Determining the moment of inertia of triaxial Mars with updated global gravity models

Abstract

The principal moments of inertia (PMIs) with the principal axes are usually taken as the dynamic figure parameters of Mars; they can be deduced from satellite-observed degree-two gravitational potentials in recent global gravity models and from the dynamic ellipticities resulting from precession observations. These PMIs are natural and significant for the geodetic, geophysical, and geodynamic problems of Mars, which are functions of internal density distributions. In this study, a closed and concise formula for determining the PMIs of the entire planet and its core was developed based on the second invariants of gravity and a multipole expansion. We deduced the polar oblateness J₂ and the equatorial ellipticity J₂₂ of Mars to be 1.9566 × 10⁻³ and 6.3106 × 10⁻⁵, respectively. The preferred principal moments of inertia of Mars are A = 2.66589 × 10³⁶ kg·m², B = 2.66775 × 10³⁶ kg·m², and C = 2.68125 × 10³⁶ kg·m². These values indicate that Mar is slightly triaxial. The equatorial principal moment of inertia of the Martian core is 1.46008 × 10³⁵ kg·m², accounting for ~5.47% of the planet’s PMI; this result is critical for investigating the density and size of the core of Mars, and the planet’s free core nutation.