Gravitational and topographic isotropy of the Earth, Moon, Mars, and Venus

The internal structures and surface shapes of the terrestrial planets are expected to be dominantly isotropic. We attempt to test this hypothesis by developing a criterion for recognizing statistical isotropy of spherical scalar fields and applying that test to the nonhydrostatic components of the gravitational and topographic fields of the Earth, Moon, Mars, and Venus. The criterion for topographic or geoidal surfaces is that the directional variance should be independent of azimuth. That is, the mean square east-west slopes should be equal to the mean square north-south slopes. All four planets generally pass the criteria, with a few minor exceptions. Most of the exceptions are likely to be artifacts of the current generation of planetary gravity and topography models rather than real features of the planets. Of the several broad-band departures from isotropy which we found, the only one likely to be real is the tendency for the Earth's gravity and topography to have only 80% as much variance in a north-south direction as in an east-west direction.