The influence of the electromagnetic core-mantle coupling torques on earth's rotation

The electromagnetic core-mantle coupling is one of the most likely hypotheses to explain the connections between both, the decade fluctuations of the Earth rotation and such of the magnetic field of the Earth. Within this paper, the axial and equatorial electromagnetic torques are computed at time intervals of two years from 1903.5 to 1975.5. They are compared with mechanical torques necessary for the excitation of the decade variations of the rotation of the Earth. The comparison is made with regard to the magnitude of the torques, to their time behaviour and to the periods within the time variations of both types of the torques. The computed electromagnetic torques are comparable with that necessary to excite the variations of the rotation of the Earth. But they are two or three orders less than that necessary to excite the decade variations of the polar motion. Some comparable periods were found within the spectra of the electromagnetic and the mechanical torques. This speaks in favour of the core-mantle coupling. But there are differences between both spectra too hinting at other processes which we cannot describe by a simple model of the core-mantle coupling.     

Kinetic energy of a non-spherical elastic earth mantle with andoyer variables

Continuing the study of the rotation of a deformable Earth begun by Getino and Ferrandiz (1990, 1991a, 1991b, 1993, 1994) for an Earth model with an elastic spherical mantle, in this paper on one hand we deal with the effect of the ellipticity, and on the other hand, we include the toroidal solution of the displacement vector. Taking an axis symmetrical, slightly ellipsoidal Earth, the modification due to the ellipticity is introduced into the solution of the displacement vector for both spheroidal and toroidal modes, and, after defining the adequate variables, we give the canonical formulation of the corresponding increase in the kinetic energy.     

Researches in China on the Effects of Tides on the Earth Rotation

In this paper the tidal phenomena on the Earth are concisely specified, including solid tides, ocean tides and atmospheric tides due to the luni-solar tide-generating force, and the Earth pole tide due to the motion of the Earth's rotation axis (polar motion); as well as their effects on the Earth rotation. The outcomes of scientific researches of Chinese astronomers on these topics are described in some detail. These researches deal with the mechanisms responsible for tidal effects on the earth rotation, and on the measurements of the Earth rotation parameters. Finally, the effects discovered by Chinese researchers on the measurements of the period and change in period of pulsars are discussed. These effects are very small in magnitude but not negligible.     

The Effect Of Zonal Tides On The DynamicalEllipticity Of The EarthAnd Its Influence On The Nutation

In this paper, the expressions of variations of the dynamical ellipticity and the principal moments of inertia due to the deformations produced by the zonal part of the tidal potential are obtained. Starting from these expressions, we have studied from equations related to Hamiltonian theory, their effects on the nutation and finally we have evaluated numerically such influences, with a level of truncation at 0.1 μas. Thus we have shown that some coefficients are quite large with respect to the usual accuracy of up-to-date observations. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the “rotational angular momentum” of the oceans and the corresponding polar motion

Periodic polar motions caused by ocean tides are predicted. In the Liouville equations for rotational motion the complete excitation functions for the ocean tides have to be used. This does not depend on the fact that hydrodynamical ocean tide models do not consider the centrifugal acceleration. The observable polar motion of the Celestial Ephemeris Pole CEP (more exactly: the terrestrial location of the CEP) is tabulated for the ten ocean tides M₂, S₂, N₂, K₁, O₁, P₁, M f, M f′, M m, Ssa. Typical amplitudes for the largest ocean tides are 0.4 milliarcseconds. This is within the reach of geodetic VLBI and SLR observations.     

Contribution of the atmosphere to the seasonal changes in earth's rotation

Using new data of atmospheric angular momentum for the period 1975–1995, the contributions of the atmosphere to the changes in LCD and polar motion on the seasonal time scale are investigated. The results show that, when the effects of wind and atmospheric pressure are considered, the atmosphere's contribution on the annual and semi-annual time scales may reach, respectively, 95% and 88%. We also give some quantitative results of the atmosphere's excitation of polar motion. On the annual time scale, the contribution to the X-component of polar motion is 16% and that to the Y-component is 43%. On the semi-annual time scale, the contributions to the X- and Y-components are, respectively, 9% and 30%. From the above results, it is clear that the contribution of the ocean should also be included in a more complete solution of the problem of excitation of the earth's rotation.     

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.     

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。     

RDAN97: An Analytical Development of Rigid Earth Nutation Series Using the Torque Approach

New series of rigid Earth nutations for the angular momemtum axis, the rotation axis and the figure axis, named RDAN97, are computed using the torque approach. Besides the classical J2 terms coming from the Moon and the Sun, we also consider several additional effects: terms coming from J3 and J4 in the case of the Moon, direct and indirect planetary effects, lunar inequality, J2 tilt, planetary‐tilt, effects of the precession and nutations on the nutations, secular variations of the amplitudes, effects due to the triaxiality of the Earth, new additional out‐of‐phase terms coming from second order effect and relativistic effects. Finally, we obtain rigid Earth nutation series of 1529 terms in longitude and 984 terms in obliquity with a truncation level of 0.1 μ (microarcsecond) and 8 significant digits. The value of the dynamical flattening used in this theory is HD=(C-A)/C=0.0032737674 computed from the initial value pa=50′.2877/yr for the precession rate. These new rigid Earth nutation series are then compared with the most recent models (Hartmann et al., 1998; Souchay and Kinoshita, 1996, 1997; Bretagnon et al., 1997, 1998. We also compute a benchmark series (RDNN97) from the numerical ephemerides DE403/LE403 (Standish et al., 1995) in order to test our model. The comparison between our model (RDAN97) and the benchmark series (RDNN97) shows a maximum difference, in the time domain, of 69 μas in longitude and 29 μas in obliquity. In the frequency domain, the maximum differences are 6 μas in longitude and 4 μ as in obliquity which is below the level of precision of the most recent observations (0.2 mas in time domain (temporal resolution of 1 day) and 0.02 mas in frequency domain). This revised version was published online in July 2006 with corrections to the Cover Date.     

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 rotation of rigid Venus

According to A.A. Khentov Venus' rotation is in the quasi-stationary state as a result of the balance interaction of the solar tidal torque with the aerodynamical torque of the rotating Venus' atmosphere. In case of the nonconservative forces are negligible and the solar attraction is the stabilizing factor, the rotation of the rigid Venus may be assumed as the first approximation. The theory of the rotation of the rigid Venus in the coordinates,, had been constructed. It have been found that Venus rotates almost uniformly and the libration harmonics are negligible.     

A rigorous Hamiltonian approach to the rotation of elastic bodies

When the problem of the rotation of a non-rigid body is studied, the usual procedure consists of adding perturbations to the Hamiltonian of the rigid solid. In some cases, as occurs with the centrifugal deformation, the new perturbations contains potentials which depend on the velocity, but usually one alter neither the definition of the canonical variables nor the method for obtaining the Hamiltonian. Although this procedure gives good estimates and its formulation is simpler, it is incorrect from a theoretical point of view.In this paper we rigorously develop a Hamiltonian formulation of the problem, considering potentials that depend on the velocity. Thus the differences between the two procedures are clearly shown, giving special emphasis to the case of the elastic Earth, for which we show that the differences obtained cannot be ignored within the accuracy limits at present required.     

On the solar rotation and activity

The interaction between differential rotation and magnetic fields in the solar convection zone was recently modelled by Brun (2004). One consequence of that model is that the Maxwell stresses can oppose the Reynolds stresses, and thus contribute to the transport of the angular momentum towards the solar poles, leading to a reduced differential rotation. So, when magnetic fields are weaker, a more pronounced differential rotation can be expected, yielding a higher rotation velocity at low latitudes taken on the average. This hypothesis is consistent with the behaviour of the solar rotation during the Maunder minimum. In this work we search for similar signatures of the relationship between the solar activity and rotation determined tracing sunspot groups and coronal bright points. We use the extended Greenwich data set (1878–1981) and a series of full-disc solar images taken at 28.4 nm with the EIT instrument on the SOHO spacecraft (1998–2000). We investigate the dependence of the solar rotation on the solar activity (described by the relative sunspot number) and the interplanetary magnetic field (calculated from the interdiurnal variability index). Possible rotational signatures of two weak solar activity cycles at the beginning of the 20th century (Gleissberg minimum) are discussed. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Secular Variation of Earth's Rotation: Inferred from the Chinese Ancient Shoushi Calendar (Ad 1281)

The Shoushi calendar (epoch of AD 1281, Yuan dynasty) is famous and very accurate in ancient China. It has evolved perfect and complete theoretical models of solar system objects, such as solar and lunar motions during that period. Almost every part of this work corresponds to the modern astronomical yearbooks. Compiled by native Chinese astronomers, it sums up through their studies many real observing results. The mathematical methods were adopted in this calendar before the foundation of Newton’s mechanical system. It is presented in this paper that the indirect system is also very useful to recover the real observing historical material. By selecting these calculating results, we may sum up the integral data of the secular variation of the Earth’s rotation from 1000 BC to AD 1500. This revised version was published online in July 2006 with corrections to the Cover Date.     

The theory of canonical perturbations applied to attitude dynamics and to the Earth rotation. Osculating and nonosculating Andoyer variables

In the method of variation of parameters we express the Cartesian coordinates or the Euler angles as functions of the time and six constants. If, under disturbance, we endow the “constants” with time dependence, the perturbed orbital or angular velocity will consist of a partial time derivative and a convective term that includes time derivatives of the “constants”. The Lagrange constraint, often imposed for convenience, nullifies the convective term and thereby guarantees that the functional dependence of the velocity on the time and “constants” stays unaltered under disturbance. “Constants” satisfying this constraint are called osculating elements. Otherwise, they are simply termed orbital or rotational elements. When the equations for the elements are required to be canonical, it is normally the Delaunay variables that are chosen to be the orbital elements, and it is the Andoyer variables that are typically chosen to play the role of rotational elements. (Since some of the Andoyer elements are time-dependent even in the unperturbed setting, the role of “constants” is actually played by their initial values.) The Delaunay and Andoyer sets of variables share a subtle peculiarity: under certain circumstances the standard equations render the elements nonosculating. In the theory of orbits, the planetary equations yield nonosculating elements when perturbations depend on velocities. To keep the elements osculating, the equations must be amended with extra terms that are not parts of the disturbing function [Efroimsky, M., Goldreich, P.: J. Math. Phys. 44, 5958–5977 (2003); Astron. Astrophys. 415, 1187–1199 (2004); Efroimsky, M.: Celest. Mech. Dyn. Astron. 91, 75–108 (2005); Ann. New York Acad. Sci. 1065, 346–374 (2006)]. It complicates both the Lagrange- and Delaunay-type planetary equations and makes the Delaunay equations noncanonical. In attitude dynamics, whenever a perturbation depends upon the angular velocity (like a switch to a noninertial frame), a mere amendment of the Hamiltonian makes the equations yield nonosculating Andoyer elements. To make them osculating, extra terms should be added to the equations (but then the equations will no longer be canonical). Calculations in nonosculating variables are mathematically valid, but their physical interpretation is not easy. Nonosculating orbital elements parameterise instantaneous conics not tangent to the orbit. (A nonosculating i may differ much from the real inclination of the orbit, given by the osculating i.) Nonosculating Andoyer elements correctly describe perturbed attitude, but their interconnection with the angular velocity is a nontrivial issue. The Kinoshita–Souchay theory tacitly employs nonosculating Andoyer elements. For this reason, even though the elements are introduced in a precessing frame, they nevertheless return the inertial velocity, not the velocity relative to the precessing frame. To amend the Kinoshita–Souchay theory, we derive the precessing-frame-related directional angles of the angular velocity relative to the precessing frame. The loss of osculation should not necessarily be considered a flaw of the Kinoshita–Souchay theory, because in some situations it is the inertial, not the relative, angular velocity that is measurable [Schreiber, K. U. et al.: J. Geophys. Res. 109, B06405 (2004); Petrov, L.: Astron. Astrophys. 467, 359–369 (2007)]. Under these circumstances, the Kinoshita–Souchay formulae for the angular velocity should be employed (as long as they are rightly identified as the formulae for the inertial angular velocity).     

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.     

A Check on the Variations of Earth‘s Rotation with an Ancient Solar Eclipse

We address the relation between an ancient total eclipse, which occurred on A.D.1542 August 11 and the variation of Earth‘‘s rotation. The total eclipse was recorded in some ancient Chinese books, especially in local chronicles. Some of the documents include useful information for determining the location of the totality zone. The parameters of the eclipse are calculated by using the DE406 Ephemeris.A high-precision value of AT which expresses the variation of the Earth‘‘s rotation,of about 300 ～ 380 s, is obtained.     

Effects On the Nutation of the Non-Zonal Harmonics of Third Degree

In this paper, we calculate the coefficients of the nutation for a rigid Earth model due to the C _3m and S _3m (m ≠ 0) harmonics of the geopotential, starting from the Hamiltonian theory as developped by Kinoshita (1977). We show that these coefficients are far from being negligible as given the level of truncation of 0.1 μas which is necessary in the reconstruction of the tables of nutation, and also that their value is very close to that given by Bretagnon et al. (1997). This revised version was published online in July 2006 with corrections to the Cover Date.     

20世纪中国8级大地震与日长关系的初析

本文分析了20世纪中国8级地震与日长变化的关系,并介绍了日长与地球自转速率间的换算,为使其均一化提供了方法。