Abstract
In the preceding chapter of this book we have given an outline of the phenomena to be expected in the Moon’s interior if its material behaves as an elastic solid. The physical reason why the Moon should behave so at least in the outer parts of its interior are indeed overwhelming; but is this necessarily the case also in the deep interior of our satellite? The relatively high temperatures which we have reasons to expect there as a result of radiogenic heating, as discussed in Chapter 8, entail a number of interesting consequences; and one should be at least a partial melting of rocks exposed to them for a sufficiently long time. The problem of the occurrence of melting at pressures encountered in the lunar interior has, in recent years, been discussed in particular by Urey (1962); and indications of the temperatures at which the melting of the silicate rocks should commence (or become complete) under these conditions are shown on Figures 8–2 and 8–4. If so, however, it is reasonable to inquire as to whether such material would be susceptible of actual hydrodynamical flow over time intervals comparable with the age of the Moon; but before attempting to answer this question, let us inquire first about a possible cause of such a motion.
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Bibliographical Notes
The possibility that internal temperatures attained by secular release of radiogenic heat could be sufficient to melt at least a part of the matter in the lunar interior, which would then behave dynamically as a highly viscous liquid, was implicit in Urey’s early work on the thermal history of the Moon (cf. Urey, 1952, 1962). Although Urey himself has remained consistently sceptical as to the extent of such a melting (cf. Urey, 1960a), the realization that molten rocks of lunar interior would be convectively unstable (Kopal, 1961) lent some interest to theoretical investigations of the type of a flow which could be expected to arise in the lunar interior as a result of continuous release of radiogenic heat.
A mathematical theory of convection in incompressible homogeneous spheres (or shells) of viscous liquid, developed in recent years by Chandrasekhar (1952, 1953, 1961), should be closely applicable to the lunar problem; and its generalization, by Kopal (1963a) to compressible configurations in which the density ρ(r) and viscosity μ(r) can be arbitrary functions of the distance r from the centre * has been largely followed in this chapter.
Qualitative applications of this theory to construct a case for lunar convection have been made by Runcorn (1962, 1963), who attempted to account in this way for the anomalously large value of the ratio (C - A)/B ≡ ² of the lunar moments of inertia, as given previously by Equation (4–119), in terms of convection currents operative in the radioactively heated interior of the Moon — currents which might give rise to a nonradial temperature distribution; and through thermal expansion influence also the internal density distribution and thus also the moments of inertia. Simultaneous work by the present writer (Kopal, 1962b, 1963d, 1965b) has, however, revealed the existence of considerable quantitative difficulties which have been mentioned in the text.
The basic assumption underlying Runcorn’s approach to the problem — namely, that the Moon is internally hot enough for a large part of its mass to behave as a molten globe — has recently been weakened by several new facts emerging from selenodetic studies (cf. Chapter 13). For the latter Runcorn relied largely on the data by Baldwin (1963), the reliability of which will be put in proper perspective in Chapter 13. Secondly, a selenodetic establishment of level differences amounting to several kilometres over extensive regions of the lunar surface reveals that the Moon must possess a greater degree of rigidity than would be compatible with a largely molten interior. Third, a recent confirmation by Koziel (1964) of significant free libration of the Moon in longitude endows the lunar globe with a property which is again characteristic of solids rather than liquids. But quite apart from all these facts, in making a case for internal convection as the cause of the observed constant β for the Moon, Runcorn invoked two different processes which are not mutually compatible : namely, he postulated internal convection to establish nonradial temperature field, and then called on the corresponding thermal expansion to deform the Moon in such a way as to account for the observed value of β. These steps lack, however, any logical connection; for one postulates the Moon to behave like a viscous liquid; the other, like an elastic solid; and both cannot be true at the same time. In point of fact, nonradial temperature distribution of convective origin can, in principle, account for any arbitrary value of β for a perfectly spherical outer boundary (implied in Chandrasekhar’s theory) — or, for that matter, a boundary of any shape — provided only that the convection currents can be made sufficiently rapid. However, the stability of such a flow seems incompatible with the observed value of β as given by Equation (4–119) for any reasonable choice of physical parameters characterizing the lunar globe.
The concluding part of this section, discussing possible heat production in the lunar interior by viscous dissipation of bodily tides, is largely based on previous work by Kopal (1963b). For a corresponding problem of heat production by dissipation of bodily tides in an imperfectly elastic Moon cf., Kaula (1963).
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© 1966 Springer Science+Business Media Dordrecht
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Kopal, Z. (1966). Possible Convection in Lunar Interior. In: An Introduction to the Study of the Moon. Astrophysics and Space Science Library. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-6320-2_10
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DOI: https://doi.org/10.1007/978-94-017-6320-2_10
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