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

The Earth’s principal axes and principal moments of inertia were determined from the 2nd degree harmonic coefficients of recent Earth gravity field models and several values of the dynamical ellipticity. Closed exact formulae for the estimation of these parameters are developed based upon the exact analytical solution of eigenvalue-eigenvector problem and error propagation. These formulae are applied to determine (a) the “time-independent” components at epoch of the Earth’s tensor of inertia and their accuracies and (b) the time-dependent components of the tensor of inertia, which are based on satellite solutions for the secular variation in the degree 2 zonal coefficient and periodic variations in the degree 2 tesseral coefficients resolved from the IERS 0.05-yr polar motion data. Special attention was given to the evolution with time of the polar axis C of inertia in view of the creation of a dynamical reference frame. The time evolution of the Earth mechanical and geometrical parameters can be compared with their accuracy estimates at epoch.