Orientation of the Geometrically Best fitting Triaxial Lunar Ellipsoid with Respect to the Mean Earth/Polar Axis Reference Frame

This study provides new estimates for the orientation of a geometrically best fitting lunar triaxial ellipsoid with respect to the mean Earth/polar axis reference frame calculated from the footprint positions of the Chang'E-1 (CE-1), SELenological and ENgineering Explorer (SELENE) laser altimetry measurements and Unified Lunar Control Networks 2005, (ULCN 2005) station coordinates. The semi-principal axes of the triaxial ellipsoid and the coordinates of its geometric center are also calculated simultaneously. All the estimated parameters from all three data sets are found to be consistent. In particular, the RMS differences of the semi-principal axes of the triaxial ellipsoids and the locations of their geometric centers from solutions with and without modeling Euler angles (orientation of the triaxial ellipsoid) using uniformly distributed laser altimetry (LAL) footprints are 29 and 31 m respectively. The misclosures of all the solutions indicate a better fit for the triaxial ellipsoid to the footprint and station coordinates if the Euler angles are included in the models.