Abstract
The most important characteristic of any celestial body is, indeed, its mass; and in the case of the Moon this is known (cf. Chapter 1) to be 7.35 × 1025 g or 1.2 per cent of that of the Earth. This mass is, moreover, contained inside a globe of r c = 1738 km mean radius, rendering its mean density ρ m = 3.34 g/cm3. What is the corresponding pressure inside such a configuration? If the latter were in hydrostatic equilibrium — an assumption which will have to be tested on its merits — the pressure P(r) and the density ρ(r) at a distance r from the Moon’s center should, to a high degree of approximation* be related by the well-known equation
, of hydrostatic equilibrium where the gravitational acceleration g inside a spherically-symmetrical configuration will be given by
, where G is the constant of gravitation and m(r), the mass interior to a volume of radius r, follows from the equation
.
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Bibliographical Notes
The model of a self-compressed Moon based on equation of state of the form (7–7) has first been worked out by Jeffreys (1952, pp. 147–153), with further contributions made more recently by MacDonald (1962) and Lyttleton (1963).
Clairaut’s theory of the figures of equilibrium of celestial bodies, underlying the evaluation of the lunar moments of inertia, is classical; for its fuller account cf. Sections II 1–2 of Kopal (1959); or, more completely, Kopal (1960). For theoretical tides in a solid Moon cf. Sutton, Meidell, and Kovach (1963).
For recent discussion of the observational determination of the lunar moments of inertia and of the “mechanical ellipticity constant” f cf., e.g., Fridland (1961), Habibullin (1961), Gorynia (1962), Nefediev (1963) or Shakirov (1963); while for theoretical investigations of the lunar moments of inertia and the associated gravity field cf., Grushinski and Sagitov (1962), or Goudas (1964b, c, 1965b) and Mikhailov (1965). For a position of the centre of mass of the Moon cf., also Bystrov (1962) or O’Keefe and Cameron (1962).
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© 1966 Springer Science+Business Media Dordrecht
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Kopal, Z. (1966). Hydrostatic Equilibrium. 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_7
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DOI: https://doi.org/10.1007/978-94-017-6320-2_7
Publisher Name: Springer, Dordrecht
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