月球卫星轨道力学综述

月球探测器的运动通常可分为3个阶段，这3个阶段分别对应3种不同类型的轨道：近地停泊轨道、向月飞行的过渡轨道与环月飞行的月球卫星轨道。近地停泊轨道实为一种地球卫星轨道；过渡轨道则涉及不同的过渡方式(大推力或小推力等)；环月飞行的月球卫星轨道则与地球卫星轨道有很多不同之处，它决不是地球卫星轨道的简单克隆。针对这一点，全面阐述月球卫星的轨道力学问题，特别是环月飞行中的一些热点问题，如轨道摄动解的构造、近月点高度的下降及其涉及的卫星轨道寿命、各种特殊卫星(如太阳同步卫星和冻结轨道卫星等)的轨道特征、月球卫星定轨等。     

中英科学家加蓬联合观测日全食

地球围绕太阳公转,每年365．26天旋转一周,地球的轨道平面被称为黄道。月亮围绕地球公转,每27．3天完成一次周期运转,月亮的公转轨道面称为白道。白道与黄道之间的夹角略有变化,平均为509’。由于地球和月球的轨道运动,如果地球、月球和太阳恰好位于同一条直线上,月球处在地球和太阳之间时,在地球上处在太阳和月球连线方向的区域便会观看到日全食现象。     

月球探测器过渡轨道的短弧定轨方法

论述的短弧定轨,是指在无先验信息情况下又避开多变元迭代的初轨计算方法,它需要相应的动力学问题有一能反映短弧内达到一定精度的近似分析解．探测器进入月球引力作用范围后接近月球时可以处理成相对月球的受摄二体问题,而在地球附近,则可处理成相对地球的受摄二体问题,但在整个过渡段的力模型只能处理成一个受摄的限制性三体问题．而限制性三体问题无分析解,即使在月球引力作用范围外,对于大推力脉冲式的过渡方式,相对地球的变化椭圆轨道的偏心率很大(超过Laplace极限),在考虑月球引力摄动时亦无法构造摄动分析解．就此问题,考虑在地球非球形引力(只包含J2项)和月球引力共同作用下,构造了探测器飞抵月球过渡轨道段的时间幂级数解,在此基础上给出一种受摄二体问题意义下的初轨计算方法,经数值验证,定轨方法有效,可供地面测控系统参考．     

谈谈印度首颗探月卫星

一、印度月球初航1号如何奔月 2008年10月22日,印度用极轨卫星运载火箭－XL（PSLV—XL）发射了其首颗探月卫星——月球初航1号（Chandrayaan-1,又叫月船1号）。探测器首先进入了近地点255千米、远地点22860千米的大椭圆轨道。在绕地运行两个星期的时间里,探测器上的液体发动机适时点火工作5次,     

近地小行星轨道演化的研究

主要阐述近年来在近地小行星轨道演化研究工作中所获得的一些基本结果，即合理的力学模型和相应的有效算法，并以实际预报算例（近地小行星与地球的交会状态）与有关权威性的结果作了比较，证实这些研究结果确实是可信的。在给出的力学模型中，考虑了所有可能影响近地小行星运动的力学因素，包括各大天体和较大的主带小行星的引力作用、有关天体的扁率影响以及源于太阳引力的后牛顿效应。而在计算方法中，合理地处理了变步长问题和月球位置量这种相对而言的快变化问题，使得数值求解一个高维方程组时，对各天体而言，可采用同一步长进行 积分，避免了求解过程中的复杂性。     

月球物理天平动对环月轨道器运动的影响

月球物理天平动是月球赤道在空间真实的摆动，会导致月球引力场在空间坐标系中的变化，从而引起环月轨道器(以下称为月球卫星)的轨道变化，这与地球的岁差章动现象对地球卫星轨道的影响类似．采用类似对地球岁差章动的处理方法，讨论月球物理天平动对月球卫星轨道的影响，给出相应的引力位的变化及卫星轨道的摄动解，清楚地表明了月球卫星轨道的变化规律，并和数值解进行了比对，从定性和定量方面作一讨论．     

满足约束条件的月球卫星飞行轨道的初步设计

讨论满足约束条件的月球卫星飞行轨道的设计问题，将约束条件分类为只与太阳，月球，地球，飞行器和观测站之间的相对位置有关的运行学约束条件以及涉及到飞行器轨道运行的动力学约束条件，在考虑月球卫星轨道的受力情况后，给出一种准确快速地计算和设计满足约束条件的标准飞行轨道的方法，并应用于不同约束条件下月球卫星的轨道预设计，初步讨论了轨道设计的误差分析，轨道跟踪及实时精密定轨等正在进行的其它相关工作。     

竞赛试卷

竞赛试卷一、选择题（共１６题）：①１９９４年６月～９月飞临太阳极区的宇宙探测器发现了太阳高纬区域，日球磁场的极性是紊乱的，磁场强度几乎不随日面纬度的不同而变化。这个探测器是。（Ａ）太阳峰年使者（ＳＭＭ）；（Ｂ）太阳神（Ｈｅｌｉｏｓ）；（Ｃ）尤利西斯（...     

利用双行根数计算太阳相位角的精度评估

光度特性测量是获取空间目标的物理特性的重要技术手段之一,无论是光变曲线的事后分析还是建立光度变化的仿真模型,都离不开一个重要的参数——太阳相位角（太阳-空间目标-测站的空间夹角）.目前空间目标的位置通常是通过双行根数（TLE）外推获得,存在一定误差,且随外推时间的延长而变大,因而有必要对其计算所得的太阳相位角的精度进行评估.以典型的不同高度的激光测距卫星LAGEOS1、AJISAI、STELLA为研究对象,以全球激光测距资料解算所得的高精度轨道作为参考轨道,对2012年全年利用双行根数计算所得的太阳相位角数据进行了比对分析,结果表明对于LAGEOS1、AJISAI这样的中高轨卫星,由于轨道较高,表征阻力的B＊恒定,计算所得的太阳相位角偏差较小,角分量级,且随外推时间的延长不会导致偏差明显增大;而对于STELLA这样的低轨卫星,因轨道较低、受变化的大气的影响显著,计算所得的太阳相位角偏差较大,尤其是当B＊比较大、变化较快时,偏差显著变大,且随外推时间的延长显著增大,在最差情况下：外推1d约为13＇,外推3d约为50＇,外推7d约为251＇,已超出目前的精度要求.因此,在事后分析中应尽可能使用1d之内的TLE计算太阳相位角,对于B＊较大且变化较快情况尤其需要注意.另外,针对UTC闰秒的情况,提出了一种处理方法,即在双行根数外推时判断外推时段是否跨越了闰秒时刻,若跨越了则进行修正：增加或减少1s,相应地需要修改结果对应的时间戳计算方法.     

“月球人”回到人间之后

“月球人”回到人间之后张明昌规模空前的“阿波罗”计划曾使前苏联在太空中的一切优势荡然无存，它的确实现了“把苏联人击败在月球上”的目标。“阿波罗”计划曾造就了２４个“月球人”，２７人次到“广寒宫”作客（表１、２）。如今他们中已有２人作古，其余亦都垂垂老...     

Controlled Solar Sail Transfers into Near-Sun Regions Combined with Planetary Gravity-Assist Flybys

Results of numerical simulations of 'local-optimal' (or 'instantaneously optimal') trajectories of a space probe with a flat solar sail which moves from the circular Earth orbit to near-Sun regions are presented. We examine planar (ecliptic) solar sail transfer with gravity-assist flybys of Earth, Venus and Mercury. Several complex control modes of the sail tilt orientation angle for near-Sun orbits and for some 'falling onto the Sun' trajectories are investigated. The numerical simulations are used to examine the flight duration of some sail missions and to investigate the evolution of osculating elliptical orbits.     

Long-term evaluation of three-dimensional heliocentric solar sail trajectories with arbitrary fixed sail setting

The solar radiation effects upon the orbital behaviour of an arbitrarily shaped spacecraft (or a solar sail in particular) in a general fixed orientation with respect to the local coordinate frame are investigated. Through introduction of a quasi-angle in the osculating plane, the motion of the orbital plane becomes uncoupled from the in-plane perturbations. Exact solutions in the form of conic sections and logarithmic spirals can readily be formulated for certain specific initial conditions. An effective out-of-plane spiral transfer trajectory is obtained by reversing the force component normal to the orbital plane at specified positions in the orbit. By choosing the appropriate control angles for the sail orientation, any point in space can be reached eventually. In the case of general initial conditions, the long-term orbital behaviour is assessed asymptotically by means of the two-variable expansion procedure. An implicit expression for the eccentricity is derived and explicit results are established by an iteration scheme. The other orbital elements can be expressed in terms of the eccentricity and their asymptotic series for near-circular initial orbits are also obtained. While equations for the higher-order contributions as well as the periodic parts of their solutions can be formulated readily, their secular terms are determined only for a circular initial orbit.     

Solar sail time-optimal interplanetary transfer trajectory design

The fuel consumption associated with some interplanetary transfer trajectories using chemical propulsion is not affordable. A solar sail is a method of propulsion that does not consume fuel. Transfer time is one of the most pressing problems of solar sail transfer trajectory design. This paper investigates the time-optimal interplanetary transfer trajectories to a circular orbit of given inclination and radius. The optimal control law is derived from the principle of maximization. An indirect method is used...     

Solar Sail Halo Orbits at the Sun–Earth Artificial L 1 Point

Halo orbits for solar sails at artificial Sun–Earth L₁ points are investigated by a third order approximate solution. Two families of halo orbits are explored as defined by the sail attitude. Case I: the sail normal is directed along the Sun-sail line. Case II: the sail normal is directed along the Sun–Earth line. In both cases the minimum amplitude of a halo orbit increases as the lightness number of the solar sail increases. The effect of the z-direction amplitude on x- or y-direction amplitude is also investigated and the results show that the effect is relatively small. In case I, the orbit period increases as the sail lightness number increases, while in case II, as the lightness number increases, the orbit period increases first and then decreases after the lightness number exceeds ~0.01.     

Periodic orbits of solar sail equipped with reflectance control device in Earth–Moon system

In this paper, families of Lyapunov and halo orbits are presented with a solar sail equipped with a reflectance control device in the Earth–Moon system. System dynamical model is established considering solar sail acceleration, and four solar sail steering laws and two initial Sun-sail configurations are introduced. The initial natural periodic orbits with suitable periods are firstly identified. Subsequently, families of solar sail Lyapunov and halo orbits around the \(L_{1}\) and \(L_{2}\) points are designed with fixed solar sail characteristic acceleration and varying reflectivity rate and pitching angle by the combination of the modified differential correction method and continuation approach. The linear stabilities of solar sail periodic orbits are investigated, and a nonlinear sliding model controller is designed for station keeping. In addition, orbit transfer between the same family of solar sail orbits is investigated preliminarily to showcase reflectance control device solar sail maneuver capability.     

定点在日-地(月)系L1点附近的探测器的发射及维持

在限制性三体问题中共线平动点附近的运动虽然是不稳定的,但可以是有条件稳定的,该动力学特征使得一些有特殊目的的探测器只需消耗较少的能量即可定点在这些点附近(如ISEE-3、SOHO).以日-地(月)系的L1点为例,根据其附近的运动特征,探讨定点探测器的发射与轨道控制问题,给出了相应的数值模拟结果,为工程上的实现提供理论依据.     

Error Analysis and Trajectory Correction Maneuvers of Lunar Transfer Orbit

For a returnable lunar probe, this paper studies the characteristics of both the Earth-Moon transfer orbit and the return orbit. On the basis of the error propagation matrix, the linear equation to estimate the ?rst midcourse trajectory correction maneuver (TCM) is ?gured out. Numerical simulations are performed, and the features of error propagation in lunar transfer orbit are given. The advantages, disadvantages, and applications of two TCM strategies are discussed, and the computation of the second TCM of the return orbit is also simulated under the conditions at the reentry time.     

Non-Keplerian orbits for electric sails

An electric sail is capable of guaranteeing the fulfilment of a class of trajectories that would be otherwise unfeasible through conventional propulsion systems. In particular, the aim of this paper is to analyze the electric sail capabilities of generating a class of displaced non-Keplerian orbits, useful for the observation of the Sun’s polar regions. These orbits are characterized through their physical parameters (orbital period and solar distance) and the spacecraft propulsion capabilities. A comparison with a solar sail is made to highlight which of the two systems is more convenient for a given mission scenario. The optimal (minimum time) transfer trajectories towards the displaced orbits are found with an indirect approach.     

Utilization of an H-reversal trajectory of a solar sail for asteroid deflection

Near Earth Asteroids have a possibility of impacting the Earth and always represent a threat. This paper proposes a way of changing the orbit of the asteroid to avoid an impact. A solar sail evolving in an H-reversal trajectory is utilized for asteroid deflection. Firstly, the dynamics of the solar sail and the characteristics of the H-reversal trajectory are analyzed. Then, the attitude of the solar sail is optimized to guide the sail to impact the target asteroid along an H-reversal trajectory. The impact...     

Formation flying solar-sail gravity tractors in displaced orbit for towing near-Earth asteroids

Several methods of asteroid deflection have been proposed in literature and the gravitational tractor is a new method using gravitational coupling for near-Earth object orbit modification. One weak point of gravitational tractor is that the deflection capability is limited by the mass and propellant of the spacecraft. To enhance the deflection capability, formation flying solar sail gravitational tractor is proposed and its deflection capability is compared with that of a single solar sail gravitational tractor. The results show that the orbital deflection can be greatly increased by increasing the number of the sails. The formation flying solar sail gravitational tractor requires several sails to evolve on a small displaced orbit above the asteroid. Therefore, a proper control should be applied to guarantee that the gravitational tractor is stable and free of collisions. Two control strategies are investigated in this paper: a loose formation flying realized by a simple controller with only thrust modulation and a tight formation realized by the sliding-mode controller and equilibrium shaping method. The merits of the loose and tight formations are the simplicity and robustness of their controllers, respectively.