Estimation of the Earth’s tensor of Inertia from recent geodetic and astronomical data

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Department of Geodesy, Institute of Geodesy, Lviv Polytechnic National University
Lviv Polytechnic National University

The transformation of the second-degree harmonic coefficients  and  in the case of a finite commutative rotation was derived instead of the traditional Lambeck’s approach based on an infinitesimal rotation. The modified Lambeck’s formulae avoid uncertainty in the deviatoric part of inertia tensor and allow simple transformation of the 2nd-degree harmonic coefficients and zonal coefficients of an arbitrary degree (including their temporal changes) via orthogonal matrixes. These formulae together with exact solution of the eigenvalue-eigenvector problem are applied to determine static components and accuracy of the Earth’s tensor of inertia from the adjustment in the principal axes system of ,  from recent four gravity field models (EGM2008, GGM03S, ITG-GRACE03S, and EIGEN-GL04S1) and eight values HD of the dynamical ellipticity all reduced to the common MHB2000 precession constant at the epoch J2000. The second solution contains the same parameters based on these four sets of  and only one HD from the MHB2000 model and corresponds better to the IERS Conventions 2003 and latest gravity field determinations. Two solutions for static components consist of the adjusted five 2nd-degree harmonic coefficients related to the IERS reference pole given by the conventional mean pole coordinates at the epoch 2000 (IERS Conventions 2003), the orientation of principal axes in this system, the principal moments (A, B, C) of inertia, and other associated parameters. The evolution with time of the above-mentioned static parameters was estimated in the principal axes system from the GRACE time series of ,  derived in five different centers of analysis over the time interval from 2002 to 2008. Special attention is given to the direct computation of temporally varying principal axes and moments of inertia based on ,  and the estimation of their mean values together with periodic constituents on given time-period. Stability of the positions of the equatorial inertia axes (, ) and the angle between two quadrupole axes located in the plane of the axes  and  of inertia is found. The estimated longitude  of the principal axis  as the parameter of the Earth’s triaxiality in the precession-nutation theory and  precession rate  of the precession constant are recommended for the Earth’s rotation theory. Additionally to some permanent constituents periodic components at seasonal and shorter time scale were evaluated.

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