Change in the zonal harmonic coefficient C20, Earth’s polar flattening, and dynamical ellipticity from SLR data
Received: October 16, 2018
Revised: December 16, 2018
Accepted: December 28, 2018
Department of Geodesy, Institute of Geodesy, Lviv Polytechnic National University
Lviv Polytechnic National University

We examine the change in the Earth’s second degree zonal harmonic coefficient derived from UTCSR SRL time series of  given (a) for the period from 1976 to 2017 as monthly solutions of the zonal coefficient  and (b) for the period from 1992 to 2017 as weekly solutions of the zonal coefficient  obtained via the eigenvalue-eigenvector problem and related to the principal axes system. The mean difference between the coefficients  or  given in various systems consists of the value  which is smaller than time variations in the coefficients  or . These time series of  were modeled by polynomials’ different degrees simultaneously with Fourier series with seasonal signals (for annual, semiannual, and quarter-year periods). Final representation was chosen at the epoch J2000 by means of the polynomial of second degree. Then the models for the time-dependent astronomical dynamical ellipticity  and the precession constant   with respect to the common value  were constructed using the model for the zonal coefficient  for the time-interval of about 25 yr. As the third step these time series of  were applied to determine a basic trend and periodic variations of the time-dependent Earth’s polar flattening from 1992 to 2017. A variation of the global dynamical and geometrical figure of the Earth was investigated and some important quantitative results were found: the polar flattening  is increasing within the considered 25 year time-interval. Therefore, this study aims to derive the variation of the global geometrical figure of the Earth, represented by the second-degree coefficients of time-series and the astronomical dynamical ellipticity . As a result, a special attention was given to the study of temporally varying components including seasonal variations of some fundamental parameters of the Earth.

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