Tests of random density models of terrestrial planets

Abstract

Random density models are analyzed to determine the low degree harmonics of the gravity field of a planet, and therefrom two properties: an axiality Pl, the percent of the degree variance in the zonal term referred to an axis through the maximum for degree l; and an angularity Eln, the angle between the maxima for two degrees l, n. The random density distributions give solutions reasonably consistent with the axialities and angularities for the low degrees, l < 5, of Earth, Venus, and Moon, but not for Mars, which has improbably large axialities and small angularities. Hence the random density model is an unreliable predictor for the non‐hydrostatic second‐degree gravity of Mars, and thus for the moment‐of‐inertia, which is more plausibly close to 0.365MR2.