Chandler wobble resonance model: possibility of using for prediction free Earth’s rotations contribution to the pole motion and the celestial pole offset

The parameters of the Earth's rotation determine the relationship between the terrestrial and celestial reference systems. In the Russian Federation, the task of determining and predicting the parameters of the Earth's rotation is assigned to the State Service of Time, Frequency and Determination of the Parameters of the Earth's Rotation. When predicting the parameters of the Earth's rotation, such modes of free rotation of the Earth as the Chandler pole motion and the free nutation of the core have a special influence. These modes are also of great theoretical importance, since their frequencies are part of the transfer function of the accepted theory of nutation and precession of the Earth MAS2000. The measurement data of the pole motion and the displacement of the celestial pole obtained by the International Earth Rotation and Reference Systems Service (IERS) have been preprocessed. The processing was carried out in order to exclude trends from these data, as well as the annual movement of the pole (for pole coordinates). Lomb-Scargle periodograms of the preprocessed measurement data are constructed. A resonant model of the Chandler pole motion based on solving the equations of free oscillations is proposed and substantiated. To verify it, we used a comparison of two Lomb-Scargle periodograms, one of which is calculated using an idealized resonance model of the Chandler pole motion, and the second is based on the results of preprocessed measurement data. The analysis of these periodograms made it possible to specify the period of the Chandler pole motion. The value of the period of the Chandler pole motion is equal to (432.47±0.03) days relative to the rotating Earth. Also, the coincidence of the Lomba-Scargle periodograms of the idealized model and the model based on the results of preprocessed measurement data confirmed the possibility of using the same principle to build a more realistic model. A numerical implementation of a more realistic resonant model of the Chandler pole motion is constructed. The parameters of this model and the results of comparing the calculated contribution to the pole coordinates with the preprocessed measurement data are presented in this article. The behavior of the Lomb-Scargle periodogram, constructed from preprocessed measurement data, was explained using the resonant model of the Chandler pole motion without involving additional assumptions about frequency splitting or slow changes in the resonant properties of planet Earth over time. The constructed (more realistic) resonance model can be used to predict the contribution of the Chandler pole motion to the pole coordinates, which leads to increased forecasting accuracy and theoretically confirms the single-frequency structure of the free nutation of the nucleus, adopted in the current theory of precession and nutation. The impossibility of using a more realistic resonance model to predict the contribution of free nuclear nutation to the coordinates of the celestial pole shift from a theoretical point of view confirms the contradiction between the single-frequency structure of free nuclear nutation accepted in the current theory of precession and nutation and the lack of confirmation of this by measurement results.

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