国际地球参考框架:现状与未来

地球参考框架是研究地球整体和局部运动以及探讨地球各圈层运动机制的一个重要基准。简要回顾地球参考架的发展和现状，主要分析当前取得的成绩及其存在问题和局限性，着重提出未来地球参考架的目标和若干建议。     

A core-mantle interaction in the rotation of the Earth

Effects of an interaction between the mantle and the core of the Earth on its rotational motion are investigated. Assuming that the Earth consists of a rigid mantle and a rigid core with a frictional coupling and a kind of inertial coupling between them, the equations of motion are derived, and they are solved in a close approximation. The solution gives the expressions for the precession, the nutation, the secular changes in the obliquity and the rotational speed, the polar motion and so on as functions of the magnitudes of these forces. A numerical estimation shows that the effect of the friction on the amplitude and phase of the nutation is small for a reasonable intensity of the friction while inertial coupling force has a decisive influence on the amplitude, and an appropriately chosen value of the latter force gives a nutation which closely agrees with observations. It is also indicated that this torque remarkably lessens the rates of the secular changes in the obliquity and the rotational speed. The possibility of a periodical change in the amplitude of the polar motion is suggested as a result of the interaction between the two consituents.     

Precision Analytical Calculation of Geodynamical Effects on Satellite Motion

A new analytical method for calculating satellite orbital perturbations due to different disturbing forces is developed. It is based on the Poincaré method of small parameter but takes advantages of modern high-performance computers and of the tools of computer algebra. All perturbations proportional up to and including the 5th-order of small parameters are obtained. The method can precisely calculate the effects of all geodynamical forces on satellite motion given by the most up-to-date IAU and IERS models, such as non-central Earth gravity potential, precession and nutation of the geoequator, polar motion and irregularities in the Earth's rotation, effect of ocean and solid Earth tides, pole tide, and secular variations of gravity coefficients.Numerical tests prove the method's accuracy to be equivalent to 1–2 cm when calculating positions of high altitude geodetic satellites (like ETALON), and/or of GLONASS navigational spacecraft. The accuracy is stable over 1 year at least and comparable to that of the best tracking measurements of satellites.Positions of low altitude geodynamical satellites (like STARLETTE) by the analytical method are calculated to an accuracy of about 70cm over a month's interval. The method is developed for future use in GLONASS/GPS on-board ephemeris computation where it can improve the current scheme of their flight control.This revised version was published online in October 2005 with corrections to the Cover Date.     

中国地球自转和地壳运动监测的研究工作

主要介绍了１９９５年至１９９８年期间有关中国地球自转和地壳运动监测的研究工作及取 得的进展。     

地球动力学扁率及其与岁差章动的关系

由岁差常数求得的日月岁差是天文学的重要参数之一,它和地球动力学扁率相联系。地球动力学扁率在章动理论的计算中也是一个重要的物理量。介绍了由不同的观测方法和模型给出的地球动力扁率值,并讨论了它也岁差的关系和对章动计算的影响。在刚体地球章动振幅的计算中,地球动力学扁率值起着尺度因子的作用,要改善刚体地球章动振幅的计算,需要修改目前的黄经总岁差值。非刚体地球章动的转换函数中所采用的简正模和常数都直接或间接地依赖地球动力学扁率值。在IAU1980章动理论中,计算刚体地球章动振幅所使用的地球动力学扁率值计算转换函数中简正模频率和常数所使用的地球动力学扁率值并不一致。随着观测和计算精度的提高,地球动力学扁率值的不一致将影响章动振幅的计算。在建立刚体地球章地动理论中,如何解释地球动力学扁率值的差异,如何选取地球动力学扁率值,还有待进一步的研究。     

弹性地球各种几何轴和物理轴的定义

基于经典的弹性地球自转动力学理论,建立了极移和章动的联合动力学方程。由此给出了弹性地球各种几何轴和物理轴(Tisserand轴、自转轴、瞬时形状轴、角动量轴、CEP和CIP轴)的极移、岁差章动的动力学方程,明确了各种轴的定义及其之间的理论关系。理论研究表明,联合动力学方程要比经典动力学方程综合性强易于理解,可同时求解极移和章动,特别是在文[1]理论中出现的倾斜模(TOM),在此只是作为了一个特解而存在。     

国内天文地球动力学中的潮汐研究

简要说明了天文地球动力学范畴内所研究的潮汐现象，包括由日月引潮力引起的固体潮、海洋潮、大气潮和由于地球自转轴的极移引起的极潮，以及这些潮汐对地球自转和地球自转的测量产生的效应。重点阐述中国天文学界在这一领域里的研究成果。这些研究涉及潮汐影响地球自转的机制，也就是各种潮汐效应与极移、自转速率变化和章动的关系，包括构建这类关系的理论模型，分析潮汐对它们的影响，利用中国古代丰富的天象记录计算地球自转的长期减慢，计算弹性或滞弹地球的洛夫数，依据某一地球模型计算潮汐效应或章动序列等等。研究也涉及在测量地球自转参数的不同技术中各种潮汐效应对测量结果产生的影响及其改正，并涉及与潮汐有关的观测方法的优化和数据处理过程的改进。最后介绍了中国学者所发现的脉冲星的周期和周期变率测量中的潮汐效应，尽管它们的量级甚微，但不容忽视。     

Some results of geodetic referring of the radio telescope and SLR stations to GPS markers in the Crimean geodynamical test area Simeiz-Katsyveli

Positions of space-geodetic instruments are calculated in the International Terrestrial Reference Frame (ITRF2000) by referring the instrument reference points to the local geodetic network and GPS markers. The eccentricities of the SLR stations CrAO and CLO and the permanent GPS station CrAO with respect to the reference point of the radio telescope RT-22 are determined. The local relative deformations of the Earth’s surface are presented as shifts of the instrument reference points with respect to the nearest points of the local geodetic network and with respect to each other.     

火星的岁差和章动

火星是类地行星，火星动力学的研究不仅具有科学意义，而且还具有实际应用价值。火星的空间探测获得了许多有关火星极运动的重要资料，它与理论值的比较是检验火星内部结构的重要手段，也是为改进火星岁差章动理论提供依据的有效途径。介绍了当前国际上有关火星的岁差和章动研究的进展，分别对刚体火星的章动序列、火星内部结构参数化模型的建立和火星自转的简正模作了描述，并进行了简单的讨论。     

Theory of the rotation of the rigid earth

An analytical theory is developed for planes normal to the angular-momentum axis, to the figure axis, and to the rotational axis of the triaxial rigid Earth. One of the purposes of this paper is to determine the effect on nutation and precession of Eckertet al.'s improvement to Brown's tables of the Moon and to check Woolard's theory from a different point of view. The present theory is characterized by the use of Andoyer variables, a moving reference plane, and Hori's averaging perturbation method. A comparison with Woolard's results shows that (1) the maximum difference in nutation for the plane normal to the angular-momentum axis, calculated from the same constants as Woolard adopted, reaches 0.0017, (2) the discrepancy in Oppolzer terms is large compared with the discrepancy in nutation for the plane normal to the angular-momentum axis, and (3) the present theory does not include some of the secular terms that are incorporated in Woolard's theory and that have an effect on the establishment of a reference system. The nutation coefficients 0.0001 for the three above-mentioned planes are calculated by using the numerical values recommended at the working meeting of the International Astronomical Union held in Washington in September 1974. The effects on precession and nutation due to the higher geopotential (n3) are also investigated. Any future revision of the lunar theory will not alter the values of the coefficients of the nutational terms derived here.     

关于章动序列计算中的地球动力学扁率的取值

刚体地球章动序列和非刚体地球章动的转换函数都和地球动力学扁率有关。ＩＡＵ１９８０章动理论中采用了一个不一致的地球动力学扁率值,从而影响了章动振幅的计算。本文介绍了章动序列计算中地球动力学扁率的取值。由地球模型１０６６Ａ或ＰＲＥＭ得到的地球动力学扁率值比由岁差观测得到的约小１％,并且不可靠。当考虑体静力学平衡被破坏时新的地球物理模型,可得到与岁差常数相一致的地球动力学扁率值。地球动力学扁率值Ｈ＝０．     

根据空间大地测量结果建立的中国地壳构造块体的运动模型

本文利用空间大地测量的结果初步建立了中国地壳各构造块体的运动模型,该模型与由地质资料建立的地质学模型相比呈现较好的一致性,反映了中国及邻近地区的板块、亚板块和活动构造块体的水平运动特征和趋势。     

On the effect of the mantle elasticity on the earth's rotation

Starting from the Hamiltonian model for a solid Earth with an elastic mantle previously developped by the authors, analytical expressions are derived which give the nutation series corresponding to the plane perpendicular to the angular momentum vector, to the plane perpendicular to the rotational axis and to the equator of figure, as well as the series that give the polar motion. The effects of the different perturbations — solid Earth, centrifugal and tidal potentials — are calculated separately. The corrections due to the elasticity of the mantle, which mostly correspond to the Oppolzer terms, are calculated with an accuracy of 10^–6 arc sec., given that the intrinsic observational accuracy has reached 0.01 mas.     

On the possibility of creating a radio-astronomical inertial coordinate system based on the measurement of arcs between QSOs with the aid of VLBI

The aim of this paper has been to discuss a possibility of the formation of an inertial system of coordinates, precise within 0″.001, with the aid of the measures of mutual angular distances of quasars by the VLBI technique used in radio-astronomy. Such a system depends on neither the rotation, nor revolution of the Earth around the Sun — a fact which permits a separation of the astronomical and geophysical aspects of the problem. The proposed system should permit us to resolve some general astrometric problems — such as of the precession and nutation of the Earth as well as of the motion of the terrestrial axis of rotation within the Earth, or fluctuations in the angular veoocity of terrestrial rotation.     

Solution to the rotation of the elastic earth by method of rigid dynamics

Hamiltonian mechanics is applied to the problem of the rotation of the elastic Earth. We first show the process for the formulation of the Hamiltonian for rotation of a deformable body and the derivation of the equations of motion from it. Then, based on a simple model of deformation, the solution is given for the period of Euler motion, UT1 and the nutation of the elastic Earth. In particular it is shown that the elasticity of the Earth acts on the nutation so as to decrease the Oppolzer terms of the nutation of the rigid Earth by about 30 per cent. The solution is in good agreement with results which have been obtained by other, different approaches.     

An Abridged Model of the Precession–Nutation of the Celestial Pole

Precise astrometric observations show that significant systematic differences of the order of 10 milliarcseconds (mas) exist between the observed position of the celestial pole in the International Celestial Reference Frame (ICRF) and the position determined using the International Astronomical Union (IAU) 1976 Precession (Lieske et al., 1977) and the IAU 1980 Nutation Theory (Seidelmann, 1982). The International Earth Rotation Service routinely publishes these 'celestial pole offsets', and the IERS Conventions (McCarthy, 1996) recommends a procedure to account for these errors. The IAU, at its General Assembly in 2000, adopted a new precession/nutation model (Mathews et al., 2002). This model, designated IAU2000A, which includes nearly 1400 terms, provides the direction of the celestial pole in the ICRF with an accuracy of ±0.1 mas. Users requiring accuracy no better than 1 mas, however, may not require the full model, particularly if computational time or storage are issues. Consequently, the IAU also adopted an abridged procedure designated IAU2000B to model the celestial pole motion with an accuracy that does not result in a difference greater than 1 mas with respect to that of the IAU2000A model. That IAU2000B model, presented here, is shown to have the required accuracy for a period of more than 50 years from 1995 to 2050.     

Normal modes of synchronous rotation

The dynamics of synchronous rotation and physical librations are revisited in order to establish a conceptually simple and general theoretical framework applicable to a variety of problems. Our motivation comes from disagreements between the results of numerical simulations and those of previous theoretical studies, and also because different theoretical studies disagree on basic features of the dynamics. We approach the problem by decomposing the orientation matrix of the body into perfectly synchronous rotation and deviation from the equilibrium state. The normal modes of the linearized equations are computed in the case of a circular satellite orbit, yielding both the periods and the eigenspaces of three librations. Libration in longitude decouples from the other two, vertical modes. There is a fast vertical mode with a period very close to the average rotational period. It corresponds to tilting the body around a horizontal axis while retaining nearly principal-axis rotation. In the inertial frame, this mode appears as nutation and free precession. The other vertical mode, a slow one, is the free wobble. The effects of the nodal precession of the orbit are investigated from the point of view of Cassini states. We test our theory using numerical simulations of the full equations of the dynamics and discuss the disagreements among our study and previous ones. The numerical simulations also reveal that in the case of eccentric orbits large departures from principal-axis rotation are possible due to a resonance between free precession and wobble. We also revisit the history of the Moon's rotational state and show that it switched from one Cassini state to another when it was at 46.2 Earth radii. This number disagrees with the value 34.2 derived in a previous study.     

Fundamental physics and absolute positioning metrology with the MAGIA lunar orbiter

MAGIA is a mission approved by the Italian Space Agency (ASI) for Phase A study. Using a single large-diameter laser retroreflector, a large laser retroreflector array and an atomic clock onboard MAGIA we propose to perform several fundamental physics and absolute positioning metrology experiments: VESPUCCI, an improved test of the gravitational redshift in the Earth?CMoon system predicted by General Relativity; MoonLIGHT-P, a precursor test of a second generation Lunar Laser Ranging (LLR) payload for precision gravity and lunar science measurements under development for NASA, ASI and robotic missions of the proposed International Lunar Network (ILN); Selenocenter (the center of mass of the Moon), the determination of the position of the Moon center of mass with respect to the International Terrestrial Reference Frame/System (ITRF/ITRS); this will be compared to the one from Apollo and Lunokhod retroreflectors on the surface; MapRef, the absolute referencing of MAGIA??s lunar altimetry, gravity and geochemical maps with respect to the ITRF/ITRS. The absolute positioning of MAGIA will be achieved thanks to: (1) the laboratory characterization of the retroreflector performance at INFN-LNF; (2) the precision tracking by the International Laser Ranging Service (ILRS), which gives two fundamental contributions to the ITRF/ITRS, i.e. the metrological definition of the geocenter (the Earth center of mass) and of the scale of length; (3) the radio science and accelerometer payloads; (4) support by the ASI Space Geodesy Center in Matera, Italy. Future ILN geodetic nodes equipped with MoonLIGHT and the Apollo/Lunokhod retroreflectors will become the first realization of the International Moon Reference Frame (IMRF), the lunar analog of the ITRF.