人员和货物运输轨道规划模型。以载人月球探测中国科学家命名的环形山为假想背景,给出仿真实例,仿真结果验证了文章所提方法的正确性,为探月工程任务提供了一种有效的窗口与轨道设计工具。     

从日地系统L2出发借力月球飞越近地小行星

对于停留在日地系统L2的“嫦娥2号”探测器,其后续飞行方案有多个选项,例如主动撞月或重返月球轨道、返回地球轨道或再入大气、飞往地月系统L1/L2或日地系统L1、进入深空飞越近地小行星(最终,“嫦娥2号”于2012年12月13日成功地实现了对Toutatis小行星的近距离飞越)。探讨上述的飞行方案需要对飞行轨道进行初步设计,总的速度脉冲限制在100 m/s以内并且需要考虑探测器同时受到太阳、地球、月球的引力作用。本研究设计了探测器从日地系统L2出发借力月球实现Toutatis小行星飞越的飞行方案,与直接飞越方案相比,借力月球可以进一步节省探测器的燃料消耗,其等效速度脉冲设计值为58.47 m/s。     

地月拉格朗日L2点中继星轨道分析与设计

地月L2点位于地月连线的延长线上,在地月L2点运行的卫星可以连续观测月球背面,解决月球背面与地球之间的通讯问题,在月球背面着陆探测任务中起着至关重要的作用。对从地球出发、利用月球引力辅助变轨、形成地月L2点的轨道进行了研究,分析了发射窗口、地月转移时间、近月点高度、近月点倾角、轨道振幅等多项因素对转移轨道和使命轨道特性的影响,寻求满足地月L2点中继任务需求的飞行轨道。通过分析研究,文章明确了转移和使命轨道的相关特性,可为中继星任务轨道的参数设计和优化提供有益参考。     

Long-wavelength lunar gravity field recovery from simulated orbit and inter-satellite tracking data

As has been demonstrated recently, inter-satellite Ka-band tracking data collected by the GRAIL (Gravity Recovery And Interior Laboratory) spacecraft have the potential to improve the resolution and accuracy of the lunar gravity field by several orders of magnitude compared to previous models. By means of a series of simulation studies, here we investigate the contribution of inter-satellite ranging for the recovery of the Moon’s gravitational features; the evaluation of results is made against findings from ground-based Doppler tracking. For this purpose we make use of classical dynamic orbit determination, supported by the analysis of satellite-to-satellite tracking observations. This study sheds particularly light on the influence of the angular distance between the two satellites, solar radiation modeling and the co-estimation of the lunar Love number k₂. The quality of the obtained results is assessed by gravity field power spectra, gravity anomalies and precision orbit determination. We expect our simulation results to be supportive for the processing of real GRAIL data.     

基于双二体模型的月球探测器返回轨道初步设计及特性分析

双二体模型是深空探测初步轨道设计普遍采用的假设.本文针对月球探测器从月球驻留轨道返回的任务,对直接返回型轨道和间接返回型轨道,建立了基于直观六参数的返回轨道模型.通过对直观六参数及出口点时刻这些可选参数的分析,得到了约束条件和可选参数的定性关系,易于搜索满足要求的返回轨道.最后针对两种返回轨道类型的算例表明该方法是有效的.     

给定条件下直接命中月球轨道计算方法

在给定飞行时间、着月时间、着月入射角及停泊轨道等约束条件下，建立飞月轨道数学模型；采用可变容差多面体算法及罚函数方法进行二点边值搜索，借助双二体理论近似确定迭代初始条件，得到满足要求直接命中月球的飞月轨道。     

载人月球极地探测定点返回轨道设计

针对载人月球极地探测任务，对定点返回轨道优化设计问题进行了研究。根据月球极地轨道的特性，介绍了三种返回轨道机动方案。结合三脉冲变轨方案，采用了从初步计算到精确计算的串行求解策略，对定点返回轨道进行优化设计。初步计算阶段，建立了基于近月点伪参数的三段二体拼接模型，将三脉冲机动段与月球逃逸段解耦，求解轨道初值；精确计算阶段，提出了两段拼接方法，分别进行逆向和正向高精度数值积分。经过仿真测试，验证了该策略求解的有效性和准确性。最后，通过大量的仿真计算，分析了定点返回轨道的特性。研究结论对未来载人月球极地探测定点返回轨道方案的设计具有重要的参考价值。     

直接再入大气的月地转移轨道设计

针对从月球停泊轨道出发直接再入大气的月地转移轨道设计问题，提出了一种数值求解算法。该算法由初值设计和精确解求解两部分组成。首先，根据轨道设计的相应约束，采用伪状态理论，通过简单迭代求解高精度的初值。然后，考虑精确的动力学模型，通过数值积分计算真实轨道和状态转移矩阵，并利用微分修正方法搜索精确解。该算法通过设计高精度的初值，降低了月地转移轨道的设计难度。数值仿真表明:该算法求解效率高，具有良好的鲁棒性。      

miniSAR卫星精密参考轨道设计

为满足轻小型合成孔径雷达(miniSAR)卫星干涉测量任务对空间基线的要求,通过分析卫星参考轨道特性,建立了一套精密参考轨道设计算法。所建算法以miniSAR卫星成功入轨后的一组定轨数据及根据参考轨道特性解析得到的参考轨道预估值为输入,基于仅考虑中心天体非球形高阶引力摄动的轨道外推模型、Eckstein-Hechler平根模型及嵌套式迭代修正方法,设计输出其任务周期内使用的参考轨道。数值实验表明:所建算法设计的参考轨道生成的参考轨迹在三维空间的回归精度优于0.01 m,满足实际工程应用需求。