Higher order statistics of planetary gravities and topographies

The statistical properties of Earth, Venus, Mars, Moon, and a 3-D mantle convection model are compared. The higher order properties are expressed by third and fourth moments: i.e., as mean products over equilateral triangles (defined as coskewance) and equilateral quadrangles (defined as coexance). For point values, all the fields of real planets have positive skewness, ranging from slightly above zero for Lunar gravity to 2.6 sigma(exp 3) for Martian gravity (sigma is rms magnitude). Six of the eight excesses are greater than Gaussian (3 sigma(exp 4)), ranging from 2.0 sigma(exp 4) for Earth topography to 18.6 sigma(exp 4), for Martian topography. The coskewances and coexances drop off to zero within 20 deg arc in most cases. The mantle convective model has zero skewness and excess slightly less than Gaussian, probably arising from viscosity variations being only radial.