HIGHER-ORDER STATISTICS OF PLANETARY GRAVITIES AND TOPOGRAPHIES

The statistical properties of Earth, Venus, Mars, Moon, and a 3-D mant le convection model are compared. The higher order properties are expr essed by third and fourth moments: i.e., as mean products over equilat eral triangles (defined as coskewance) and equilateral quadrangles (de fined as coexance). For point values, all the fields of real planets h ave positive skewness, ranging from slightly above zero for Lunar grav ity to 2.6sigma3 for Martian gravity (sigma is rms magnitude). Six of the eight excesses are greater than Gaussian (3sigma4), ranging from 2 .0sigma4 for Earth topography to 18.6sigma4 for Martian topography. Th e coskewances and coexances drop off to zero within 20-degrees arc in most cases. The mantle convective model has zero skewness and excess s lightly less than Gaussian, probably arising from viscosity variations being only radial.