从地面发射月球探测器的窗口选择

典型的月球探测器飞行轨道包括地球停泊轨道段、地月转移轨道段、月球卫星轨道段和着月轨道段。首先介绍了设计从地面发射月球探测器轨道典型的约束条件;然后,借助于二体假设,建立解析表达式,分析各种约束对窗口选择的影响,给出了各轨道段概略的飞行时间和粗窗口;最后,利用精确的探测器轨道动力学模型,计算精窗口,并给出了一则算例,所得结论可为月球探测器轨道发射、轨道设计提供依据。     

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。     

满足一定约束条件的登月飞行轨道的设计

讨论满足约束条件的登月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动学约束条件以及小及到飞行器轨道云动的动力学约束条件，在考虑登月飞行轨道的特征后，给出一种设计满足约束条件的标准飞行轨道的方法，并将方法应用于不同约束条件下的我国登月飞行以及月球卫星的轨道预测计。     

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．     

月球重力场对绕月低轨卫星的长期影响

从解析形式出发,利用月球重力场模型JGL165P1,分析了月球重力场(带谐项)对绕月低轨卫星的长期影响。为了减少计算误差,保证计算精度,在分析解中使用循环公式来计算倾角函数。结果指出对于一个高度为100km的极月轨道卫星,冻结轨道存在的可能性不大,但是当轨道倾角在i=90°附近或者高度再高一些,则有可能存在冻结轨道;对于100km高的初始圆轨道,卫星在无控的情况下半年内将会坠落到月球表面,如果高度增加到200km,则不进行轨道控制也不会坠落到月面上。利用仿真软件GEODYN解算出来的结果证实了上述结论。     

古怪的月球重力场

日历翻回到1972年4月24日,阿波罗16号的3位宇航员感到似乎可以松一口气了。在他们返回地球之前,只需要执行最后一项任务：释放小型子卫星PSF-2号——它将大约每2小时环绕月球一周（参见图1）。这颗小卫星将加入到8个月前由阿波罗15号释放的PSF-1号的工作中去,测量月球周围的带电粒子和磁场。这两颗子卫星都有着比较低的椭圆轨道,离开月面只有89到122千米。     

借助光压将探测器推向月球

若采用圆型限制性三体问题模型，从近地停泊轨道上发射一个月球探测器，其最小初始速度必须使相应的Jacobi常数C小于某一临界值C2。但这仅仅是探测器可能飞向月球的必要条件，而且这样飞向月球耗时过长。若采用Hohmann转移轨道，则需要获得较大的变轨冲量，能量消耗较大。如果需要仔细探测地月空间环境，而又不必很快地飞往月球，那么采用较大的太阳帆板，并使其法向有一特殊指向，可借助太阳光压加速引导探测器在不长的时间内飞向月球。利用相应的分析和计算，证实上述考虑是有效的，而且若使太阳帆板截面积大到一定程度（如果技术上能实现），则无需任何动力，也可借助光压将探测器推向月球，就像一条太空帆船（简称太空帆）。     

关于月球低轨卫星运动的两个问题

对月球低轨卫星的轨道寿命特征和冻结轨道晶状态作了详尽的理论分析,给出它们与轨道倾角之间的关系以及它们相互之间的某种联系,并考虑低轨卫星的主要摄动源,在完整力模型下作了相应的模拟计算,不仅证实了理论分析的正确性,而且为环月运行探测器的轨道设计提供了极有参考价值的数值结果．     

卫星轨道偏心率的变化特征及其对轨道寿命的影响

轨道偏心率的变化极其重要,它是制约各类(不同高度)空间飞行体轨道寿命的关键因素之一.对于地球低轨卫星,主要受大气耗散作用的影响,而对环月(或环火星)低轨卫星,主要受非球形引力位中奇次带谐项的影响,会出现变幅较大的长周期变化,从而导致近星点高度hp在一段时间内有明显的下降趋势.对大偏心率轨道和高轨道,第三体的引力作用也会使e出现变幅较大的长周期变化,近星点高度hp也会有明显下降的现象,这都会影响卫星的轨道寿命,但这一动力学机制与大气耗散机制和非球形引力机制都不相同.即对轨道偏心率的变化特征及其对轨道寿命的影响作一综述.     

Zonal harmonics of azimuthally averaged potential of rotating inhomogeneous ellipsoids

The distant retrograde orbits (DROs) can serve as the parking orbits for a long-term cis-lunar space station. This paper gives a comprehensive study on the transfer problem from DROs to Earth orbits, including low Earth orbits (LEOs), medium Earth orbits (MEOs), and geosynchronous orbits (GSOs), in the bicircular restricted four-body problem (BR4BP) via optimizations within a large solution space. The planar transfer problem is firstly solved by grid search and optimization techniques, and two types of transfer orbits, direct ones and low-energy ones, are both constructed. Then, the nonplanar transfer problem to Earth orbits with inclinations between 0 and 90 degrees are solved via sequential optimizations based on the planar transfers. The transfer characteristics in the cases of different destination orbit inclinations are discussed for both the direct and the low-energy transfer orbits. The important role of the lunar gravity in the low-energy transfers is also discussed, which can overcome the increase of transfer cost caused by the high inclination of Earth orbits. The distinct features of different transfer scenarios, including multiple revolutions around the Earth and Moon, the exterior phase, and the lunar flyby, are discovered. The energy of transfer orbits is exploited to discuss the effects of close lunar flybys. The results will be helpful for the transfer design in future manned or unmanned return missions, and can also provide valuable information for selecting proper parking DROs for cis-lunar space stations.

     

Study of the transfer between libration point orbits and lunar orbits in Earth–Moon system

This paper is devoted to the study of the transfer problem from a libration point orbit of the Earth–Moon system to an orbit around the Moon. The transfer procedure analysed has two legs: the first one is an orbit of the unstable manifold of the libration orbit and the second one is a transfer orbit between a certain point on the manifold and the final lunar orbit. There are only two manoeuvres involved in the method and they are applied at the beginning and at the end of the second leg. Although the numerical results given in this paper correspond to transfers between halo orbits around the \(L_1\) point (of several amplitudes) and lunar polar orbits with altitudes varying between 100 and 500 km, the procedure we develop can be applied to any kind of lunar orbits, libration orbits around the \(L_1\) or \(L_2\) points of the Earth–Moon system, or to other similar cases with different values of the mass ratio.     

Numerical investigation of collision orbits of lunar satellites

In the present study an investigation of the collision orbits of natural satellites of the Moon (considered to be of finite dimensions) is developed, and the tendency of natural satellites of the Moon to collide on the visible or the far side of the Moon is studied. The collision course of the satellite is studied up to its impact on the lunar surface for perturbations of its initial orbit arbitrarily induced, for example, by the explosion of a meteorite. Several initial conditions regarding the position of the satellite to collide with the Moon on its near (visible) or far (invisible) side is examined in connection to the initial conditions and the direction of the motion of the satellite. The distribution of the lunar craters-originating impact of lunar satellites or celestial bodies which followed a course around the Moon and lost their stability - is examined. First, we consider the planar motion of the natural satellite and its collision on the Moon's surface without the presence of the Earth and Sun. The initial velocities of the satellite are determined in such a way so its impact on the lunar surface takes place on the visible side of the Moon. Then, we continue imparting these velocities to the satellite, but now in the presence of the Earth and Sun; and study the forementioned impacts of the satellites but now in the Earth-Moon-Satellite system influenced also by the Sun. The initial distances of the satellite are taken as the distances which have been used to compute periodic orbits in the planar restricted three-body problem (cf. Gousidou-Koutita, 1980) and its direction takes different angles with the x-axis (Earth-Moon axis). Finally, we summarise the tendency of the satellite's impact on the visible or invisible side of the Moon.     

Using space manifold dynamics to deploy a small satellite constellation around the Moon

The possibility of communicating with the far side of the Moon is essential for keeping a continuous radio link with lunar orbiting spacecraft, as well as with manned or unmanned surface facilities in locations characterized by poor coverage from Earth. If the exploration and the exploitation of the Moon must be sustainable in the medium/long term, we need to develop the capability to realize and service such facilities at an affordable cost. Minimizing the spacecraft mass and the number of launches is a driving parameter to this end. The aim of this study is to show how Space Manifold Dynamics can be profitably applied in order to launch three small spacecraft onboard the same launch vehicle and send them to different orbits around the Moon with no significant difference in the Delta-V budgets. Internal manifold transfers are considered to minimize also the transfer time. The approach used is the following: we used the linearized solution of the equations of motion in the Circular Restricted Three Body Problem to determine a first–guess state vector associated with the Weak Stability Boundary regions, either around the collinear Lagrangian point L1 or around the Moon. The resulting vector is then used as initial state in a numerical backward-integration sequence that outputs a trajectory on a manifold. The dynamical model used in the numerical integration is four-body and non-circular, i.e. the perturbations of the Sun and the lunar orbital eccentricity are accounted for. The trajectory found in this way is used as the principal segment of the lunar transfer. After separation, with minor maneuvers each satellite is injected into different orbits that lead to ballistic capture around the Moon. Finally, one or more circularization maneuvers are needed in order to achieve the final circular orbits. The whole mission profile, from launch to insertion into the final lunar orbits, is modeled numerically with the commercial software STK.     

Origin and evolution of the earth-moon system

The origin and evolution of the Earth-Moon system is studied by comparing it to the satellite systems of other planets. The normal structure of a system of secondary bodies orbiting around a central body depends essentially on the mass of the central body. The Earth with a mass intermediate between Uranus and Mars should have a normal satellite system that consists of about half a dozen satellites each with a mass of a fraction of a percent of the lunar mass. Hence, the Moon is not likely to have been generated in the environment of the Earth by a normal accretion process as is claimed by some authors.Capture of satellites is quite a common process as shown by the fact that there are six satellites in the solar system which, because they are retrograde, must have been captured. There is little doubt that the Moon is also a captured satellite, but its capture orbit and tidal evolution are still incompletely understood.The Earth and the Moon are likely to have been formed from planetesimals accreting in particle swarms in Kepler orbits (jet streams). This process leads to the formation of a cool lunar interior with an outer layer accreted at increasingly higher temperatures. The primeval Earth should similarly have formed with a cool inner core surrounded in this case by a very strongly heated outer core and with a mantle accreted slowly and with a low average temperature but with intense transient heating at each individual impact site.     

Study of lunar gravity assist orbits in the restricted four-body problem

In this paper, the lunar gravity assist (LGA) orbits starting from the Earth are investigated in the Sun–Earth–Moon–spacecraft restricted four-body problem (RFBP). First of all, the sphere of influence of the Earth–Moon system (SOIEM) is derived. Numerical calculation displays that inside the SOIEM, the effect of the Sun on the LGA orbits is quite small, but outside the SOIEM, the Sun perturbation can remarkably influence the trend of the LGA orbit. To analyze the effect of the Sun, the RFBP outside the SOIEM is approximately replaced by a planar circular restricted three-body problem, where, in the latter case, the Sun and the Earth–Moon barycenter act as primaries. The stable manifolds associated with the libration point orbit and their Poincaré sections on the SOIEM are applied to investigating the LGA orbit. According to our research, the patched LGA orbits on the Poincaré sections can efficiently distinguish the transit LGA orbits from the non-transit LGA orbits under the RFBP. The former orbits can pass through the region around libration point away from the SOIEM, but the latter orbits will bounce back to the SOIEM. Besides, the stable transit probability is defined and analyzed. According to the variant requirement of the space mission, the results obtained can help us select the LGA orbit and the launch window.     

Comparison of low-energy lunar transfer trajectories to invariant manifolds

In this study, transfer trajectories from the Earth to the Moon that encounter the Moon at various flight path angles are examined, and lunar approach trajectories are compared to the invariant manifolds of selected unstable orbits in the circular restricted three-body problem. Previous work focused on lunar impact and landing trajectories encountering the Moon normal to the surface, and this research extends the problem with different flight path angles in three dimensions. The lunar landing geometry for a range of Jacobi constants is computed, and approaches to the Moon via invariant manifolds from unstable orbits are analyzed for different energy levels.     

Distribution of lunar impacts by objects in parabolic low inclination orbits

This paper presents a computer investigation extending to the case of parabolic orbits, an earlier investigation conducted by Barricelli and Metcalfe (1969) on lunar impacts by external low eccentricity satellites as a means to interpret the asymmetric distribution of lunar maria. Parabolic orbits can be approximated by two kinds of objects:

1. High eccentricity external satellites may, near periapsis, approach the Moon with orbital velocity and other characteristics closely resembling those of a parabolic orbit.
2. Asteroids and meteoroids approaching the Earth-Moon system with a low velocity may have moved in a nearly parabolic orbit when they reached the lunar distance from the Earth at the time when the impacts which carved the lunar maria took place.

The investigation gives, therefore, not only additional information relevant to the interpretation of the distribution of lunar maria by the satellite impacts hypothesis (in this case high eccentricity ones), but also information about the alternative hypothesis (Wood, 1973) that asteroid impacts rather than satellite impacts were involved.     

Some orbital characteristics of lunar artificial satellites

In this paper we present an analytical theory with numerical simulations to study the orbital motion of lunar artificial satellites. We consider the problem of an artificial satellite perturbed by the non-uniform distribution of mass of the Moon and by a third-body in elliptical orbit (Earth is considered). Legendre polynomials are expanded in powers of the eccentricity up to the degree four and are used for the disturbing potential due to the third-body. We show a new approximated equation to compute the critical semi-major axis for the orbit of the satellite. Lie-Hori perturbation method up to the second-order is applied to eliminate the terms of short-period of the disturbing potential. Coupling terms are analyzed. Emphasis is given to the case of frozen orbits and critical inclination. Numerical simulations for hypothetical lunar artificial satellites are performed, considering that the perturbations are acting together or one at a time.