Mass and moment of inertia constraints on the lunar crustal thickness : Relations between crustal density, mantle density, and the reference radius of the crust-mantle boundary

The gravity inversion for the lunar crustal thickness needs three parameters: the crustal density, mantle density, and the reference radius of the crust-mantle boundary. The assumption of crust and mantle densities is found to significantly affect on the resultant crustal thickness variations. Moreover, the recent seismic analyses suggest the possibility of thinner crustal thickness around the Apollo 12 site than that proposed in the Apollo-era, on which the previous gravity inversions relied upon. Therefore the validity of the assumption used in previous gravity-inversion studies must be re-examined in detail. By using a simple three-layered mass model of the Moon including a uniform crust, mantle, and core, we determine possible combinations of the three parameters, satisfying the mass and moment of inertia constraints. The results show that the set of the parameters used in Neumann et al. (1996) can be consistent with mass and moment of inertia constraints, while those in Wieczorek and Phillips (1998) does not satisfy the constraints.