Formation of a planet temperature field by tides / V. G. Vil'ke, A. N. Danilkin. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2012. № 4. P. 36-43 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].
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.