The principal moments of inertia calculated with the hydrostatic equilibrium figure of the Earth

Abstract

As an indication of the Earth's mass distribution, the principal moments of inertia (PMOI, i.e., A, B, C) of the Earth are the basic parameters in studies of the global dynamics of the earth, like earth nutation, and the geophysics. From the aspect of observation, the PMOI can be calculated from the spherical coefficients of observed gravity field. In this paper, the PMOI are calculated directly according to its definition with the figures of the Earth's interior derived by a generalized theory of the hydrostatic equilibrium figure of the Earth. We obtain that the angle between the principal axis of the maximum moment of PMOI and the rotational axis is 0.184°, which means that the other two principal axes are very closely in the equatorial plane. Meanwhile, B-A is 1.60 × 10−5MR2, and the global dynamical flattening (H) is calculated to be 3.29587 × 10−3, which is 0.67% different from the latest observation derived value Hobs(3.273795 × 10−3) (Petit and Luzum, 2010), and this is a significant improvement from the 1.1% difference between the value of H derived from traditional theories of the figure of the Earth and the value of Hobs. It shows that we can calculate the PMOI and H with an appropriate accuracy by a generalized theory of the hydrostatic equilibrium figure of the Earth.