Abstract
A two-component theoretical model of the physical libration of the Moon in longitude is constructed with account taken of the viscosity of the core. In the new version, a hydrodynamic problem of motion of a fluid filling a solid rotating shell is solved. It is found that surfaces of equal angular velocity are spherical, and a velocity field of the fluid core of the Moon is described by elementary functions. A distribution of the internal pressure in the core is found. An angular momentum exchange between the fluid core and solid mantle is described by a third-order differential equation with a right-hand side. The roots of a characteristic equation are studied and the stability of rotation is proved. A libration angle as a function of time is found using the derived solution of the differential equation. Limiting cases of infinitely large and infinitely small viscosity are considered and an effect of lag of a libration phase from a phase of action of an external moment of forces is ascertained. This makes it possible to estimate the viscosity and sizes of the lunar fluid core from data of observations.
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Original Russian Text © B.P. Kondratyev, 2013, published in Astronomicheskii Vestnik, 2013, Vol. 47, No. 1, pp. 3–12.
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Kondratyev, B.P. Accounting for the viscosity of the fluid core in the problem of the physical libration of the moon. Sol Syst Res 47, 1–10 (2013). https://doi.org/10.1134/S0038094612060032
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DOI: https://doi.org/10.1134/S0038094612060032