Principal axes and principal moments of inertia from recent satellite gravity field solutions

On the current estimation of some mechanical and geometrical parameters of the Earth

“…Current estimation of the Earth's mechanical and geometrical parameters of common relevance of Astronomy, Geodesy, and Geodynamics represents traditionally one of the basic objectives of different Commissions and Study Groups of the IAG (see, for instance, Groten 2000). Consistent sets of the Earth's mechanical and geometrical parameters associated with the degree 2 coefficients m C 2 , m S 2 of the spherical harmonic expansion of the geopotential and the Earth's inertial tensor was obtained recently by (Marchenko and Schwintzer, 2001; Marchenko and Shwintzer, 2002). The Earth's principal axes ( A , B , C ), principal moments of inertia (A, B, C), and other fundamental constants were estimated in the mentioned papers from satellitederived gravitational harmonic coefficients of second degree in global Earth gravity models and from the dynamical ellipticity resulting from the precession constant observed through VLBI.…”

“…where the matrix P -1 was derived also in an analytical way. By this the expression (9) epoch by definition, if the axis Z and the figure axis C are coinciding. The obtained differences from zero lead to the conclusion that each of the considered gravity models is referred to its own reference system.…”

“…at epoch 1997) was determine from the least squares adjustment as in the preceding solution(Marchenko and Schwintzer, 2001). For 4 adopted gravity models we compute the harmonic coefficients for each j.…”

Geodynamics

“…as the sum of constant and variable (secular or/and periodic) parts caused by mass redistribution within the Earth's system [Marchenko and Schwintzer, 2001; Bourda and Capitaine, 2004;Chen et al, 2005;Fernández, 2007;Gross et al, 2007]. The consistency of such investigations and the modeling of the time evolution require additionally to the consistent set of fundamental constants more precise theories to determine the dynamic figure of the Earth, the orientation of the principal axes in the Earth's-fixed system and its evolution with time from geodetic ) ( This study aims to derive more accurate expressions for the transformation of the seconddegree coefficients and zonal coefficients of an arbitrary degree through a finite commutative rotation instead of the most widely used approximate Lambeck's approach based on an infinitesimal rotation [Lambeck, 1971;Reigber, 1981].…”

Drift of the Earth’s Principal Axes of Inertia from GRACE and Satellite Laser Ranging Data

“…However, space geodetic techniques were unable to provide accurate solutions for the Earth's PAI until recent years, due to the level of uncertainty of the second-degree Stokes coefficients. For instance, according to the Groten 2004 "best" estimates [8] of fundamental parameters of interest in astronomy and geodesy, the Earth's axis of major inertia was aligned with the axis of figure (or pole-to-pole axis) and the other two laid on the equatorial plane, with the minor axis pointing to the longitude 14.92910 • ± 0.00012 • W. However, a few earlier interesting studies addressing aspects of the PAI time evolution from satellite-based gravity models had already been published, mainly related to the creation of a dynamical reference frame (e.g., [9]).…”