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.     

Materials trade study for lunar/gateway missions.

The National Aeronautics and Space Administration (NASA) administrator has identified protection from radiation hazards as one of the two biggest problems of the agency with respect to human deep space missions. The intensity and strength of cosmic radiation in deep space makes this a 'must solve' problem for space missions. The Moon and two Earth-Moon Lagrange points near Moon are being proposed as hubs for deep space missions. The focus of this study is to identify approaches to protecting astronauts and habitats from adverse effects from space radiation both for single missions and multiple missions for career astronauts to these destinations. As the great cost of added radiation shielding is a potential limiting factor in deep space missions, reduction of mass, without compromising safety, is of paramount importance. The choice of material and selection of the crew profile play major roles in design and mission operations. Material trade studies in shield design over multi-segmented missions involving multiple work and living areas in the transport and duty phase of space mission's to two Earth-Moon co-linear Lagrange points (L1) between Earth and the Moon and (L2) on back side of the moon as seen from Earth, and to the Moon have been studied. It is found that, for single missions, current state-of-the-art knowledge of material provides adequate shielding. On the other hand, the choice of shield material is absolutely critical for career astronauts and revolutionary materials need to be developed for these missions. This study also provides a guide to the effectiveness of multifunctional materials in preparation for more detailed geometry studies in progress.     

地月系L2平动点轨道长期维持过程研究

针对地月系L2平动点附近两种常用轨道——拟halo轨道和Lissajous轨道,研究了轨道长期维持过程。采用穿越xz平面单圈控制的轨道维持策略,控制量通过单步预测法进行寻优。在全摄动动力学模型下对拟halo轨道和Lissajous轨道受控维持下的一年飞行过程分别进行了仿真和比较,结果显示Lissajous轨道的维持控制代价优于拟halo轨道,从轨道拓扑构型保持方面对该结果进行解释,并设计对比实验加以验证。研究结论对地月系L2平动点轨道选择、维持控制策略设计、长期飞行效果分析等方面具有工程参考意义。     

考虑月球升交点黄经的地月低能转移轨道

地月转移轨道研究的基本模型主要是限制性二体模型和限制性三体模型。在限制性三体建模下,基于轨道分类理论的地月脉冲变轨比传统的霍曼变轨节省了更多的燃料(至少13%以上)。单独的"地球-月球-飞行器"的限制性三体问题无法应用轨道分类的理论进行轨道设计,必须加入太阳。文章考虑了月球升交点赤经、黄白交角,以及正确的地月系统稳定流形的方向,整个"太阳-地球-月球-飞行器"系统拆分为"地球-月球-飞行器"的平面圆型限制性三体问题,和"太阳-地球-飞行器"三维圆型限制性三体问题进行分析,并利用Matlab仿真验证了方案的可行性。     

地月平动点中继应用轨道维持

地月平动点中继应用轨道对于月球背面探测具有十分重要的应用价值,由于地月平动点的不稳定性,必须进行轨道维持。文章研究了真实力模型下月球平动点中继应用轨道的维持。首先,基于限制性三体问题下平动点轨道的运动特性,研究了平动点轨道维持的数学模型与维持策略,提出了平动点轨道维持的连续环绕控制方法,并给出了轨道维持的Halo和Lissajous两种控制方式;其次,充分考虑各天体和光压摄动下,采用数值手段研究了不同幅值的地月平动点周期中继应用轨道的维持间隔与速度增量等。研究结果表明:Lissajous控制方式适用于月球平动点中继应用轨道的维持,在给定测控精度条件下,维持间隔约7.4d,速度增量优于20m/s/a。该方法已经成功应用于我国"嫦娥2号"日地平动点任务和"嫦娥5T1"地月平动点任务并获得了良好的控制效果,还可直接应用于我国未来"嫦娥4号"等月球背面探测任务。     

高精度模型下Halo轨道设计研究

针对未来地月L2点Halo轨道空间站长期停泊任务,研究了高精度模型下Halo轨道设计方法。首先,详细推导了圆型限制性三体问题(Circular Restricted Three Body Problem,CR3BP)质心会合坐标系与高精度模型地心J2000坐标系之间的转换关系,并在此基础上,将CR3BP下的闭合Halo轨道转换到地心J2000坐标系得到了高精度模型下Halo轨道迭代初值。其次,采用序列二次规划(Sequence Quadratic Program,SQP)构造多层迭代格式,在高精度模型下对初值进行逐层修正。最后,通过仿真测试,验证了该方法的可行性与有效性。该研究结果可为未来平动点任务标称轨道设计方案的制定提供参考。     

Low-energy near Earth asteroid capture using Earth flybys and aerobraking

Since the Sun-Earth libration points L₁ and L₂ are regarded as ideal locations for space science missions and candidate gateways for future crewed interplanetary missions, capturing near-Earth asteroids (NEAs) around the Sun-Earth L₁/L₂ points has generated significant interest. Therefore, this paper proposes the concept of coupling together a flyby of the Earth and then capturing small NEAs onto Sun–Earth L₁/L₂ periodic orbits. In this capture strategy, the Sun-Earth circular restricted three-body problem (CRTBP) is used to calculate target Lypaunov orbits and their invariant manifolds. A periapsis map is then employed to determine the required perigee of the Earth flyby. Moreover, depending on the perigee distance of the flyby, Earth flybys with and without aerobraking are investigated to design a transfer trajectory capturing a small NEA from its initial orbit to the stable manifolds associated with Sun-Earth L₁/L₂ periodic orbits. Finally, a global optimization is carried out, based on a detailed design procedure for NEA capture using an Earth flyby. Results show that the NEA capture strategies using an Earth flyby with and without aerobraking both have the potential to be of lower cost in terms of energy requirements than a direct NEA capture strategy without the Earth flyby. Moreover, NEA capture with an Earth flyby also has the potential for a shorter flight time compared to the NEA capture strategy without the Earth flyby.     

A lunar cargo mission design strategy using variable low thrust

A design technique for a near optimal, Earth–Moon transfer trajectory using continuous variable low thrust is proposed. For the Earth–Moon transfer trajectory, analytical and numerical methods are combined to formulate the trajectory optimization problem. The basic concept of the proposed technique is to utilize analytically optimized solutions when the spacecraft is flying near a central body where the transfer trajectories are nearly circular shaped, and to use a numerical optimization method to match the spacecraft’s states to establish a final near optimal trajectory. The plasma thruster is considered as the main propulsion system which is currently being developed for crewed/cargo missions for interplanetary flight. The gravitational effects of the 3rd body and geopotential effects are included during the trajectory optimization process. With the proposed design technique, Earth–Moon transfer trajectory is successfully designed with the plasma thruster having a thrust direction sequence of “fixed-varied-fixed” and a thrust acceleration sequence of “constant-variable-constant”. As this strategy has the characteristics of a lesser computational load, little sensitivity to initial conditions, and obtaining solutions quickly, this method can be utilized in the initial scoping studies for mission design and analysis. Additionally, derived near optimal trajectory solution can be used as for initial trajectory solution for further detailed optimization problem. The demonstrated results will give various insights into future lunar cargo trajectories using plasma thrusters with continuous variable low thrust, establishing approximate costs as well as trajectory characteristics.     

基于引力场不对称性的三体系统轨道自主导航

以月球背面的中继通信为背景,提出了基于三体系统引力场不对称特性的星–星测距自主定轨方案。该方案以环月极轨卫星和地–月L2点Halo轨道卫星组成中继通信网,以实现对月球两极和背面的覆盖。通过采集极轨卫星与Halo轨道卫星的测距信息,结合卡尔曼滤波在日–地–月动力学模型下获得两颗卫星的绝对轨道。数值仿真结果表明:本文方法能将导航的位置精度和速度精度分别提高到百米和厘米/秒量级。该自主导航方法还可以扩展到不规则引力场小天体附近星群运动的自主导航。     

飞向晕轨道的探测器轨道优化

晕轨道的稳定流形为从地球到晕轨道的转移轨道设计提供了便利．以往都采用在晕轨道上的目标点施加脉冲,这样,稳定流形只是为转移轨道的设计提供一个初始猜想,探测器并没有运行在稳定流形上,因而并未真正利用稳定流形节省燃料的优势．利用基于序优化理论的微分修正法,研究从晕轨道近地点稳定流形上不同点进入稳定流形所需要的燃料消耗,寻找燃耗最少的转移轨道．仿真表明,对于晕轨道近地点入轨,找到的稳定流形射入点机动比以往的晕轨道入轨点机动节省约33％的燃料消耗．此外,还对晕轨道上不同入轨点的入轨代价进行了研究,得到了晕轨道近地点入轨的最小燃耗解．     

A lunar laboratory

An international research laboratory can be established on the Moon in the early years of the 21st Century. It can be built using the transportation system now envisioned by the National Aeronautics and Space Administration, which includes a space station for Earth orbital logistics and orbital transfer vehicles for Earth-Moon transportation. A scientific laboratory on the Moon would permit extended surface and subsurface geological exploration; long-duration experiments defining the lunar environment and its modification by surface activity; new classes of observations in astronomy; space plasma and fundamental physics experiments; and lunar resource development. The discovery of a lunar source for propellants may reduce the cost of constructing large facilities in space and enhance other space programs such as Mars exploration.     

China's Lunar and Deep Space Exploration Program for the Next Decade (2020-2030)

China has carried out four unmanned missions to the Moon since it launched Chang'E-1, the first lunar orbiter in 2007. With the implementation of the Chang'E-5 mission this year, the three phases of the lunar exploration program, namely orbiting, landing and returning, have been completed. In the plan of follow-up unmanned lunar exploration missions, it is planned to establish an experimental lunar research station at the lunar south pole by 2030 through the implementation of several missions, laying a foundation for the establishment of practical lunar research station in the future. China successfully launched its first Mars probe on 23 July 2020, followed in future by an asteroid mission, second Mars mission, and a mission to explore Jupiter and its moons.      

我国探月工程技术发展综述

我国的探月工程,在2020年前分“绕、落、回”三步实施。本文以我国探月工程各次任务为脉络,针对目前已经完成的“嫦娥1号”“嫦娥2号”“嫦娥3号”及“嫦娥5号”高速再入试验任务,简述了工程和科学目标,介绍了实施效果,总结了主要技术成就。在此基础上,展望了探月工程未来的发展趋势,给出了月球后续任务的总体思路和框架。     

平动点周期轨道间小推力转移的Gauss伪谱法

针对三体问题共线平动点附近周期轨道间的小推力转移问题,构造了一种新的形状函数,在此基础上提出了一种基于Gauss伪谱法的优化设计方法。首先,建立小推力轨道转移动力学模型,参考初始轨道和目标轨道的类型,构造一种新的形状函数以近似小推力转移轨道。为满足不同的约束要求,提出了振幅和相位按多项式变化的假设,推导了小推力转移轨道的近似解析解;然后利用Gauss伪谱法将小推力轨道转移的最优控制问题转化为非线性规划问题,并对推导的近似解析解进行解算和处理,为Gauss伪谱法求解非线性规划问题提供较为有效的控制变量的初始猜测值;最后以地月系统L1点附近Halo轨道间的小推力转移问题为例进行了仿真分析。仿真结果表明,小推力转移轨道近似解析解具备有效性和普适性,使得Gauss伪谱法的迭代效率提高55%以上,同时也表明Gauss伪谱法可有效解决平动点周期轨道间的小推力转移轨道优化设计问题。     

空间增材制造技术的应用

中国空间站旨在进行大量在轨科学实验和空间应用研究,在轨保障是支持空间站在全寿命周期内完成载人航天任务的重要途径.传统地面制造及上行补给方式难以满足较大规模应用的需求,亟需一种创新性的保障模式突破资源瓶颈,空间增材制造技术具有极大的潜力实现即造即用的资源保障模式.本文根据空间增材制造技术的最新研究进展,结合中国空间站和载人深空探测任务需求,对空间增材制造技术的在轨应用模式进行分析,提出了中国空间增材制造技术未来发展所面临的问题和解决途径.      

Improved environment radiation models

The two components of the space radiation environment, galactic cosmic rays and solar energetic particles, are of special importance for the planning of space missions and designing space vehicles for flights in the inner heliosphere. There is a constant need for developing and updating the models for calculating the fluxes of these particles for purposes of forecasting radiation conditions anticipated for future flights, including missions to the Moon and Mars.     

“嫦娥一号”卫星的调相轨道设计

中国第一颗月球探测卫星"嫦娥一号"的飞行轨道的设计中采用了调相轨道,在"长征三号甲"运载火箭提供的超地球同步转移轨道与地月转移轨道之间增加了一段由周期为24h和48h轨道构成的环绕地球飞行的调相轨道。为了将几条不同的轨道精确地拼接起来,必须考虑地球引力场对轨道的摄动影响。克服这个难点的做法是基于经典的轨道摄动理论,先将整段调相轨道设计为考虑地球引力场J2项影响的平轨道,在与运载的发射轨道拼接时,先将运载的包括短周期摄动的瞬时轨道转换为平轨道,在与地月转移轨道拼接时将调相轨道转换成拼接点的瞬时轨道。由于采用了平轨道的处理方法使得轨道控制策略的表述十分简明并易于操作。     

低成本多小天体并行交会技术

小天体资源开发方兴未艾,为降低开发风险和成本,需要发射无人探测器交会观测多个待选目标小天体。传统多目标探测方案存在无法多次交会、成本高,周期长等不足。提出的低成本多小天体并行交会技术,能够对多小天体探测任务进行解耦,实现基于微纳飞行器的低成本多目标并行交会勘查,从而降低探测成本,缩短探测周期。该技术结合行星借力与不变流形机制构建了低能量星际转移方案。然后引入扰动流形思想,使微纳飞行器能够实现与目标小天体的快速交会。进一步,提出了一种多目标小天体探测全局搜索方法,该方法基于在日地halo轨道上停泊的微纳飞行器集群,逐次确定小天体探测目标,并利用上述方法完成了多微纳飞行器与多小天体的交会。数值仿真结果表明,该方案能够大幅度降低转移过程的燃料消耗,并缩短转移时间。     

“嫦娥4号”中继星任务分析与系统设计

作为"嫦娥4号"任务的重要组成部分,中继星将为着陆器和巡视器提供中继通信支持。不同于其它月球探测器,中继星首次选择了绕地月L2平动点运行的晕(Halo)轨道以保证对月球背面的着陆器和巡视器提供连续的中继通信服务,面临诸多技术挑战。在对中继星任务特点进行分析的基础上,梳理了研制中的技术难题,包括使命轨道的选择、使命轨道的到达和长期维持、中继通信体制选择等,并提出了解决方案。中继星的总体设计方案概述也在文中给出。     

地月L2点中继星长阴影影响研究

地月L2点中继星环绕地月L2点飞行时,会经历由地球或月球遮挡太阳而产生的阴影,部分阴影时长较长,中继星进入长阴影,严重时会威胁卫星平台安全。基于月球背面软着陆探测工程目标和中继星绕飞地月L2点halo轨道特性,分析长阴影的分布特征,以及阴影时长与轨道相位、振幅、构型等因素的关系,进而对长阴影的规避方法和适用范围进行探讨。研究结果为地月L2点中继星长阴影问题提供了分析方法和应对方案。