The size, shape and orientation of the asteroid Vesta based on data from the Dawn mission

The aim of this paper is to study the size, shape, and orientation of the asteroid Vesta based on the Dawn spacecraft observations. In this line, three main reference surfaces are defined; the geoid, reference ellipsoid, and best-fit ellipsoid. To be consistent with International Astronomical Union (IAU) standards, all the computations are done in the Claudia Double-Prime coordinate system. The geoid and its potential value W0 are computed by fitting an equipotential surface to the shape of Vesta in a least-squares sense regarding the topographic bias effect. We find that the topographic bias effect on the geoid potential value as well as the geoidal and topographic heights is significant. The geoid potential value W0 is estimated equal to 68709±24 m2/s2. The reference ellipsoid is defined as an equipotential ellipsoid which best fits the geoid. The reference ellipsoid is computed based on the fundamental geodetic constants which define a geodetic reference system (GRS). The semi-axes of the triaxial reference ellipsoid are found to be equal to 280413±104 m, 274572±102 m, and 231253±86 m with the equatorial semi-major axis longitude 8.29°E, while the semi-axes of the biaxial reference ellipsoid are 278556±117 m and 229921±76 m. The results show that the geoidal heights with respect to the triaxial reference ellipsoid are significantly different from the geoidal heights with respect to the biaxial reference ellipsoid. The parameters of the best-fit ellipsoid are estimated by fitting geometrical ellipsoids with various degrees of freedom to Vesta's shape in a least-squares sense. We report the semi-axes of the general best-fit ellipsoid with 9 degrees of freedom equal to 284562±75 m, 277248±73 m, and 226405±57 m. Regarding the orientation of Vesta, we find that the angle between the equatorial semi-major axis of the general best-fit ellipsoid and the X-axis of the coordinate system is 9.17∘±0.47, and the angle between its polar axis and the Z-axis is equal to 0.63∘±0.05. Furthermore, the spherical harmonic coefficients of the shape model of Vesta up to degree 180 are computed, giving the ability to estimate the parameters of the general best-fit ellipsoid. The significant differences observed between the parameters of the general best-fit ellipsoid derived from the spherical harmonic coefficients of the shape model, and those derived from the fitting are due to the large polar and equatorial flattenings of Vesta. We estimate that the offset of the center of figure from the center of mass is 1350±53 m, and the mean radius of Vesta is 261403±39 m.