The shape of the Moon, its internal structure and moments of inertia

Abstract

Harmonic analysis of the Moon’s shape based on all available sets of hypsometric data disclose that the surface of the Moon, far from being a mere spheroid or ellipsoid, contains many significant harmonic terms, the single largest of which are of fourth order (being about three times as large as the second harmonics). Their sum makes the Moon to deviate from a mean sphere by ± 2 km over extensive regions; and local differences attaining 8 to 9 km in eleva­tion have been noted on the limb. These facts reveal that the lunar globe must possess sufficient strength to sustain stress differences of the order of 10 9 dyn/cm 2 ; and this could scarcely be the case if the large part of the Moon’s interior were molten. As melting should be expected if the Moon contained the same proportion of radioactive elements as chondritic meteroites, it is concluded that the mean radioactive content of the lunar interior must be less than that found in stony meteorites, or the terrestrial crust. The moments of inertia about the principal axes of inertia of the lunar globe, as determined from the Moon’s physical librations, are seriously at variance with a state of hydrostatic equilibrium—for any distance between the Earth and the Moon—of a homogeneous body, and can be accounted for only by assuming an asymmetric nonhomogeneity of the lunar globe, or the existence of internal processes which could support nonequilibrium from hydrodynamically. However, an application of Chandrasekhar’s theory of viscous convection in fluid globes reveals that, if such a globe is to possess the same difference, C – A , of momenta as the Moon, the velocity of convective motion should be of the order of 10 –8 cm/s (i. e. too small for the establishment of steady flow in 10 9 y); and the 'observed' value of the Rayleigh number characteristic of the Moon is several hundred times as large as that required theoretically for the stability of the respective flow. Thermoelastic effects due to secular insolation of the lunar globe, considered recently by Levin, are shown incapable to account for a value of the ratio (C – A)/B exceeding 0∙00005; while its empirical value deduced from librations is close to 0∙00063.