I. Dynamical considerations - Dynamics of the Moon

Abstract

We know the mass of the Moon very well from the amount it pulls the Earth about in the course of a month; this is measured by the resulting apparent displacements of an asteroid when it is near us. Combining this with the radius shows that the mean density is close to 3.33 g/cm 3 . The velocities of earthquake waves at depths of 30 km or so are too high for common surface rocks but agree with dunite, a rock composed mainly of olivine (Mg, Fe II ) 2 SiO 4 . This has a density of about 3.27 at ordinary pressures. The veloci­ties increase with depth, the rate of increase being apparently a maximum at depth about 0.055 R in Europe and 0.075 R in Japan. It appeared at one time that there was a discontinuity in the velocities at that depth, corresponding to a transition of olivine from a rhombic to a cubic form under pressure. It now seems that the transition, though rapid, is continuous, presumably owing to impurities, but the main point is that the facts are explained by a change of state, and that the pressure at the relevant depth is reached nowhere in the Moon, on account of its smaller size. There will, however, be some compression, and we can work out how much it would be if the Moon is made of a single material. It turns out that the actual mean density of the Moon would be matched if the density at atmospheric pressure is 3.27—just agreeing with the specimen of dunite originally used for comparison. The density at the centre would be 3.41. Thus for most purposes the Moon can be treated as of uniform density. With a few small corrections the ratio 3 C /2 Ma 2 would be 0.5956 ± 0.0010, as against 0.6 for a homogeneous body. To make it appreciably less would require a much greater thickness of lighter surface rocks than in the Earth.