Estimation of the Earth's tensor of inertia from recent global gravity field solutions

Abstract

The dynamic figure of the Earth, characterized by the principal axes and principal moments of inertia, is estimated from satellite-derived gravitational harmonic coefficients of second degree in recent global Earth gravity models and from the dynamic ellipticity resulting from the precession constant observed through very-long-baseline interferometry (VLBI). Closed, exact formulae for the determination of these parameters of the Earth's tensor of inertia are developed based on the exact solution of the eigenvalue–eigenvector problem, including a rigorous error propagation. These formulae are applied to determine (a) static components and accuracy of the Earth's tensor of inertia at epoch and (b) the variation with time of the Earth's tensor of inertia and its accuracy. The best-fitting principal moments of inertia and second-degree harmonic coefficients in the principal-axes system are found from an adjustment involving four global gravity field models and six different values for the dynamic ellipticity. The evolution with time of the dynamic figure of the Earth is determined from the mean pole path and the observed secular rate of change in the second-degree zonal coefficient. It is found that differences in the principal moments of inertia change significantly over the time interval from 1962 to 2000, whereas changes in the absolute values cannot be reliably resolved due to the uncertainty in the dynamic ellipticity.