地月空间的远距离逆行轨道族及其分岔研究

地月系统中存在着一类绕月逆行、高度稳定的轨道族,称为远距离逆行轨道族(DRO)。以圆型限制性三体问题(CR3BP)为动力学模型研究了DRO轨道族周边的动力系统结构。利用Broucke稳定性图寻找分叉点,判断分叉类型,基于数值延拓计算分岔后产生的一系列新轨道分支。分叉类型主要有切分叉与多倍周期分叉(从3倍周期开始),轨道维度包含平面轨道族与三维轨道族。计算新轨道族的特征,包括形状、周期、能量、稳定性、双曲流形结构等。探讨周期轨道的轨道周期与能量的关系,以几何化的方式展现分叉结构、多周期轨道的双曲流形结构等。该动力结构将为基于DRO轨道族的地月空间任务提供重要的理论支持。      

火卫一周期准卫星轨道及入轨分析

围绕火卫一的准卫星轨道（QSOs）因其具有良好的稳定性,是火卫一探测任务最为实用的轨道。在平面圆型限制性三体问题模型下,利用庞加莱截面和KAM环迭代方法探究了准卫星轨道的周期轨道族,并给出不同能量准卫星周期轨道的初始条件。针对火卫一周期准卫星轨道入轨,提出一种转移轨道设计方法:对准卫星周期轨道调整速度后进行反向积分,直至离开火卫一邻近区域,从而得到由火星环绕轨道向火卫一周期准卫星轨道的转移轨道,并调整转移轨道参数对燃料与时间消耗进行优化。研究结果表明,当周期准卫星轨道能量处于特定区间时,存在特定速度脉冲区间,可利用火卫一引力实现较少燃料消耗的轨道转移;在该速度脉冲区间中,通过选取较小的速度脉冲,可缩短转移时间。      

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.     

Resonant motion, ballistic escape, and their applications in astrodynamics

A special set of solutions governing the motion of a particle, subject to the gravitational attractions of the Earth, the Moon, and, eventually, the Sun, is discussed in this paper. These solutions, called resonant orbits, correspond to a special motion where the particle is in resonance with the Moon. For a restricted set of initial conditions the particle performs a resonance transition in the vicinity of the Moon. In this paper, the nature of the resonance transition is investigated under the perspective of the dynamical system theory and the energy approach. In particular, using a new definition of weak stability boundary, we show that the resonance transition mechanism is strictly related to the concept of weak capture. This is shown through a carefully computed set of Poincaré surfaces, at different energy levels, on which both the weak stability boundary and the resonant orbits are represented. It is numerically demonstrated that resonance transitioning orbits pass through the weak stability boundaries. In the second part of the paper the solar perturbation is taken into account, and the motion of the resonant orbits is studied within a four-body dynamics. We show that, for a wide class of initial conditions, the particle escapes from the Earth–Moon system and targets an heliocentric orbit. This is a free ejection called a ballistic escape. Astrodynamical applications are discussed.     

基于交会模式的月球大椭圆轨道编队飞行控制

两颗微卫星进入环月大椭圆轨道后,在地面测控支持下,通过执行若干次轨道机动,最终实现从相距上千或上万km至相距1～10 km范围变化的环月轨道编队飞行。针对月球大椭圆轨道,基于多脉冲交会控制模式,设计了交会点满足编队飞行状态的轨道控制策略,采用线性制导方法迭代计算精确轨道控制参数;设计了顺序优化的5脉冲控制策略,对轨道平面、拱线、形状和相位等轨道全要素进行控制,通过远距离接近、中距离调整和近距离捕获的渐进式分段控制,在月球大椭圆轨道差异较大条件下,相对运动轨迹渐进稳定,最终实现近距离编队。     

Attitude stability and periodic attitudes of rigid spacecrafts on the stationary orbits around asteroid 216 Kleopatra

In this work, equilibrium attitude configurations, attitude stability and periodic attitude families are investigated for rigid spacecrafts moving on stationary orbits around asteroid 216 Kleopatra. The polyhedral approach is adopted to formulate the equations of rotational motion. In this dynamical model, six equilibrium attitude configurations with non-zero Euler angles are identified for a spacecraft moving on each stationary orbit. Then the linearized equations of attitude motion at equilibrium attitudes are derived. Based on the linear system, the necessary conditions of stability of equilibrium attitudes are provided, and stability domains on the spacecraft’s characteristic plane are obtained. It is found that the stability domains are distributed in the first and third quadrants of the characteristic plane and the stability domain in the third quadrant is separated into two regions by an unstable belt. Subsequently, we present the linear solution around a stable equilibrium attitude point, indicating that there are three types of elemental periodic attitudes. By means of numerical approaches, three fundamental families of periodic solutions are determined in the full attitude model.     

Families of halo orbits in the elliptic restricted three-body problem for a solar sail with reflectivity control devices

Solar sail halo orbits designed in the Sun-Earth circular restricted three-body problem (CR3BP) provide inefficient reference orbits for station-keeping since the disturbance due to the eccentricity of the Earth’s orbit has to be compensated for. This paper presents a strategy to compute families of halo orbits around the collinear artificial equilibrium points in the Sun-Earth elliptic restricted three-body problem (ER3BP) for a solar sail with reflectivity control devices (RCDs). In this non-autonomous model, periodic halo orbits only exist when their periods are equal to integer multiples of one year. Here multi-revolution halo orbits with periods equal to integer multiples of one year are constructed in the CR3BP and then used as seeds to numerically continue the halo orbits in the ER3BP. The linear stability of the orbits is analyzed which shows that the in-plane motion is unstable while the out-of-plane motion is neutrally stable and a bifurcation is identified. Finally, station-keeping is performed which shows that a reference orbit designed in the ER3BP is significantly more efficient than that designed in the CR3BP, while the addition of RCDs improve station-keeping performance and robustness to uncertainty in the sail lightness number.     

“火卫1”轨道预报与动力学分析

使用数值积分的方法对"火卫1"(Phobos)轨道进行预报计算,介绍了计算"火卫1"轨道时考虑的动力模型与数值积分方法,分析了不同动力模型及参量对轨道计算结果的影响,并确定最终选择的模型。最后将计算结果与不同机构发布的最新历表进行比较,计算位置和轨道根数的差异。得到的结果与各星历之间差异的量级相同,进而验证了相关模型和算法的精度和可靠性。该轨道预报算法模型与分析结果将对"火卫1"探测任务提供参考。     

微纳卫星L1点Halo轨道转移轨道设计

针对地月空间探测任务的高风险、高成本,提出了利用微纳卫星完成地月空间环境监测、未知空间探索及地月空间动力学验证的方案,从而为未来建立地月空间运输系统建立良好基础。借助地月空间三体动力学和小推力轨道设计中的直接法,设计了针对微纳卫星的低能耗地月转移方案。结果表明:微纳卫星借助火箭上面级,从GEO轨道出发飞向L1点Halo轨道,所需速度增量为1.033 km/s,转移时间为40.02 d;不借助火箭上面级,所需速度增量为1.397 5 km/s,转移时间为48.7 d。     

三小行星系统216 Kleopatra引力场中的动力学

主带三小行星系统216 Kleopatra是由主星216 Kleopatra及两个小月亮(moonlet)Alexhelios[S/2008(216)1]和Cleoselene[S/2008(216)2]组成。其中主星216Kleopatra是一个具有强不规则形状如哑铃的连接双星,大小为217km×94km×81km,外小月亮Alexhelios大小约为8.9km,内小月亮大小约为6.9km。其动力学行为具有非常丰富的科学内涵。研究了三小行星系统216Kleopatra自身的动力学机制及其引力场中探测器的运动规律,分析了主星质心固连系中探测器的动力学方程,给出了三小行星引力全多体问题的动力学方程及Jacobi积分,方程考虑了三个小行星的不规则外形、轨道与姿态。发现三小行星系统216Kleopatra主星引力场中一种新的周期轨道族的倍周期分岔。考虑主星的不规则精确外形与引力、两个小月亮的相互作用,研究了该三小行星系统的动力学构形。发现Kleopatra的强不规则几何外形及两个小月亮Alexhelios和Cleoselene的相互作用引起两个小月亮的轨道参数的显著变化。     

Dynamics of a spacecraft and normalization around Lagrangian points in the Neptune–Triton system

The problem of a spacecraft orbiting the Neptune–Triton system is presented. The new ingredients in this restricted three body problem are the Neptune oblateness and the high inclined and retrograde motion of Triton. First we present some interesting simulations showing the role played by the oblateness on a Neptune’s satellite, disturbed by Triton. We also give an extensive numerical exploration in the case when the spacecraft orbits Triton, considering Sun, Neptune and its planetary oblateness as disturbers. In the plane a × I (a = semi-major axis, I = inclination), we give a plot of the stable regions where the massless body can survive for thousand of years. Retrograde and direct orbits were considered and as usual, the region of stability is much more significant for the case of direct orbit of the spacecraft (Triton’s orbit is retrograde). Next we explore the dynamics in a vicinity of the Lagrangian points. The Birkhoff normalization is constructed around L₂, followed by its reduction to the center manifold. In this reduced dynamics, a convenient Poincaré section shows the interplay of the Lyapunov and halo periodic orbits, Lissajous and quasi-halo tori as well as the stable and unstable manifolds of the planar Lyapunov orbit. To show the effect of the oblateness, the planar Lyapunov family emanating from the Lagrangian points and three-dimensional halo orbits are obtained by the numerical continuation method.     

考虑太阳摄动的小行星附近轨道动力学

本文研究了艳后星(216 Kleopatra)和爱神星(433 Eros)附近的周期轨道,在考虑太阳引力摄动的情况下,发现了以往所遗漏的216 Kleopatra轨道族和环绕433 Eros的12族周期轨道,并且给出了它们的特性。研究结果表明,太阳引力对小行星平衡点位置的影响很小,但是对平衡点上航天器运动的影响较大。同族不稳定轨道中,大Jacobi常数轨道更容易在摄动后保持轨道原来特性,这很好地解释了小行星卫星在较远轨道上长期存在的可能性。     

DRO计算及其在地月系中的摄动力研究

针对远距逆行轨道（DRO）的航天工程应用问题,研究了DRO的计算方法以及轨道特性,分析了DRO在实际力环境中的主要摄动因素,为DRO的精确建模和标称轨道设计奠定一定的理论基础。首先,利用仿真算例验证流函数法在计算DRO周期轨道族中的有效性。然后,利用该方法,通过改变雅可比常数,延拓计算DRO周期轨道族,获得不同共振比的DRO,仿真结果表明整数共振比的DRO在地月惯性坐标系中的轨迹是封闭的曲线,而共振比非整数的DRO则不封闭。最后,通过轨道外推分析影响DRO稳定性的主要摄动因素,仿真结果表明太阳引力和月球轨道偏心率是影响DRO稳定性的主要摄动因素。在动力学模型中,使用标准星历表示行星的运动状态,当积分时间多于10天时模型误差为km量级,因此在地月系这样大尺度的空间范围内,可以使用星历模型近似的分析DRO在真实力环境中的运动状态,为任务轨道设计提供依据。      

Mars Phobos and Deimos Survey (M-PADS) – A martian Moons orbiter and Phobos lander

We describe a Mars ‘Micro Mission’ for detailed study of the martian satellites Phobos and Deimos. The mission involves two ∼330 kg spacecraft equipped with solar electric propulsion to reach Mars orbit. The two spacecraft are stacked for launch: an orbiter for remote investigation of the moons and in situ studies of their environment in Mars orbit, and another carrying a lander for in situ measurements on the surface of Phobos (or alternatively Deimos). Phobos and Deimos remain only partially studied, and Deimos less well than Phobos. Mars has almost always been the primary mission objective, while the more dedicated Phobos project (1988–89) failed to realise its full potential. Many questions remain concerning the moons’ origins, evolution, physical nature and composition. Current missions, such as Mars Express, are extending our knowledge of Phobos in some areas but largely neglect Deimos. The objectives of M-PADS focus on: origins and evolution, interactions with Mars, volatiles and interiors, surface features, and differences. The consequent measurement requirements imply both landed and remote sensing payloads. M-PADS is expected to accommodate a 60 kg orbital payload and a 16 kg lander payload. M-PADS resulted from a BNSC-funded study carried out in 2003 to define candidate Mars Micro Mission concepts for ESA’s Aurora programme.     

星间洛仑兹力编队飞行的平衡点及零速度曲面

提出了一种新的利用星间洛仑兹力控制卫星相对运动的方法:使主星产生自旋磁场,副星带电,通过控制副星所受的星间洛仑兹力进行编队。假设主星产生的人造磁场表现为偶极子并且运动在一条开普勒圆形轨道上,副星恒定带电并在主星附近运动,同时假设星间洛仑兹力只影响副星的运动而不影响主星的运动。推导了副星在主星HCW(当地垂直当地地平坐标系)坐标系下的相对运动动力学方程。针对偶极子与HCW坐标轴X轴重合的情况下,推导了动力系统下的平衡点(并采用稳定性分析方法分析其线性化意义下的稳定性)、积分常数和零速度曲面,证明了有界相对运动的存在。最后用数值仿真验证了上述结论。     

Cosmic dust measurements in lunar orbit

On 15th February 1992, ISAS space engineering satellite HITEN was successfully inserted into an elliptical orbit around the moon with perilune between some 100 km and 8000 km and apolune of about 50.000 km. On board was a small scientific experiment designed to detect cosmic dust particles, MDC - Munich Dust Counter. During a period of more than one year, until Hiten's hard landing on the moon surface at 10th of April 1993 (UTC), measurements of impact velocity, mass and crude flight direction of micrometeoroid particles have been performed. In total 150 cosmic dust impacts were detected and evaluated. From these measurements, the impact rate versus time and the dust flux versus distance from the moon are derived. The evidence of moon ejecta and some indications of particles which are orbiting the moon will be discussed. The spatial distribution of the measured particles is shown in lunarcentric as well as in heliocentric coordinate systems. The directional distribution is also given, showing the different populations of cosmic dust particles. Finally, the gathered data will be compared with previous results from measurements in the vicinity of the Earth and in the geomagnetic tail region.     

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。     

Dynamical evolution of high area-to-mass ratio objects in Molniya orbits

For special demands, some notable orbit types have been developed by human, including the Molniya orbits, which have a relatively high eccentricity up to about 0.7, and a period of 12 h. Considering that space debris with high area-to-mass ratio (A/M) has been discovered, such objects may also exist in Molniya orbits due to spacecraft and upper stages fragmentation events. However, there are not sufficient studies of the complex dynamical phenomena of such orbits. These studies can enrich the knowledge about the long-term evolution of these orbits, be helpful to propose uncatalogued objects observation and identification, and also set the protected region as well as active debris removal. In this paper, the characteristics of 2:1 resonance of Molniya satellite orbits are studied. A large set of numerical simulations, including all the relevant perturbations, is carried out to further investigate the main characteristics, and special attention is payed to the dynamical evolution of objects with high A/M, particularly affected by the direct solar radiation pressure. The long-term dynamical evolution of orbital elements, as well as the dependency of lifetime on the A/M value, is discussed.     

基于混杂系统的空间飞行器悬停控制

基于空间飞行器的轨道动力学原理,利用混杂系统模型研究了悬停轨道问题,建立了悬停轨道的混杂系统模型;借此模型,针对目标星轨道为椭圆的情况,提出了等距离悬停轨道控制和椭圆悬停轨道控制两种方案,分别推导出在这两种方案下对悬停星所施加的控制力。数值仿真结果表明,分别对悬停星施加相应的控制力,能够实现对目标星的悬停。     

Configuration space and stability analysis of solar sail near-vertical earth-trailing orbits

Regions outside the reach of traditional propulsion systems or the ones that require significant propellant, may be reached by harnessing the solar radiation pressure and leveraging coupled dynamics to maneuver a sail-based spacecraft. Earth-trailing orbits have recently been investigated for getting a unique perspective of the Sun while maintaining the spacecraft in close proximity to Earth. Vertical orbits trailing the Earth exhibit the additional capability to view the Sun from above and below the ecliptic plane. In this work, families of sail-based orbits are explored for varying Earth-trailing angles and Z amplitudes in the Sun-Earth circular restricted three-body problem. Optimization is carried out to ensure that the non-traditional vertical orbits exhibit a constant pitch angle control history, as well as symmetry across the X-Y plane. The stability of the resulting orbit families is assessed using an extension of Flouquet theory to Differential Algebraic Equations. Results indicate that sail-based Earth-trailing vertical orbits can be more stable than traditional sub-L₁ sail-based vertical orbits.