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JOURNALS // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika // Archive

Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012 Number 4, Pages 36–43 (Mi vmumm511)

Mechanics

Temperature field formation in a planet due to tidal deformations

V. G. Vil'ke, A. N. Danilkin

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A model of a planet considered as a homogeneous viscoelastic sphere in the gravitational field of point mass is discussed. Tidal deformations occur in the process of their mutual motion. The strain rate tensor and the corresponding dissipative function are found. The time variation of the strain tensor components accompanied by the heat release at each point of the planet causes the formation of a temperature field described by the nonhomogeneous heat conduction equation. The temperature field is determined by averaging with respect to the proper rotation angle and is estimated for the Moon.

Key words: tidal deformations, temperature field of planet.

UDC: 531.391

Received: 14.09.2011


 English version:
Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 2012, 67:4, 84–91

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