L. D. Akulenko

A gravitational-tidal mechanism for the Earth’s polar oscillations

Perturbed, rotational-oscillational motions of the Earth induced by the gravitational torques exerted by the Sun and Moon are studied using a linear mechanical model for a viscoelastic rigid body. A tidal mechanism is identified for the excitation of polar oscillations, i.e., for oscillations of the angular-velocity vector specified in a fixed coordinate frame, attributed to the rotational-progressive motion of the barycenter of the Earth-Moon “binary planet” about the Sun. The main features of the oscillations remain stable and do not change considerably over time intervals significantly exceeding the precessional period of the Earth’s axis. A simple mathematical model containing two frequencies, namely, the Chandler and annual frequencies, is constructed using the methods of celestial mechanics. This model is adequate to the astrometric measurements performed by the International Earth Rotation Service (IERS). The parameters of the model are identified via least-squares fitting and a spectral analysis of the IERS data. Statistically valid interpolations of the data for time intervals covering from several months to 15–20 yr are obtained. High-accuracy forecasting of the polar motions for 0.5–1 yr and reasonably trustworthy forecasting for 1–3 yr demonstrated by observations over the last few years are presented for the first time. The results obtained are of theoretical interest for dynamical astronomy, geodynamics, and celestial mechanics, and are also important for astrometrical, navigational, and geophysical applications.

Forecasting the polar motions of the deformable Earth

A mathematical model for the complicated phenomenon of the polar oscillations of the deformable Earth that adequately describes the astrometric data of the International Earth Rotation Service is constructed using celestial mechanics and asymptotic techniques. This model enables us to describe the observed phenomena (free nutation, annual oscillations, and trends) simply and with statistical reliability. The model contains a small number of parameters determined via a least-squares solution using well-known basis functions. Interpolations of the polar trajectory for intervals of 6 and 12 yrs and forecasts for 1–3 yrs are obtained using the theoretical curve. The calculated coordinates demonstrate a higher accuracy than those known earlier.

Analysis of multifrequency effects in oscillations of the earth's pole

A least-squares analysis of measurements of the Earth-rotation parameters is used to interpolate these data in order to redict the polar motion using a basic mathematical model that includes two frequencies: the Chandler and annual frequencies. A model taking into account the oscillations induced by the influence of the Moon is considered. The manifestation of high-frequency lunar oscillations in the beat period is demonstrated, together with the feasibility of interpolating these oscillations over short time intervals. A comparative analysis of models taking into account the monthly and bi-weekly frequencies is presented. A reasonable model explaining anomalous phenomena in the six-year beating is proposed.

A Model for the polar motion of the deformable Earth adequate for astrometric data

Refined analytical expressions for the frequencies corresponding to the Chandler motion of the pole and the diurnal rotation of the deformable Earth are derived. Numerical estimates of the period and amplitude of the polar oscillations are presented. The trajectory of the Chandler polar motion derived via numerical modeling is in qualitative and quantitative agreement with experimental data from the International Earth Rotation Service (IERS). An evolutionary model describing slow variations in the Earth’s rotation parameters under the action of the dissipative moments of the tidal gravitational forces on time scales considerably longer than the precession period of the Earth’s axis is constructed. The axis of the Earth’s figure tends to approach the angular momentum vector of the proper rotation.

Rapid rotations of a satellite with a cavity filled with viscous fluid under the action of moments of gravity and light pressure forces

Rapid rotational motion of a dynamically asymmetric satellite relative to the center of mass is studied. The satellite has a cavity filled with viscous fluid at low Reynolds numbers, and it moves under the action of moments of gravity and light pressure forces. Orbital motions with an arbitrary eccentricity are supposed to be specified. The system, obtained after averaging over the Euler-Poinsot motion and applying the modified averaging method, is analyzed. The numerical analysis in the general case is performed, and the analytical study in the axial rotation vicinity is carried out. The motion in the specific case of a dynamically symmetric satellite is considered.

Simulation of subdiurnal variation in the earth’s rotation

On the basis of the celestialmechanical approach, the mathematical model of subdiurnal tidal variation in the rotation of the deformable Earth is developed taking into account the gravity-tidal lunar and solar disturbances, which is adequate for astrometric mea� surements of the International Earth Rotation Service (IERS) (1). The subdiurnal and nearly diurnal varia� tions of the Earths axial rotation are investigated using the third Euler-Liouville equation and the results of these measurements within a day (IGS). The model parameters were identified by the least squares method, and the features of the Earths axial rotation within a day were revealed. The combinational fre� quencies confirmed by the IERS observations were found. For solving very actual problems of celestial mechanics and astrometry, it is necessary to create a precision model of the motion of Earthsrotation with respect to the center of mass. The analysis of equations of motion (2, 3) and observation data (1, 4) indicates the necessity of taking into account the dis� turbing moments of forces of various physical natures and the considerable deformability of the Earths fig� ure. The gravity-tidal moments of forces from the Sun and the Moon exert the major effect. However, a sig� nificant correction of the model results in the compli� cation of processes of the filtration of unknown parameters including the estimation of the initial data. In a number of important problems of astrometry, navigation, and geophysics, the precision forecast of the Earths rotation is of substantial significance for relatively short time intervals. For applications, it is the extreme precision forecast for the intervals from 1-2 to 10-30 days of length that can be of interest. Analysis of the theoretical model indicates the fact that an accuracy of about 10 -4 -10 -5 s can be achieved. It is necessary to accomplish the construction of an ade� quate set of basic functions, the choice of optimum length of the interpolation interval, and the adjust� ment of the filtration algorithm by the method of weighed least squares. The error in the IERS data (1) amounts to several μs. The achieved very high accuracy of measurements is sufficient for construct� ing an adequate model of the Earths rotation (1-3). 1. The universal time (UT1) related to the Earths rotation is a reasonably important value, which requires continuous measurements. Because the aver� age solar time, and consequently, the UT1 is not suffi� ciently accurate time scale, the atomic time scale (TAI) having a relative stability of 10 -14 can be used as such a scale on reasonably short intervals (several years). The creation of the unified atomic time scale accepted as the international standard, precisely, the international atomic time (TAI), made it possible to accept it as the practical timescale standard. It is adapted for supporting the relation to the scale UT1 determined by the Earths rotation and is known as the coordinated universal time (UTC).

A celestial mechanics model of the Earth’s rotation irregularity

A mathematical model of perturbed rotational motions of the deformable Earth, adequate to astrometric measurements of the International Earth Rotation Service (IERS), is constructed using methods of celestial mechanics. It is based on the gravitational tidal mechanism of the influence of the Sun and Moon. The authors have found fine resonant structure of interaction of long-period zonal tides (annual, semi-annual, monthly, and two-week) with diurnal and semidiurnal tides. This essential property is reliably confirmed by spectral analysis of the IERS data. In this paper, a numerical simulation of tidal irregularities of the Earth’s axial rotation is performed. The primary emphasis is placed on the analysis of variations of the duration of the day on short time intervals with periods of one year and less (intra-annual oscillations) and their forecast.

High-accuracy forecasting of the Earth’s polar motion

The fundamental astrometrical problem of high-accuracy interpolation of the trajectory of the Earth’s pole and construction of an adequate theoretical model for associated complex multifrequency oscillations are considered. Measurements of the Earth-rotation parameters demonstrate the possibility of adjusting the filtering algorithm to make it suitable for practical navigational applications associated with a need for reliable high-accuracy predictions over the required time scales (short-and medium-terms). Numerical simulations and tests of the procedure used to optimize the adjustment parameters are presented.

Irregularities in the Earth's Rotation and the Overall Angular Momentum of the Atmosphere

Methods of celestial mechanics are used to refine a mathematical model for irregularity in the axial rotation of the Earth proposed earlier. This refinement applies corrections (residuals) introduced by perturbations of zonal tides. We examine intraday and near-diurnal variations in the Earth’s axial rotation, and a celestial-mechanical model explaining the origin of the intraday and near-diurnal oscillations in the rotational angular velocity is constructed. The correspondence between the variations of the intrayear rotational irregularity and the overall angular momentum of the atmosphere is analyzed.

Intrayear irregularities of the Earth’s rotation

The methods of celestial mechanics can be used to construct a mathematical model for the perturbed rotational motions of the deformable Earth that can adequately describe the astrometric measurements of the International Earth Rotation Service (IERS). This model describes the gravitational and tidal influences of the Sun and Moon. Fine resonant interactions of long-period zonal tides (annual, semiannual, monthly, and biweekly) with the diurnal and semidiurnal tides are revealed. These interactions can be reliably confirmed via a spectral analysis of the IERS data. Numerical modeling of tidal irregularities of the Earth’s axial rotation was carried out, focusing on the analysis and forecasting of variations of the day length occurring within short time intervals of a year or shorter (intrayear variations).