The lunar mean moment of inertia and the size of the Moon's core

In this paper the relation between the uncertainty of the Moon's mean moment of inertia (I/Ma ²) and that of the core density _c is discussed with a two-layer model of the Moon - a mantle obeying Roche's law of the density distribution and a homogeneous core (Fe-core or Fe-FeS-core). When the uncertainty of I/Ma ² is 0.0023 (that is the accuracy in present observation), a core with radius of 450 km will be appropriate to the limitation of _c about 1 g cm^–3. Considering the accuracy obtained in space explorations, and the compressibility and the quasi-homogeneity of the Moon, we suggest that the parameters C ₂₀, , , a, and GM of the Moon should define as primary constants, but C ₂₂ and C/Ma ² as derived constants. Therefore, the ratio of mass of Moon to that of Earth in the IAU (1976) system of astronomical constants will become a deducible constant.