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．     

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.     

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。     

Some simple formulas for latitude effects and lifetimes of satellites

An analysis is made of the effect which manifests itself in the orbital period of a satellite because of the latitudinal shifting of the perigee. The American satellites Discoverer V and Discoverer VI (both in 1959) offered good opportunities for such an analysis, especially after elimination of the normal aperiodic decrease of the orbital period. Hereby, the latitude effect has turned out to mean deflections in the decrease of the orbital period about 20 per cent from the average. Some consequences as to air pressure and lifetimes of satellites are implied.     

Orbital evolution of Jupiter’s new outer satellites

Data on recently discovered outer satellites of Jupiter are used to analyze their long-period orbital evolution. We determine the extreme eccentricities and inclinations, as well as the circulation periods of the pericenter arguments and of the longitudes of the ascending nodes. The satellite orbital elements are plotted against time. The methods of analysis are identical to those that we used to analyze the orbital evolution of Uranus’s and Saturn’s new outer satellites.     

Dynamics of Planetary Satellites in the Solar System

After the discovery of a huge number of satellites around Jupiter, Saturn, and Uranus, it is necessary to collect together information about all of the planetary satellite systems and to define the possible classification of objects and types of their motion. We give physical parameters of the satellites: their masses, sizes, apparent magnitudes in opposition, and geometrical albedos. We present some of the orbital quantities that characterize the orbits, their shapes and orientation in space, as well as data on the rotation of satellites. The emphasis is on the peculiarities of their motion—the forces acting on them, the main orbital perturbations, and the influence of commensurabilities in the mean motions of satellites. We list references to the main theories of their motion.     

Cratering rate over the surface of a synchronous satellite

Equations have been derived for the asymmetries of crater frequency over the surface of a synchronously rotating satellite, when the orbital velocities of projectiles about the parent planet are always larger than the satellite's circular orbital velocity. If the projectiles orbit the planet in moderately eccentric ellipses, no marked apex-antapex asymmetries of crater frequency distribution are expected. Theoretical values of apex-antapex asymmetries are presented for the Earth, the Moon, and some Jovian and Saturnian satellites, and are compared with available observational and theoretical results.     

Evolution of orbits and encounters of distant planetary satellites. Study tools and examples

This study of the orbital evolution and encounters of distant satellites of planets is aimed at determining their origin. It is also important for understanding the distribution of matter in the early stages of evolution of the Solar System. The mutual encounter of satellites is very weak because of their small sizes and masses. However, at very large time intervals, mutual encounter can be quite close to significantly changing the orbits of satellites. In order to study these factors, we have developed a special method and computer programs. For 107 distant satellites of Jupiter, Saturn, Uranus, and Neptune, motion parameters have been determined using observational data. On the basis of these parameters, a numerical integration of the equations of motion of the satellites has been carried out in time intervals of several thousand years. Using the original method of frequency analysis, we found rather simple analytical functions that correspond to the results of the numerical integration and make it possible to calculate orbital parameters at any time during a long interval. These tools make it possible to conduct extensive studies of changes in the form and relative position in space of the orbits of distant satellites of Jupiter, Saturn, Uranus, and Neptune. Several examples illustrate the possibilities offered by these tools. The computer software in the form of a service ephemeris of satellite orbits over a long interval of time is available via the Internet (http://www.sai.msu.ru/neb/nss/evolu0e.htm) on the website of the State Astronomical Institute of the Moscow State University.     

GALILEO卫星导航和定位系统PDOP仿真

简单分析了GALILEO卫星导航和定位系统与GPS的差异及特点；利用STK软件，对GALILEO卫星导航和定位系统的PDOP进行了仿真计算。给出了部分世界城市的PDOP仿真结果以及一天时间内每分钟采样间隔下部分城市的PDOP变化曲线。     

The geometry of impacts on a synchronous planetary satellite

We consider a satellite in a circular orbit about a planet that, in turn, is in a circular orbit about the Sun; we further assume that the plane of the planetocentric orbit of the satellite is the same as that of the heliocentric orbit of the planet. The pair planet–satellite is encountered by a population of small bodies on planet-crossing, inclined orbits. With this setup, and using the extension of Öpik’s theory by Valsecchi et al. (Astron Astrophys 408:1179–1196, 2003), we analytically compute the velocity, the elongation from the apex and the impact point coordinates of the bodies impacting the satellite, as simple functions of the heliocentric orbital elements of the impactor and of the longitude of the satellite at impact. The relationships so derived are of interest for satellites in synchronous rotation, since they can shed light on the degree of apex–antapex cratering asymmetry that some of these satellites show. We test these relationships on two different subsets of the known population of Near Earth Asteroids.     

Time Scales and Tidal Effects in Minor Mergers

We use controlled N-body simulation to investigate the dynamical processes (dynamical friction, tidal truncation, etc.) involved in the merging of small satellites into bigger halos. We confirm the validity of some analytic formulae proposed earlier based on simple arguments. For rigid satellites represented by softened point masses, the merging time scale depends on both the orbital shape and concentration of the satellite. The dependence on orbital ellipticity is roughly a power law, as suggested by Lacey & Cole, and the dependence on satellite concentration is similar to that proposed by White. When merging satellites are represented by non-rigid objects, Tidal effects must be considered. We found that material beyond the tidal radius are stripped off. The decrease in the satellite mass might mean an increase in the merging time scale, but in fact, the merging time is decreased, because the stripped-off material carries away a proportionately larger amount of of orbital energy and angular momentum.     

The discovery of faint irregular satellites of Uranus

We report the discovery of four new uranian irregular satellites in our deep, m_R∼25.4, optical search around that planet. The orbital properties of these satellites are diverse. There is some grouping of inclinations and one of the satellites appears to be inside the Kozai resonant zone of Uranus. Further, we find that the differential size distribution of satellites is rather shallow compared to objects in the asteroid and Kuiper belts, going as ∼r^−2.4. We also report a strong coupling between semi-major axis and orbital eccentricity. We comment on the apparent paradox between the inclination grouping, shallow size distribution, and orbital correlation as they relate to the likelihood of a collisional origin for the uranian irregulars. The currently observed irregulars appear to be consistent with a disruptive formation process and a collisional origin for Uranus' obliquity.     

关于土卫八运动的轨道解

为了适应星际探测的需求,本文建立了在新的精度要求下土星卫星运动对应的力学模型,具体讨论了土卫八的运动,并针对主要摄动源土卫六的引力作用,建立了轨道变化的分析解,以此表明建立了土卫运动理论该采取的途径和精密定轨宜采用以轨道根数作为状态量的数值定轨方法。     

Tesseral harmonic perturbations for high order and degree harmonics

A new formula has been derived for geopotential expressed in terms of orbital elements. The summation sequence was changed so that the terms of the same frequencies would be grouped and the generalized lumped coefficients were derived. The proposed formula has the same form for both odd and evenl-m.Applying Hori's perturbation method, new formulae were derived for tesseral harmonic perturbations in nonsingular orbital elements:l+g, h, e cosg,e sing, L, andH. We show the possibility of effective application of the derived formulae to the calculation of orbits of very low satellites taking into account the coefficients of tesseral harmonics of the Earth's gravitational field up to high orders and degrees. As an example the perturbations up to the order and degree of 90 for the orbit of GRM satellites were calculated. The calculations were carried out on an IBM AT personal computer.     

《大气一号》气球卫星轨道倾角变化分析

引起《大气一号》两颗气球卫星（ＤＱ－１Ａ和ＤＱ－１Ｂ）轨道倾角变化的摄动因素主要是太阳光压摄动、大气旋转和日月引力摄动。太阳光压摄动引起气球卫星轨道倾角增大，平均每天变化约０．００１７，大气旋转引起轨道倾角减小，平均每天变化不到０．０００１，但随着高度下降，变化量亦增大，陨落前达０．００２。本文根据卫星轨道摄动理论，给出气球卫星轨道倾角变化的一种定量分析方法，得到的分析结果为：（１）由太阳光压摄动     

Nonlinear theory of secular perturbations of satellites of an oblate planet

Anonlinear analytical theory of secular perturbations in the problem of the motion of a systemof small bodies around a major attractive center has been developed. Themutual perturbations of the satellites and the influence of the oblateness of the central body are taken into account in the model. In contrast to the classical Laplace-Lagrange theory based on linear equations for Lagrange elements, the third-degree terms in orbital eccentricities and inclinations are taken into account in the equations. The corresponding improvement of the solution turns out to be essential in studying the evolution of orbits over long time intervals. A program inC has been written to calculate the corrections to the fundamental frequencies of the solution and the third-degree secular perturbations in orbital eccentricities and inclinations. The proposed method has been applied to investigate the motion of the major Uranian satellites. Over time intervals longer than 100 years, allowance for the nonlinear terms in the equations is shown to give corrections to the coordinates of Miranda on the order of the orbital eccentricity, which is several thousand kilometers in linear measure. For other satellites, the effect of allowance for the nonlinear terms turns out to be smaller. Obviously, when a general analytical theory of motion for the major Uranian satellites is constructed, the nonlinear terms in the equations for the secular perturbations should be taken into account.     

The Orbital Evolution of Two Sounding Satellites and Analysis of the Accuracy of Orbit Determination

The satellites TC-1 and TC-2 are the two Chinese satellites with great elliptical orbits which are still in orbit around the earth at present. Since the launch the orbits of the two satellites have continuously evolved, which has a certain effect on the orbit determination and prediction precision. The regularities of the orbital evolution of the two sounding satellites are qualitatively and quantitatively analyzed. Under the current tracking mode the corresponding prediction precision of orbit determination is analyzed based on the different stages of the orbital evolution, thereby providing the basis for the adjustment of planning mode by the satellite application departments and the guarantee of normal satellite payload. Finally, the orbital lifetimes of the two satellites are predicted through the trend of the orbital evolution.     

Orbital variation of the synchronous satellite and its calculation

This paper investigates the orbital variation of the 24-hour synchronous satellite and gives a method for calculating the variation. The results provide a theoretical basis for the design and calculation of the orbit of the communication satellites.     

On the cause of the discrepancy between groundbased and spaceborne lightcurves of Ganymede and Callisto in the <Emphasis Type="Italic">V</Emphasis> band

Properties of the surfaces of Jupiter’s satellites—Ganymede and Callisto—are shortly described. Their images acquired in space missions are shown. Causes of the discrepancy between orbital lightcurves of the satellites obtained from the earth and spaceborne maps of the satellites are considered. The groundbased observations were carried out under phase angles of solar illumination ranging from 0° to 12°, and the maps were built from images acquired from spacecraft in a wide interval of solar phase angles. We suggest that the main cause of the discrepancies between the lightcurves is the coherent backscattering effect observed only at small phase angles of the sun.     

基于无量纲的轨道参数开展卫星性质统计研究

目前已发现了285颗围绕太阳系八大行星公转的卫星, 它们的轨道和物理性质呈现了丰富多样性. 目前为止, 几乎所有的卫星研究工作都基于单个卫星系统或者卫星群, 似乎缺少统一的研究. 提出了一个新的与行星性质无关、只与恒星半径有关的轨道参数n, 定义为以太阳半径为单位的轨道半长轴的自然对数. 不同行星的卫星的n值都存在双极分布, 绝大部分卫星在$n\gtrsim2$区间, 其次在$n\lesssim-1$区间, 位于中间区域的行星则很少. 从卫星物理参数和轨道参数与n的关系中发现, 分属六大行星的卫星有明显的共同特征. 首先, 轨道偏心率和轨道倾角偏大的卫星的n值都在3.5左右, 它们都是巨行星的不规则卫星. 其次, n值在-1和1之间的卫星绝大部分体积大、质量大、反照率高、自转速度慢. 从文献中找到11颗系外卫星候选体, 获得了它们轨道n值和卫星质量, 发现后者也是在-1< n< 1区间最大,其他区间偏小.这些统一的 规律暗示,太阳系内不同行星的卫星形成机制以及太阳系外卫星的形成机制可能一样或类似.