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．     

The lunar gravity mission MAGIA: preliminary design and performances

The importance of an accurate model of the Moon gravity field has been assessed for future navigation missions orbiting and/or landing on the Moon, in order to use our natural satellite as an intermediate base for next solar system observations and exploration as well as for lunar resources mapping and exploitation. One of the main scientific goals of MAGIA mission, whose Phase A study has been recently funded by the Italian Space Agency (ASI), is the mapping of lunar gravitational anomalies, and in particular those on the hidden side of the Moon, with an accuracy of 1 mGal RMS at lunar surface in the global solution of the gravitational field up to degree and order 80. MAGIA gravimetric experiment is performed into two phases: the first one, along which the main satellite shall perform remote sensing of the Moon surface, foresees the use of Precise Orbit Determination (POD) data available from ground tracking of the main satellite for the determination of the long wavelength components of gravitational field. Improvement in the accuracy of POD results are expected by the use of ISA, the Italian accelerometer on board the main satellite. Additional gravitational data from recent missions, like Kaguya/Selene, could be used in order to enhance the accuracy of such results. In the second phase the medium/short wavelength components of gravitational field shall be obtained through a low-to-low (GRACE-like) Satellite-to-Satellite Tracking (SST) experiment. POD data shall be acquired during the whole mission duration, while the SST data shall be available after the remote sensing phase, when the sub-satellite shall be released from the main one and both satellites shall be left in a free-fall dynamics in the gravity field of the Moon. SST range-rate data between the two satellites shall be measured through an inter-satellite link with accuracy compliant with current state of art space qualified technology. SST processing and gravitational anomalies retrieval shall benefit from a second ISA accelerometer on the sub-satellite in order to decouple lunar gravitational signal from other accelerations. Experiment performance analysis shows that the stated scientific requirements can be achieved with a low mass and low cost sub-satellite, with a SST gravimetric mission of just few months.     

Utilisation of the lunar field for interplanetary travel by the Oslo system

This paper presents preliminary results of orbital investigations by a data processing machine aimed at the utilisation of the lunar gravitational field in interplanetary travel. The lunar field is utilised in two successive steps. In the first step a spacecraft in an Earth-bound orbit is deviated into an orbit similar to but separated from the Earth's orbit around the Sun. In a successive approach between the spacecraft and the Earth-Moon system the combined fields of the Earth and the Moon are utilised as a means to convey to the spacecraft a main portion of the momentum required in order to carry it to the proximity of Venus.A substantial portion of the fuel required for space travel can be saved by this kind of procedure.The CD 3300 machine time needed for this investigation was supplied by the computing facility of the University of Oslo at Blindern.     

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。     

Analytical lunar libration tables

We have developed a theory of the rotation of the Moon, for the purpose of obtaining libration series explicitly dependent upon lunar gravitational field model parameters. A nonlinear model is used in which the rigid Moon, whose motion in space is that of the main problem of lunar theory, and whose gravity potential is represented through its third degree harmonics, is torqued by the Earth and Sun. The analytical series are then obtained as Poisson series. Numerical comparisons with Eckhardt's solution are briefly exposed.     

Constraints on the source of lunar cataclysm impactors

Multiple impact basins formed on the Moon about 3.8 Gyr ago in what is known as the lunar cataclysm or Late Heavy Bombardment. Many workers currently interpret the lunar cataclysm as an impact spike primarily caused by main-belt asteroids destabilized by delayed planetary migration. We show that morphologically fresh (class 1) craters on the lunar highlands were mostly formed during the brief tail of the cataclysm, as they have absolute crater number density similar to that of the Orientale basin and ejecta blanket. The connection between class 1 craters and the cataclysm is supported by the similarity of their size-frequency distribution to that of stratigraphically-identified Imbrian craters. Majority of lunar craters younger than the Imbrium basin (including class 1 craters) thus record the size-frequency distribution of the lunar cataclysm impactors. This distribution is much steeper than that of main-belt asteroids. We argue that the projectiles bombarding the Moon at the time of the cataclysm could not have been main-belt asteroids ejected by purely gravitational means.     

The spatial distribution of long lived gas clouds emitted by satellites in the outer solar system

Simple models are presented for the spatial distribution of gases emitted by satellites in the outer solar system with emphasis on Io and Titan. The models, valid for long lived species in regions of space outside the gravitational zone of the parent satellite are applied to observed hydrogen and sodium clouds orbiting Jupiter and to an expected hydrogen cloud around Saturn.     

云南天文台人造卫星观测与相关应用研究

回顾了过去２０年，特别是近１０年来云南天文台人造卫星的观测与应用情况。介绍在观测仪器的研制、改进和观测方法研究以及有关激光测月资料的归算与应用方面所作过的工作。根据既有的条件，就今后若干年内可能进行的几项工作提出了粗浅的看法。     

Effects of physical librations of the Moon on the orbital elements of a lunar satellite

Physical librations of the Moon are small cyclic perturbations with periods of one month and longer, and amplitudes of 100 arc seconds or less. These cause the selenographic axes fixed in the true Moon to have a different orientation than similar axes fixed in the mean Moon.Physical librations have two types of effects of present interest. If the orbital elements of a lunar satellite are referred to selenographic axes in the true Moon as it rotates and librates, then the librations cause changes in the orientation angles (node, inclination, and periapsis argument of the satellite) large enough that long-period perturbation theory cannot be used without compensation for such geometrical effects. As a second effect, the gravitational potential of the Moon is actually wobbled in inertial space, a condition not included in the potential expression used in perturbation theory.This paper gives data on the magnitude of the physical librations, the geometrical effects on the orbital elements and the equivalent changes in the coefficients in the potential. It is shown that geometrical effects can be accommodated either by using an inertial axes system or by compensating for the lunar librations and precession when the selenographic axes are used. Further, it is shown that physical effects are small and negligible for all but the most exacting endeavors.     

Cosmic influences on the early history of the lunar surface

It is pointed out that the observed random distribution of low-angle impact craters over the lunar surface rules out the possibility that particles initially responsible for the origin of such craters had, prior to impact, been in heliocentric orbits. The observed facts are more consistent with a view that particles responsible for most of large primary impact at the earliest stage of lunar history were moving with the Earth-Moon gravitational dipole, and may have represented leftovers from the formation of this pair of cosmic bodies. The application of a similar argument to an equally obvious lack of directional effects in Martian cratering is, however, invalidated by a relatively large inclination of the Martian equator to the orbital plane of this planet.Presented at the NATO Advanced Study Institute on Lunar Studies in Patras, Greece, September 1971.Normally at the Department of Astronomy, University of Manchester, England.     

月球卫星轨道变化的分析解

由于月球自转缓慢及其引力位的特点,使得讨论月球卫星与人造地球卫星轨道变化的方法有所不同。     

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。     

Lunar occultation of Saturn: IV. Astrometric results from observations of the satellites

The method of determining local lunar limb slopes, and the consequent time scale needed for diameter studies, from accurate occultation timings at two nearby telescope is described. The results for the photoelectric observations made at Mauna Kea Observatory during the occultation of Saturn's satellites on March 30, 1974, are discussed. Analysis of all observations of occultations of Saturn's satellites during 1974 indicates possible errors in the ephemerides of Saturn and its satellites.     

Simple mass distribution for the lunar potential

A set of twenty-one point masses gravitationally equivalent to the L1 lunar potential model is presented. By construction, the equivalence is valid only in a region of space sampled by Apollo spacecraft. That region is taken to be a finite, torus-shaped shell. When used in place of the L1 model for Apollo 12 lunar orbit determination, the solution set gives spacecraft positions identical to within about 100 m.The solution is developed in two steps: first the L1 potential is examined to determine favorable mass locations, and then the mass values are computed to force an optimum matching of the L1 potential. Therefore the solution set is artificial. It is related to the Moon's actual mass distribution only in its similar gravitational effects in a limited region of space.     

Distribution of gravitational potential energy within the solar system

The orbital gravitational potential energies of the planets and of the satellites have been estimated and compared to the gravitational potential energies of the bodies themselves and to the gravitational potential energy of the Sun. From the point of view of the gravitational potential energy distribution two quite different groups of the planets can be distinguished clearly. However, the gravitational potential energy of the systems is mainly concentrated within the central bodies, only about 10^–5 in orbiting bodies.     

Stability and evolution of primeval lunar satellite orbits

There are several independent sources of evidence which suggest that the multiring basins of the lunar surface were created by the impact of natural satellites of the Moon, early in solar system history. If this hypothesis is correct the orbits of these primeval satellites would need to be stable for significant periods, to account for the known age differences of these basins. The stability of these primeval satellite orbits is considered. We find constraints on the satellite masses and initial orbits for long-term and short-term orbit stability. Dissipation due to lunar tidal friction may contribute significantly to the stability of close orbits.     

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.     

On the gravitational fields of Pandora and Prometheus

Utilizing topographic models of Saturn's F-ring shepherd satellites Prometheus (S16 1980S27) and Pandora (S15 1980S26), derived by Stooke (1994), and supposing that their mass density is constant, we derived basic geometrical and dynamical characteristics of the moons. They include the volume and mass, the mean radii, the tensor of inertia, and Stokes coefficients of the harmonic expansions of external gravitational potential. The best fitting ellipsoid approximations of the topography were calculated. A simple method of determining the gravitational potential on the surface of an irregular satellite is presented. Examples of equipotential surfaces of the satellites are shown     

Determination of some physical parameters of the Moon with Lunar Laser Ranging data

Information about the structure of lunar interior and evolution could be obtained from measurements of lunar free librations, gravitational field, dissipation etc.. In this paper the precision of determining free librations with Lunar Laser Ranging (LLR) data are estimated. Using the observing data from four telescopes for eighteen years the amplitudes and phases of free librations, the moments of inertia ratio of The Moon were determined.