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Tr. Mat. Inst. Steklova, 2015, Volume 289, Pages 195–205 (Mi tm3619)  

Perturbation theory for the stress tensor in the Moon's body with tidal effects taken into account

V. P. Pavlov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: On the basis of the seismic data from the Apollo project, we show that one can use linear elasticity theory to process these data, which yields information on the mechanical parameters of the Moon's body with an accuracy of 10%. Within this theory, we obtain a theoretical formula for the dependence of pressure on depth in the Moon's body in the presence of tidal effects. We also derive theoretical dependence of the variations of the free energy density due to tidal effects on latitude and depth. In all these formulas the contribution of shear stresses is taken into account. It turns out that the main contribution is made by the Earth tides. Estimates for the dissipation of the energy of tidal oscillations show that this energy is certainly enough to explain where the energy released in deep focus moonquakes comes from.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968515020119

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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 289, 183–193

Bibliographic databases:

UDC: 550.348.32
Received: March 15, 2015

Citation: V. P. Pavlov, “Perturbation theory for the stress tensor in the Moon's body with tidal effects taken into account”, Selected issues of mathematics and mechanics, Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov, Tr. Mat. Inst. Steklova, 289, MAIK Nauka/Interperiodica, Moscow, 2015, 195–205; Proc. Steklov Inst. Math., 289 (2015), 183–193

Citation in format AMSBIB
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\by V.~P.~Pavlov
\paper Perturbation theory for the stress tensor in the Moon's body with tidal effects taken into account
\inbook Selected issues of mathematics and mechanics
\bookinfo Collected papers. In commemoration of the 150th anniversary of Academician Vladimir Andreevich Steklov
\serial Tr. Mat. Inst. Steklova
\yr 2015
\vol 289
\pages 195--205
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\crossref{https://doi.org/10.1134/S0371968515020119}
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\jour Proc. Steklov Inst. Math.
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  • https://doi.org/10.1134/S0371968515020119
  • http://mi.mathnet.ru/eng/tm/v289/p195

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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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