Reference surfaces of the planet Mercury from MESSENGER

The aim of this work is to study the reference surfaces of the planet Mercury obtained by the MESSENGER mission in order to provide a geodetic reference system (GRS) for the planet. The reference surfaces under consideration are the geoid and the reference ellipsoid. The reference ellipsoid is a triaxial planetocentric equipotential ellipsoid that best fits the geoid. To determine the reference surfaces, two methods are presented. In this line, the shape of the planet is sampled by expanding the global shape model (GSM) GTMES_125V03_SHA only up to the degree strength of the global gravity model (GGM) GGMES_50V06_SHA. The spatial resolution of the sampling points is selected based on the degree strength and the latitude of the location. According to our preferred method, we estimate the values for the semi-major equatorial axis, semi-minor equatorial axis, and polar axis of the reference ellipsoid equal to 2,439,422±368m, 2,439,304±368m, and 2,439,178±368m, respectively. Moreover, we estimate the geoid potential value equal to 9,032,044±1361m2/s2. The three axes of the reference ellipsoid give the polar and equatorial flattenings equal to (100±213)×10-6 and (48±213)×10-6, respectively. However, we show that the best-fitting ellipsoid gives the polar and equatorial flattenings equal to (896±213)×10-6 and (426±213)×10-6, respectively. The best-fitting ellipsoid is a triaxial ellipsoid that fits the shape of Mercury in a least-squares sense. The significant discrepancy observed between the flattenings of the two ellipsoids is a consequence of Mercury's geophysical characteristics together with its non-hydrostatic equilibrium. The results provided in the present work prove adequate for defining a promised GRS for the planet Mercury.