Tests of random density models of terrestrial planets

Random density models are analyzed to determine the low degree harmonics of the gravity field of a planet, and therefrom two properties: an axiality P_l, the percent of the degree variance in the zonal term referred to an axis through the maximum for degree l; and an angularity E_ln, 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.