Simulation of subdiurnal variation in the earth’s rotation

Abstract

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 Earth's 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 Earth's 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 Earth'srotation 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 Earth's 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 Earth's 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 Earth's rotation (1-3). 1. The universal time (UT1) related to the Earth's 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 Earth's rotation and is known as the coordinated universal time (UTC).