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。