Fitting a triaxial ellipsoid to a set of quasi-selenoidal points

Abstract The aim of this work is the determination of the parameters of the triaxial ellipsoid of the Moon, as derived from a quasi-selenoid model. After a detailed description of various quasi-selenoid models of the lunar gravity field, which were proposed in the last twenty years, we prepare suitable data sets of three-dimensional Cartesian coordinates. The mathematical model adopted is the general (polynomial) equation of an ellipsoid functionally related to the nine unknowns: the coordinates of the ellipsoid center, the three rotation angles and the three ellipsoid semiaxes. Furthermore, we adopt mathematical models for one special and two degenerate cases of the triaxial ellipsoid. We implement the least-squares method of indirect observations and we derive results for eighteen data sets of quasi-selenoidal points. From the results, we report the values of the semiaxes of the triaxial ellipsoid of fitting with three unknowns, for the model GL0660B, to be 1,738,256.3 ± 0.2 m, 1,738,023.1 ± 0.2 m and 1,737,603.2 ± 0.2 m, while the other unknowns remain insignificant. This triaxial ellipsoid leads to the improvement in the RMS value of the height anomaly at about 12 per cent in comparison to the oblate spheroid.