V. V. Perepelkin

Oscillatory-rotational processes in the Earth motion about the center of mass: Interpolation and forecast

The celestial-mechanics approach (the spatial version of the problem for the Earth-Moon system in the field of gravity of the Sun) is used to construct a mathematical model of the Earth’s rotational-oscillatory motions. The fundamental aspects of the processes of tidal inhomogeneity in the Earth rotation and the Earth’s pole oscillations are studied. It is shown that the presence of the perturbing component of gravitational-tidal forces, which is orthogonal to the Moon’s orbit plane, also allows one to distinguish short-period perturbations in the Moon’s motion. The obtained model of rotational-oscillatory motions of the nonrigid Earth takes into account both the basic perturbations of large amplitudes and the more complicated small-scale properties of the motion due to the Moon short-period perturbations with combination frequencies.The astrometric data of the International Earth Rotation and Reference Systems Service (IERS) are used to perform numerical simulation (interpolation and forecast) of the Earth rotation parameters (ERP) on various time intervals.

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.

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.

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.

Rotational-oscillational motions of the nonrigid Earth about the center of mass

We use the model of a nearly axisymmetric viscoelastic rigid body to study perturbed rotational-oscillational motions of the Earth’s pole. We point out that the Chandler component of oscillations is of celestial-mechanics nature and is caused by the gravitational-tidal actions of the Sun and the Moon. We analyze the pole oscillation excitation mechanism at a frequency close to the Chandler frequency and show that the undamped pole oscillations are caused by the resonance harmonic of the external perturbation at a frequency close to the free nutation frequency. We discuss whether it is possible to solve the problem of constructing a short-term forecast of the pole motion on the basis of a polynomial filter obtained by the least-squares method without taking into account small-scale oscillations caused by wide-band random factors of arbitrary physical nature. In the present paper, we perform numerical simulation of tidal inhomogeneities in the Earth’s axial rotation. Attention is mainly paid to the analysis of day length variations on short time intervals with periods less than or equal to one year (interannual oscillations) and to their forecast.

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).

Simulation and analysis of the Earth’s polar oscillations

The fundamental model considered in [2–9] is used to interpolate and forecast the polar motion by the least-squares method applied to IERS data [1]. On the basis of the fundamental model, we consider an extended model of the Earth’s polar motion taking into account oscillations due to lunar influence. It is established that high-frequency lunar oscillations can occur on the beats period and one can interpolate them on a short time interval. A comparative analysis of models taking into account the month and two-week frequencies is performed.

Rotational-oscillatory motions of the Earth and time variations in the geopotential coefficients

Anumerical-analytical model for oscillatory motions of the Earth’s pole that can provide qualitative explanations for irregular oscillatory phenomena and improvements in the accuracy of forecasting the polar trajectories in periods of significant anomalies is proposed. The model represents a natural refinement of the main model for the polar oscillations (the Chandler and annual components) developed earlier using celestial mechanics methods and observations of the Earth’s gravitational field. The results of numerical simulations of the polar oscillations are compared with measurements carried out by the International Earth Rotation Service.

Numerical-Analytic Modeling of Perturbed Oscillatory Motions of the Earth Pole

An improved numerical-analytic model of multifrequency oscillatory motion of Earth’s pole with temporal variations in the geopotential coefficients taken into account is considered. The model is a natural improvement of the earlier developed basic model of the pole oscillations (the Chandler and annual components) by using the methods of celestial mechanics and the data of the terrestrial gravitational field observations. This model allows one to improve the accuracy of forecast of Earth’s pole motion trajectory in the periods of significant anomalies (irregular deviations). The fundamental aspects of Earth’s pole oscillation process are investigated, which allows qualitatively explaining the observed irregular effects in the oscillatory process. The results of numerical modeling of Earth’s pole coordinate oscillations are compared with the observation and measurement data of the International Earth Rotation and Reference Systems Service (IERS).