Yu. G. Markov

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.

Modeling of the Earth’s rotary—oscillatory motions in the three-body problem: Interpolation and prognosis

A mathematical model of oscillations of the Earth’s pole and uneven Earth’s rotation due to gravitational tidal forces produced by the Moon and the Sun is constructed using the dynamic Euler—Liouville equations. It is established that high-frequency lunar influences contribute appreciably when modeling the prognosis of the Earth’s pole oscillations. The developed theoretical models for Earth’s rotation parameters account for small-scale high-frequency influences of gravitational nature (short-periodic disturbances due to the Moon with combination frequencies) and geophysical nature. Statistically convincing theoretical interpolations and prognoses on long-term (from one year to several years) and short (15–25 days) time intervals compared to highly accurate observational and measuring data of the International Earth Rotation and Reference Systems Service (IERS) are provided.

Rotational-oscillatory variations in the Earth rotation parameters within short time intervals

A mathematical model for rotational-oscillatory motions of the Earth is constructed by applying celestial mechanics to the spatial problem of the Earth-Moon system subject to the Sun’s gravitation. Some basic phenomena associated with tidal irregularity in the Earth’s axial rotation and the polar oscillations are studied. It is shown that the perturbing component of the gravitational-tidal forces orthogonal to the plane of the lunar orbit is responsible for some short-term perturbations in the Moon’s motion. The constructed model for the rotational-oscillatory motions of the deformable Earth includes both the main high-amplitude perturbations and more complex small-scale motions attributed to short-term lunar perturbations with combinational frequencies. Numerical modeling (interpolation and forecasting) of the Earth rotation parameters within various time intervals based on astrometric data obtained by the International Earth Rotation Service is presented.

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.

Modeling intraday oscillations of the Earth’s pole

An amplitude-frequency analysis of a few-parameter model for intraday oscillations of the Earth’s pole induced by gravitational-tidal torques exerted by the Sun and the Moon is presented. The characteristic features of the intraday oscillations in the polar coordinates are found using the dynamical Euler-Liouville equations, taking into account irregular perturbations. The modeling results for the polar motion are compared with high-accuracy VLBI observations over short time intervals. An amplitude-frequency analysis of the polar oscillations and the second zonal harmonic c20 of the geopotential is presented.

Accounting of fundamental components of the rotation parameters of the Earth in the formation of a high-accuracy orbit of navigation satellites

An analysis of perturbing factors influencing the motion of a navigation satellite (NS) is carried out, and the degree of influence of each factor on the GLONASS orbit is estimated. It is found that fundamental components of the Earth’s rotation parameters (ERP) are one substantial factor commensurable with maximum perturbations. Algorithms for the calculation of orbital perturbations caused by these parameters are given; these algorithms can be implemented in a consumer’s equipment. The daily prediction of NS coordinates is performed on the basis of real GLONASS satellite ephemerides transmitted to a consumer, using the developed prediction algorithms taking the ERP into account. The obtained accuracy of the daily prediction of GLONASS ephemerides exceeds by tens of times the accuracy of the daily prediction performed using algorithms recommended in interface control documents.