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。      

Halo轨道族延拓方法及特性研究

对Halo轨道周期和运动范围等特性的研究是平动点任务设计的首要前提。针对大幅值Halo轨道和完整Halo轨道族的应用需求及其数值计算问题,面向当前应用广泛的地月系和日-地月系共线平动点,基于延拓法研究了圆型限制性三体问题下的Halo轨道族数值计算和运动学特性,给出了Halo轨道族延拓计算方法。数值仿真了族参数选择对轨道族计算的影响,得到了地月系和日-地月系共线平动点的大范围南北Halo轨道族,同时给出了轨道族的轨道周期变化和空间位置变化特性。研究结果表明,固定延拓步长下,L1点Halo轨道族应选择会合坐标系x坐标作为族参数,L2点Halo轨道族应选择y方向速度或者周期T作为族参数。方法适用于任意三体系统平动点的周期轨道族计算,特别是对其中的状态转移矩阵简单修改后可用于完整力模型下的Halo轨道（族）的数值设计。     

地月L2点周期轨道的月球背面覆盖分析

地月L2点附近轨道具备独特的动力学和运动学特性,是月球背面探测任务的中继卫星首选布设位置。面向未来月球背面探测任务的中继通信需求,分析并研究了地月L2点周期轨道(halo轨道)对月球背面的覆盖。在圆型限制性三体问题模型下,研究并给出了halo轨道族延拓计算方法,基于延拓法设计了地月系大范围南北halo轨道族;给出了中继卫星的月球背面覆盖计算模型,定义了相应的时间覆盖因子;数值仿真了地月系南北halo轨道族的月球背面覆盖情况。研究结果表明:地月L2点周期轨道幅值和类型决定其对月面的覆盖性,幅值较小的轨道的月面整体覆盖性较好,幅值较大的轨道对月球南北极覆盖较好,南北族轨道分别有利于月球南北半球的覆盖。文章研究可为我国"嫦娥4号"月球背面探测任务的中继星轨道设计提供有益参考和借鉴。     

空间小推力轨道最优Bang-Bang控制的两类延拓解法综述

介绍了空间小推力轨道优化问题中的最优Bang-Bang控制问题,对两类延拓解法给出了描述:第一类解法首先求解能量最优解,然后采用能量–燃耗同伦得到最优Bang-Bang控制;第二类解法引入推力开关切换准则,以双脉冲解作为初解,通过参数延拓得到最优Bang-Bang控制。对两类延拓解法进行了比较,指出了各自的优势与特点。对延拓方法应用于求解更加复杂的小推力轨道设计问题进行了展望,提出了包含初解、延拓与拼接三要素的人工智能轨道优化概念。     

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。      

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。     

一种适用于平动点周期轨道初值计算的简化路径搜索修正法

在限制性三体问题中,路径搜索修正法是一种基于平动点周期轨道垂直穿越Poincare截面的几何对称性计算平面及空间平动点周期轨道近似初值的方法.采用路径搜索修正法的一种简化形式,在圆形限制性三体模型中,对地月系中几种典型的平面及空间周期轨道近似初值进行了计算.结果表明,该简化方法得到的周期轨道近似初值不唯一,由近似初值经微分修正得到的精确结果中通常同时存在Halo轨道和大幅值逆行轨道（DRO）.进一步分析表明,在某些临界初值下,精确结果中Halo轨道将消失,同时可能出现平面Lyapunov轨道及Vertical轨道.上述计算中,搜索初值与结果中轨道类型的对应关系值得进一步研究.     

地球静止轨道空间碎片的防护与轨道保护策略

地球静止轨道是人类在太空仅有的一条独特轨道,是重要的空间资源。近年来,地球静止轨道使用状况不容乐观,面临着诸多的问题,为此,机构间空间碎片协调委员会制定了针对地球静止轨道的保护策略。1概述航天技术的高速发展,不仅是一个国家地位和综合实力的体现,更是推动经济社会进步的强大动     

基于UKF参数估计的地月自由返回轨道设计

为快速简便地设计地月自由返回轨道,提出了一种基于UKF参数估计算法的地月自由返回轨道设计方法。该算法不仅避免了传统数值方法推导相关梯度矩阵的复杂性,而且只需基于地月系统二体模型给出猜测初值,从而显著降低了自由返回轨道设计的难度,将地月自由返回轨道对应的两点边值问题的求解转化为参数估计问题,该算法可以得到高精度模型下收敛的精确解。数值仿真结果表明:该算法结构简洁,求解效率较高,所得结果精确且具有良好的鲁棒性,可以作为地月自由返回轨道设计的一个有力工具。     

基于显式制导的月地返回轨道中途修正研究

月地返回轨道存在各种摄动误差,终端约束复杂,有必要对其进行中途修正研究。显式制导法通过二体轨道与精确轨道之间的差别进行多次迭代求解给定时刻所需的修正速度。文章利用显式制导法,采用月球段及地球段分段进行中途修正的策略,给出了基于分段落点预报显式制导的月地返回轨道中途修正方案。该方案无需计算雅克比矩阵,算法简单、计算快速、实用性强,能满足再入点参数要求。算例仿真与蒙特卡洛仿真验证了该方案的适用性。     

Analytical expression for distant retrograde orbits around a small natural satellite

An analytical expression for distant retrograde orbits (DROs) is obtained in this study. Owing to the fact that a planar DRO is a closed orbit and can be expressed as an approximately elliptical orbit, respective geometries and periods of DROs are analytically calculated. A switching point, where various properties of planar DROs change abruptly with an increase in the orbital radius, is determined. The Mars–Deimos system is taken as a case study in this work. The proposed method can be applied to cases where the Hill’s approximation of the restricted three-body problem is valid. Numerical calculations are performed to validate the proposed method.     

On the stabilizing effect of Solar Radiation Pressure in the Earth-Moon system

Solar sails change the natural dynamics of systems: Trajectories that are driven by gravitational forces can be displaced and changed because of the effect of Solar Radiation Pressure (SRP). Moreover, if the lightness number of the sail is large enough, the instability of certain orbits can be diminished and even removed. In this paper we modify two models for the motion of a probe in the Earth-Moon system that include the effect of Sun’s gravity to take also into account the effect of SRP. These models, the Bicircular Problem (BCP) and the Quasi-Bicircular Problem (QBCP), are periodic perturbations of the Earth-Moon Restricted Three Body Problem (RTBP). The models are modified to consider the effect of the SRP upon a solar sail. We provide examples of periodic orbits that are stabilized (or made less unstable) due to the effect of SRP.     

Stationkeeping of halo orbits in Jupiter-Europa-Io system

Europa is one of the most promising exploration targets in search for extraterrestrial life. In the observation of Europa, halo orbits are suitable locations, because they are periodic and three-dimensional, and stationary with respect to Europa. However, halo orbits are naturally unstable and thus need stationkeeping. This study addresses the stationkeeping problem of halo orbits in the Jupiter-Europa system perturbated by another Galilean moon Io, in which case Io’s mass and orbital rate are assumed to be unknown. A tight stationkeeping scheme is proposed while accounting for autonomous navigation. To deal with the unknown gravitational perturbation from Io, the mass and orbital rate of Io are estimated during the flight and are then used to enhance the control robustness and stability, and improve the navigation accuracy. The control saturation problem is addressed by introducing adjustable parameters into the control law. The accuracy and error distribution of estimation is evaluated through Monte Carlo simulation.     

Determination of orbits with Torun Orbit Processor system

The Torun Orbit Processor system (TOP) is a multipurpose system designed to provide the research requirements of the various orbital problems for artificial satellites. The analysis of mathematical model for the TOP system began in 1991 and coding for the IBM PC and Sun SparcStation 10 computers was completed in 1993. TOP was first used for laser data processing of Lageos satellite and for simulations of satellite-to-satellite tracking technique (SST). This paper gives an overview of TOP system and highlights some problems connected with orbit recovery.     

Satellite orbits in Levi-Civita space

In this paper we consider satellite orbits in central force field with quadratic drag using two formalisms. The first using polar coordinates in which the satellite angular momentum plays a dominant role. The second is in Levi-Civita coordinates in which the energy plays a central role. We then merge these two formalisms by introducing polar coordinates in Levi-Civita space and derive a new equation for satellite orbits which unifies these two paradigms. In this equation energy and angular momentum appear on equal footing and thus characterize the orbit by its two invariants. Using this formalism we show that equatorial orbits around oblate spheroids can be expressed analytically in terms of Elliptic functions. In the second part of the paper we derive in Levi-Civita coordinates a linearized equation for the relative motion of two spacecrafts whose trajectories are in the same plane. We carry out also a numerical verification of these equations.     

远磁尾磁层顶位形的偏转

利用WIND和ARTEMIS卫星观测数据,分析远磁尾磁层顶对行星际和太阳风变化的响应,尤其是偏离日地连线的太阳风速度改变对远磁尾磁层顶的影响.研究发现在2011年9月13日的事件中,P2卫星观测到高速且高密度的磁鞘流.利用最小变量法进行分析发现,磁层顶沿着偏离日地连线的太阳风速度方向发生偏转.根据相似三角形定理,推断出本次事件中磁层顶在y方向和z方向上的偏转幅度分别达到10R_e和6R_e.P1和P2卫星的相对位置也证实了这一观点.因此,偏离日地连线的太阳风速度对远磁尾磁层顶的位形影响很大.研究结果可为建立包含太阳风速度v_y和v_z效应的磁层顶模型提供观测证据.     

Spacecraft survivability in the natural debris environment near the stable Earth-Moon Lagrange points

The theoretical analysis of the motion of natural space debris near the stable Earth-Moon Lagrange Points, $L_4$ and $L_5$, is presented with a focus on the potential debris risks to spacecraft operating near these points. Specifically, the research formulates a debris propagation model using four-body dynamics, then applies candidate probabilistic survivability models to a notional spacecraft operating at the $L_4$ and $L_5$ Lagrange points to quantify the collision risks to the spacecraft from natural debris particles. Of the survivability models implemented, the natural debris collision risks to spacecraft survivability are found to be incredibly low, but mitigation strategies to reduce the risk further are identified in this study. Overall, research into stable Lagrange point natural debris propagation improves understanding of the collision risks posed by the naturally occurring Kordylewski clouds and enhances operational planning for Lagrange point space missions.     

Earth and Mars observation using periodic orbits

This paper reports the results of a general study carried out on the Periodic Multi-SunSynchronous Orbits (PMSSOs), which the classical Periodic SunSynchronous Orbits (PSSOs) represent a specific solution of. Such orbits allow to obtain cycles of observation of the same region in which the solar illumination regularly varies according to the value of the orbit elements and comes back to the initial condition after a time interval which is multiple of the revisit time. Therefore this kind of orbits meets all the remote sensing applications that need observations of the same area at different local times (for example the reconstruction of the day-nighttime trend of the surface temperature of the planet) and it is particularly suitable to the study of several terrestrial and martian phenomena (diurnal cycle of the hazes and clouds, dynamics of the thermal tides, density variations, meteorology phenomena, etc.). The design of PMSSO is based on the variation of the Right Ascension of the Ascending Node due to the Earth oblateness (referred as basic solution). However, with respect to the basic solution, the analysis of the perturbative effects has demonstrated the need, especially in the case of Mars, to take into account all the superior harmonics of the gravitational field. To this end a corrective factor, to add to the basic equations, has been proposed, allowing a significant saving of propellant (of the order of 2 km/s per year). Besides, single and multi-plane satellite constellations have been taken into account in order to improve the repetition of observation and the ground spatial resolution.     

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。