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。     

由PREM模型参数计算地球自转的周期变化

弹性地球在日月引潮力势作用下的形变引起其转动惯量的改变，从而导致地球自转速率的变化．本文利用PREM地球模型所给的物质密度和弹性等参数分布．计算日月引潮力势产生的地球形变附加势，进而计算转动惯量的变化．最后得到一系列包含周期同引潮势带谐项、振幅大于1微秒的自转速率周期变化系数．     

Influence of the Atmospheric Tides on the Earth Rotation

Spectral analysis of the components of the relative atmospheric angular momentum vector is performed based on the series of these components for the 6 h intervals within the period of 1958–2000. These series have been computed in the Subbureau of the Atmospheric Angular Momentum of the International Earth Rotation Service using the NCEP/NCAR reanalysis of atmospheric observations. The basic harmonics of diurnal tides are determined. New results on the fortnight's and week's duration oscillations of the equatorial components of the atmospheric angular momentum are obtained. The zonal tides transformation mechanisms in the atmosphere are discussed. It is shown that the main mechanism of the zonal tides effect on the atmospheric variability is the amplitude modulation of daily oscillations of the relative atmospheric angular momentum. The effects of the atmospheric tides on the Earth rotation are discussed.     

Lunar and terrestrial tidal effects on the Moon's rotational motion

An accurate model of the rotation of the Moon, constructed by numerical integration, has been presented in a previous paper. All direct perturbations capable of producing at least 10^–4 seconds of arc on the Moon's rotational motion have been included, and the physical librations resulting from planetary effects and Earth-Moon figure-figure interactions have been presented. The present study deals with the Moon's physical librations resulting from the non-rigidities of the Moon and the Earth. The effects of the Moon's elasticity and of a lunar phase lag are analyzed. Physical librations due to lunar tides and those due to terrestrial tides are presented and described.     

Numerical theory of rotation of the deformable Earth with the two-layer fluid core. Part 1: Mathematical model

Improved differential equations of the rotation of the deformable Earth with the two-layer fluid core are developed. The equations describe both the precession-nutational motion and the axial rotation (i.e. variations of the Universal Time UT). Poincaré’s method of modeling the dynamical effects of the fluid core, and Sasao’s approach for calculating the tidal interaction between the core and mantle in terms of the dynamical Love number are generalized for the case of the two-layer fluid core. Some important perturbations ignored in the currently adopted theory of the Earth’s rotation are considered. In particular, these are the perturbing torques induced by redistribution of the density within the Earth due to the tidal deformations of the Earth and its core (including the effects of the dissipative cross interaction of the lunar tides with the Sun and the solar tides with the Moon). Perturbations of this kind could not be accounted for in the adopted Nutation IAU 2000, in which the tidal variations of the moments of inertia of the mantle and core are the only body tide effects taken into consideration. The equations explicitly depend on the three tidal phase lags δ, δ _c, δ _i responsible for dissipation of energy in the Earth as a whole, and in its external and inner cores, respectively. Apart from the tidal effects, the differential equations account for the non-tidal interaction between the mantle and external core near their boundary. The equations are presented in a simple close form suitable for numerical integration. Such integration has been carried out with subsequent fitting the constructed numerical theory to the VLBI-based Celestial Pole positions and variations of UT for the time span 1984–2005. Details of the fitting are given in the second part of this work presented as a separate paper (Krasinsky and Vasilyev 2006) hereafter referred to as Paper 2. The resulting Weighted Root Mean Square (WRMS) errors of the residuals dθ, sin θd for the angles of nutation θ and precession are 0.136 mas and 0.129 mas, respectively. They are significantly less than the corresponding values 0.172 and 0.165 mas for IAU 2000 theory. The WRMS error of the UT residuals is 18 ms.     

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.     

滞弹地球自转速率的潮汐变化

本文根据勒夫数和负荷载夫数的数值扰动原理，利用ｈａｎｄｌｅｒ摆动的理论周期作为滞弹吸收带模型参数估计的约束条件，讨论了地幔滞弹性对有效勒夫数ｋ的直接影响，以及滞弹地球对平均海潮的响应所产生的间接扰动，分析了它们对带谐潮尺度因子ｋ／Ｃ的影响，由此定义了一个具有动力学海潮、滞弹地幔和液核地球的世界时ＵＴ１潮汐变化序列，与天文新技术观测结果相比较表明，高频带谐潮变化的理论值与实测值是一致的。频散效应对低     

地球自转和潮汐参数对地幔滞弹性的约束

利用最新的潮汐和地球自转变化在Ｍ２、Ｍｆ、Ｍｍ、Ｃｈａｎｄｌｅｒ摆动和１８．６年频率上的实测值与两种滞弹模型预测的理论值的比较,分析地幔滞弹性在不同频率上的响应,空间测地结果被用来约束理论和滞弹模型,结果表明,Ｚｓｃｈａｕ的理论模型可以解释从地震频对１８．６年频率的滞弹勒夫数的预测振幅。本文还依据滞弹模型和Ｔｏｐｅｘ／Ｐｏｓｅｉｄｏｎ卫星测高资料确定的海潮模型,给出顺及地幔滞弹性和非平衡海潮效应的     

Dynamical History of the Earth–Moon System

Differential equations describing the tidal evolution of the earth's rotation and of the lunar orbital motion are presented in a simple close form. The equations differ in form for orbits fixed to the terrestrial equator and for orbits with the nodes precessing along the ecliptic due to solar perturbations. Analytical considerations show that if the contemporary lunar orbit were equatorial the evolution would develop from an unstable geosynchronous orbit of the period about 4.42 h (in the past) to a stable geosynchronous orbit of the period about 44.8 days (in the future). It is also demonstrated that at the contemporary epoch the orbital plane of the fictitious equatorial moon would be unstable in the Liapunov's sense, being asymptotically stable at early stages of the evolution. Evolution of the currently near-ecliptical lunar orbit and of the terrestrial rotation is traced backward in time by numerical integration of the evolutional equations. It is confirmed that about 1.8 billion years ago a critical phase of the evolution took place when the equatorial inclination of the moon reached small values and the moon was in a near vicinity of the earth. Before the critical epoch t _cr two types of the evolution are possible, which at present cannot be unambiguously distinguished with the help of the purely dynamical considerations. In the scenario that seems to be the most realistic from the physical point of view, the evolution also has started from a geosynchronous equatorial lunar orbit of the period 4.19 h. At t < t _cr the lunar orbit has been fixed to the precessing terrestrial equator by strong perturbations from the earth's flattening and by tidal effects; at the critical epoch the solar perturbations begin to dominate and transfer the moon to its contemporary near-ecliptical orbit which evolves now to the stable geosynchronous state. Probably this scenario is in favour of the Darwin's hypothesis about originating the moon by its separation from the earth. Too much short time scale of the evolution in this model might be enlarged if the dissipative Q factor had somewhat larger values in the past than in the present epoch. Values of the length of day and the length of month, estimated from paleontological data, are confronted with the results of the developed model.     

On the tidal variation of the geopotential

In this paper analytical expressions are derived for the temporal variations ofJ ₂ andJ ₂₂ due to the tides of the solid Earth, taking into account only the deformation of the mantle, and employing a procedure already used by the authors in their Hamiltonian theory of the Earth's rotation, which obtain the necessary parameters in a direct way by integration of those provided by a selected model of Earth interior.Numerical tables giving the periodic variation of coefficients are given, as well as a new prediction for UT1. For J ₂ and J ₂₂ the amplitudes reach such a magnitude that both two variations should not be ignored in studies involving the analysis of highly precise satellite tracking data. Moreover, the possibility of improving our knowledge of the value of those harmonic coefficients in only a more exact digit appears as to be strongly dependent on the limitations in the theoretical modeling of the variations of the inertia tensor due to solid tides.     

A Hamiltonian theory for an elastic earth: First order analytical integration

In this article an approximate analytical integration is performed of the Hamiltonian corresponding to the rotational motion of an Earth whose elastic mantle is deformed by rotation and lunisolar attraction, using Deprit's perturbation method for the first order. Besides the usual terms, this Hamiltonian includes the perturbation of the kinetic energy and the elastic energy produced with the deformation, as well as their causes, the tidal and the centrifugal potential; these new terms have already been studied for the tidal deformation in previous articles (Getino and Ferrándiz, 1990a, 1990b). The effects of the deformation due to the centrifugal potential are studied in this article, following the same method as that used for the tidal deformation. Numerical tables of the periodic perturbations corresponding to the nutation in obliquity and longitude are obtained. As for the secular effects, a theoretical value of 457 days is obtained for Chandler's period.     

Accurate Analytical Calculation of Effects of Rorations of the Central Planet on a Staellite's Orbit

Satellite orbital perturbations due to many rotations of the planet-fixed reference frame are calculated by a general analytical method. For the International Terrestrial Reference Frame (ITRF) the effects of the Earth irregular rotation, precession, nutation, and polar motion are considered. Gravity coefficients of the Earth potential expansion are expressed in an inertial Celestial Reference Frame (CRF) as functions of the set of standard constant coefficients derived in the ITRF and of the rotation angles between the CRF and ITRF. The analytical motion theory uses time dependent gravity coefficients, and the Lagrange motion equations are integrated in the CRF, as it is done by numerical methods. Comparison of the proposed analytical method with a numerical one is presented. Motion of the ETALON-1 geodetic satellite perturbed by the geopotential (36*36) and by the full effects of the Earth irregular rotation, precession, nutation and polar motion is predicted. The r.m.s. difference between the satellite's coordinates calculated by both methods over a year interval is 2 cm. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Hamiltonian theory for an elastic earth: Secular rotational acceleration

In this article, our previous Hamiltonian theory for the rotation of an Earth whose elastic mantle is deformed by rotation and linisolar attraction is applied to the study of the secular acceleration of the Earth's rotation. Since it is a result of the inelasticity, the theory is extended to include a phase lag. So, we obtain, in a theoretical way, a value of –5.6 × 10^–22 rd sec^–2, which agrees perfectly with the latest observational results.     

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.     

引力常数变化对地球自转长期变化的影响

探讨和估计了各种引力常数变化理论对地球角速度和日长变化的影响。各种引力常数变化理论包括了引力常数G随时间、空间以及速度变化等几个方面的影响。另外也估计了对地球自转角速度和日长变化产生的效应。其中有些研究对探讨地球自转变化也有启发意义。     

大气对地球自转参数（ERP）的高频激发

本文采用１９８３—１９９２年期间由空间大地测量技术观测和归算的地球自转参数（ＥＲＰ）序列，以及由全球气象资料归算的大气角动量（ＡＡＭ）序列，分析和研究了大气对地球自转参数的日长变化（ＬＯＤ）和极移（ｘ和ｙ）在一个月时间尺度以内的高频激发作用，得到的主要结果如下：１大气对ＬＯＤ分量高频潮汐的估计值存在着影响，但是，潮汐形变参数ｋ／ｃ随时间和频率的变化却是受非大气因素的扰动引起的．２．大气可以解释３０天以下ＬＯＤ非潮汐的大部分变化．３．极移分量３０天以内的高频变化也主要由大气激发．ｘ分量与大气的相关性要强于ｙ分量，而且更为稳定，主要表现为平均时间尺度约为２７天的波动，大气对这个波动的贡献可达７０％．     

Tidal Stress Patterns on Europa's Crust

The ice crust of Europa probably floats over a deep liquid-water ocean, and has been continually resurfaced by tectonic and thermal processes driven by tides. Tidal working causes rotational torque, surface stress, internal heating, and orbital evolution. The stress patterns expected on such a crust due to reorientation of the tidal bulge by non-synchronous rotation and due to orbital eccentricity, which introduces periodic ('diurnal') variations in the tide, are shown as global maps. By taking into account the finite rate of crack propagation, global maps are generated of cycloidal features and other distinctive patterns, including the crack shapes characteristic of the wedges region and its antipode on the sub-Jovian hemisphere. Theoretical maps of tidal stress and cracking can be compared with observed tectonics, with the possibility of reconstructing the rotational history of the satellite.     

海潮模型的比较及海潮对地球自转变化的影响

近年来,由于卫星测高工作的开展,提供了丰富准确的观测资料,产生出许多新的海潮模型。这些海潮模型的相互比较为研究海洋的精细结构、海潮的动力学、地球动力学提供了依据。另一方面,由现代空间技术和新方法来监测地球自转中的高频变化研究领域也有长足的进展。用这些技术可检测出地球自转中的周日和半日变化,从而激发地球自转的变化。一般来说,海潮影响地球自转的高频变化有两种不同的激发机制。地球的惯性张量的变化即质量项     

Ocean tide perturbations in the orbits of GEOS 1 and GEOS 2

Douglaset al. (1973) have estimated tidal parameters from the orbits of GEOS 1 and GEOS 2. Their results, interpreted in terms of Love numbers, are rather dispersive due in part to their neglect of the ocean tides. The ocean tidal corrections are estimated in this paper, but although they do not explain all of the discrepancy they do emphasise the importance of these perturbations on the motion of close Earth satellites. The remaining discrepancies could result in part from the fact that part of the long period tidal perturbations have been absorbed by the zonal harmonics in the Earth's gravity field.     

The Rotation of Europa

Theoretical predictions of non-synchronous rotation and of polar wander on Europa have been tested by comparing tectonic features observed in Voyager and Galileo spacecraft images with tidal stresses. Evidence for non-synchronous rotation comes from studying changes in global scale lineaments formed over time, from the character of strike-slip faults, and from comparison of distinctively shaped cycloidal cracks with the longitudes at which such shapes should have formed, in theory. The study of cycloids constrains the rotation period (relative to the direction of Jupiter) to less than 250 000 years, while direct comparison of the orientation of Europa in Voyager and Galileo images shows the rotation is slow, with a period of >12 000 years. Comparison of strike-slip faults with their theoretical locations of formation provides evidence for substantial polar wander, supported by the distribution of various thermally produced features.