对月球形状的估算

1799年,Laplace发现月球的3个主惯量矩,与月球的轨道和自转状态并不相符.有些学者认为,这可能是现在的月球仍保留了早期的"化石"形状.大约在三十多亿年前,月球曾经离地球很近并且转得较快,然后月球逐渐迁移远离地球并且转动得慢了下来.在此迁移的较早时期,月球受到了引潮力和自转离心力的作用,成为一个椭球体.并且很快凝固.所幸的是,固态月球的岩石圈较为稳定,使我们现在仍然能够看到很早时期月球的形状.文中利用月球天平动参数以及引力场系数,计算了椭球体3个主向径a,b,c的长度和月球的平衡潮形状,得到如下3个结论:(1)开始时月球离地球是非常近的,大约在三十亿年前月球可能已经冷却和固化,现在的月球基本上保留了凝结时的形状.(2)证明了液态月球的潮汐形变是月球平衡潮高度的1.934倍.因此用月球引力场推算月球形状时,必需考虑到流体勒夫数hf=1.934的影响.(3)根据月球三个主轴a,6,c的长度之差,推算了月球临凝固时的月地距离为1.7455×1O8m,自转周期为3.652 day.从而推算出月球临凝固时的恒星月长度为8.34day.因此在月球凝结时,月球被锁定在与自转速率比为2:1的共振轨道上.     

月球天平动模型对激光测月解算UTO的影响

本文利用1987年1月－1989年3月的LLR资料解算了UTO－UTC序列，在归算中分别应用了Eckhardt-500和LLB200两个天平动模型，以便分析和比较它们对解算UTO的影响。结果表明两个天平动模型间存在着明显的系统差。它反映在两者的事前残差中，最大差值可达100ns，这就使得用Eckhardt-500天平动模型的事前残差解算得到的UTO－UTC序列对IERS的平均偏离比采用LLB200天平动模型时要大1ms，但对两结果序列的外部精度没有影响。用事后残差解算，系统差的影响减小了，确定的UT0－UTC序列更靠近IERS系统，用两种天平动模型解算的UTO－UTC结果也更接近，外部精度也几乎一样且双用事前残差解的结果略好。     

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。     

月球边缘不规则性对月掩星观测的影响

本文基于衍射原理对月球边缘具有矩形枵正方形的障碍物计算了衍射图象。结果表明：（α）月球边缘障碍物的影响主要造成附近的费涅尔条纹的下降。（b）当障碍物位于掩星点上时影响最大；当障碍物远离掩星点时，它变得很小甚至无影响。（c）障碍物的影响与障碍物的大小有关。特别是，它强烈领带于障碍物平行月球边缘的那一条边长，如果边长长于47米或短于1米（对波长为λ=0.44μ）时，它将没有影响。因此，这一长度可以看作为判断月球边缘不规则性对月球掩星观测影响的特征长度。     

环月飞行器精密定轨的模拟仿真

以中国正在实施的探月计划“嫦娥1号”工程为背景，分析了在中国联合S波段(USB)测控网和甚长基线射电干涉(VLBI)跟踪网的现有空间分布、观测精度水平下的环月飞行器精密定轨．采用的方法是模拟仿真计算，即首先模拟观测数据，然后在计入各误差源的影响后进行求解，并对解算结果进行比较．模拟仿真的工具是美国宇航局哥达德飞行中心的空间数据分析软件系统GEODYN．环月飞行的主要误差源是月球重力场，为此首先讨论了目前精度最高的月球重力场模型JGL165P1的(形式)误差．在模拟了测距、测速以及VLBI的时延、时延率数据后，计入月球重力场的误差进行精密轨道确定．定轨时采用了减缩动力学(reduced dynamic)方法，即选用合适的经验加速度参数吸收重力场误差对定轨的影响．结果表明对于一个不将月球重力场作为主要科学目标的探月计划(如“嫦娥1号”)，减缩动力学方法是一个简单、有效地提高环月飞行器定轨精度的方法．     

大行星运动对太阳黑子活动的可能影响

本文计算了由太阳系大行星轨道运动引起的日心相对于太阳系质心的轨道运动角动量变化率j_⊙,在理论上对j_⊙作展开,表明它存在多项短周期变化,与太阳黑子资料的分析结果相比较,两者结果是符合的,它们具有一致的谱结构。因此,行星的轨道运动对太阳黑子活动存在动力作用的可能性又进一步得到了验证。     

New Trends in the Development of the Lunar Physical Libration Theory

A review of the modern state of the lunar libration theory is presented. A significant progress in the lunar investigation is achieved due to the simultaneous processing of results of the satellite Doppler tracing and of the lunar laser ranging. The data evidencing existence of a small iron core in the Moon are discussed. In this connection, the further development of the theory of rotation of the Moon presents the study of internal structure and dynamics of a lunar body. A model of a two-layer Moon can have a very advanced application to explain some observed phenomena and to be as a first approach in the modelling of internal processes determining the lunar rotation.     

A Study on the Relationship between the Orbital Lifetime and Inclination of Low Lunar Satellites

A detailed theoretical analysis on the orbital lifetime and orbital inclination of a Low Moon-Orbiting satellite (LMOs) and the 'stable areas' of long orbital lifetime are given. Numerical simulations under the real force model were carried out, which not only validate the theoretical analysis and also give some valuable results for the orbit design of the LMOs.     

Effects of Planetary Migration on Natural Satellites of the Outer Planets

Numerous studies in the past few years have analyzed possible effects of planetary migration on the small bodies of the Solar System (mainly asteroids and KBOs), with the double aim of explaining certain dynamical structures in these systems, as well as placing limits on the magnitude of the radial migration of the planets. Here we undertake a similar aim, only this time concentrating on the dynamical stability of planetary satellites in a migration scenario. However, different from previous works, the strongest perturbations on satellite systems are not due to the secular variation of the semimajor axes of the planets, but from the planetesimals themselves. These perturbations result from close approaches between the planetesimals and satellites.We present results of several numerical simulations of the dynamical evolution of real and fictitious satellite systems around the outer planets, under the effects of multiple passages of a population of planetesimals representing the large-body component of a residual rocky disk. Assuming that this component dominated the total mass of the disk, our results show that the present systems of satellites of Uranus and Neptune do not seem to be compatible with a planetary migration larger than even one quarter that suggested by previous studies, unless these bodies were originated during the late stage of evaporation of the planetesimal disk. For larger variations of the semimajor axes of the planets, most of the satellites would either be ejected from the system or suffer mutual collisions due to excitation in their eccentricities. For the systems of Jupiter and Saturn, these perturbations are not so severe, and even large migrations do not introduce large instabilities.Nevertheless, even a small number of 1000-km planetesimals in the region may introduce significant excitation in the eccentricities and inclinations of satellites. Adequate values of this component may help explain the present dynamical distribution of distant satellites, including the highly peculiar orbit of Nereid.     

制约卫星轨道寿命的另一种机制(续)

对于制约低轨人造地球卫星轨道寿命的耗散机制，人们已有足够的重视，但在深空探测中，另一种制约低轨卫星轨道寿命的引力机制同样应予重视，前文讨论了高轨卫星的情况，在第三体引力作用下，有可能导致卫星轨道偏心率产生变幅较大的长周期变化。特别是极轨卫星，其轨道偏心率在一定的时间内可增大到使其近星距rp=a(1-e)≈Re（Re是中心天体的赤道半径），从而落到中心天体上，结束其轨道寿命，目前对低轨卫星作了详尽的理论分析，研究表明，与高轨卫星有类似结果，但其力学机制却不相同，低轨卫星的轨道寿命与第三体引力无关。它取决于中心天体非球形引力位中的扁率项（即J2项）与其他带谐项之间的相对大小，这不仅是一个纯理论结果，也有实际背景，在太阳系中慢自传天体（月球和金星等）的低轨卫星就存在这一问题，还给出了有关判据，并以计算实例作了验证。     

4颗卫星情况的几何优化法修正

在GPS定位与导航中,用户可以通过选择至少4颗可见卫星的观测,得到测站位置和站钟差信息,卫星相对于测站的几何关系直接影响到定位和导航的精度,考虑用4颗卫星进行定位,在当前有一定的现实意义,在KihaLra等人工作的基础上对四面体的性质进行了深入讨论,推导了4颗可见卫星构成四面体体积的计算公式,实例分析证明该计算公式更合理、更精确。     

制约卫星轨道寿命的另一种机制

近点共振会导致太阳系小天体(小行星,自然卫星以及大行星和月球的人造卫星)的轨道偏心率出现变幅较大的长周期变化,特别是以月球和大行星为中心天体的大倾角轨道(确切地说是倾角接近90°的极轨道)卫星,由于类似的原因,偏心率的增大而导致近星距rp=a(1-e)≤ae(ae是中心天体的赤道半径),使其落到中心天体上,结束轨道寿命,这与耗散机制大不相同,因此将对其作理论分析,并以计算实例加以证实.     

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．     

The Application of GIM in Precise Orbit Determination for LEO Satellites with Single-Frequency GPS Measurements

With the precise GPS ephemeris and clock error available, the iono- spheric delay is left as the dominant error source in the single-frequency GPS data. Thus, the removal of ionospheric effects is a ma jor prerequisite for an improved orbit reconstruction of LEO satellites based on the single-frequency GPS data. In this paper, the use of Global Ionospheric Maps (GIM) in kine- matic and dynamic orbit determinations for LEO satellites with single-frequency GPS pseudorange measurements is discussed first, and then, estimating the iono- spheric scale factor to remove the ionospheric effects from the C/A-code pseu- dorange measurements for both kinematic and dynamic orbit determinations is addressed. As it is known that the ionospheric delay of space-borne GPS sig- nals is strongly dependent on the orbit altitudes of LEO satellites, we select the real C/A-code pseudorange measurement data of the CHAMP, GRACE, TerraSAR-X and SAC-C satellites with altitudes between 300 km and 800 km as sample data in this paper. It is demonstrated that the approach to eliminating ionospheric effects in C/A-code pseudorange measurements by estimating the ionospheric scale factor is highly effective. Employing this approach, the accu- racy of both kinematic and dynamic orbits can be improved notably. Among those five LEO satellites, CHAMP with the lowest orbit altitude has the most remarkable improvements in orbit accuracy, which are 55.6% and 47.6% for kine- matic and dynamic orbits, respectively. SAC-C with the highest orbit altitude has the least improvements in orbit accuracy accordingly, which are 47.8% and 38.2%, respectively.