INVERSION OF SHAPE STATISTICS FOR SMALL SOLAR-SYSTEM BODIES

The irregular shapes of small solar system bodies are modelled by logn ormal statistics, i.e., assuming that the shapes are realisations of t he so-called Gaussian random sphere. The Gaussian sphere is fully desc ribed by the mean radius and the covariance function of the logarithmi c radius. The stochastic shape is thus given by the covariance functio n, or the discrete spectrum of its Legendre coefficients. A maximum li kelihood estimator is here provided for inverting the covariance funct ion from three-dimensional sample shapes. The inverse method is applie d to sophisticated shape data on altogether 14 small solar system bodi es: the asteroids 4 Vesta, 243 Ida, 951 Gaspra, 1620 Geographos, 4179 Toutatis, and 4769 Castalia; the Martian satellites Phobos and Deimos; the Jovian satellite Amalthea; the Saturnian satellites Hyperion, Epi metheus, Janus, and Prometheus; and the Neptunian satellite Proteus. I nversion yields sigma = 0.245 for the relative standard deviation of r adius, shows that most of the spectral power lies in the second-degree spherical harmonics, and gives Gamma = 32.7 degrees for the correlati on angle. Even though the first results are promising, caution is reco mmended because the number of sample shapes is still small. Omitting o ne sample shape at a time and repeating the inversion shows that the r esults are not too sensitive to any one sample shape. As an example ap plication, thermal light curves are simulated for 1000 Gaussian sample spheres in order to study the uncertainties in diameters and masses d erived for asteroids. As compared to the Standard Thermal Model that a ssumes spherical asteroids, the irregular shape is shown to cause a 5 % systematic effect with 10 % scatter in diameter estimation whereas, in mass estimation, the respective numbers are larger at 17 % and 33 % .