Abstract
A planet model as a uniform elastic sphere in the gravitational field of two mass points whose mutual motion causes tidal deformations is considered. The sphere rotation about its mass center is studied with consideration of its deformations caused by the centrifugal force field and the gradient fields of gravitational forces. The sphere’s inertia tensor whose components are time dependent is found. The sphere’s angular velocity projections onto the axes associated with the sphere according to an integral law are determined. The results obtained are illustrated for the case of the Earth. For this case, the equivalent values of the elasticity modulus and Poisson’s ratio and the angular velocity disturbances are found.
Similar content being viewed by others
References
N. S. Sidorenkov, Physics of Instabilities in the Earth Rotation (Fizmatlit, Moscow, 2002) [in Russian].
V. V. Beletskii, The Motion of a Satellite about the Center of Mass in a Gravitational Field (Mosk. Gos. Univ., Moscow, 1975) [in Russian].
G. H. Darwin, The Tides and Kindred Phenomena in the Solar System (Houghton, Boston, 1899; Nauka, Moscow, 1969).
V. G. Vil’ke, “Motion of a Visco-Elastic Sphere in a Central Newtonian Force Field,” Prikl. Mat. Mekh. 44(3), 395–402 (1980) [J. Appl. Math. Mech. 44 (3), 280–284 (1980)].
V. G. Vil’ke and A. V. Shatina, “Translational-Rotational Motion of a Viscoelastic Sphere in the Gravitational Field of an Attracting Center and a Satellite,” Kosmich. Issled. 42(1), 95–106 (2004) [Cosmic Res. 42 (1), 91–102 (2004)].
V. G. Vil’ke, Analytical Mechanics of Systems Whose Degrees of Freedom are Infinite (Mosk. Gos. Univ., Moscow, 1997) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © E.Yu. Baranova. V.G. Vil’ke. 2014, published in Vestnik Moskovskogo Universiteta. Matematika. Mekhanika, 2014, Vol. 69, No. 3, pp. 33–40.
About this article
Cite this article
Baranova, E.Y., Vil’ke, V.G. Rotation of an elastic sphere about its mass center in the gravitational field of two attracting points. Moscow Univ. Mech. Bull. 69, 57–64 (2014). https://doi.org/10.3103/S0027133014030017
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0027133014030017