Analytical Solutions of Love Numbers for a Hydrostatic Ellipsoidal Incompressible Homogeneous Earth |
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| Authors: | Marianne Greff-Lefftz Laurent Métivier Hilaire Legros |
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| Institution: | (1) Institut de Physique du Globe de Paris, 4 place Jussieu, 75252 Paris 05, France;(2) E.O.S.T., 5 rue René Descartes, 67084 Strasbourg, France |
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| Abstract: | Tidal forces acting on the Earth cause deformations and mass redistribution inside the planet involving surface motions and
variation in the gravity field, which may be observed in geodetic experiments. Because for space geodesy it is now necessary
to achieve the mm level in tidal displacements, we take into account the hydrostatic flattening of the Earth in the computation
of the elasto-gravitational deformations. Analytical solutions are derived for the semi-diurnal tides on a slightly elliptical
homogeneous incompressible elastic model. That simple analytical Earth’s model is not a realistic representation of any real
planet, but it is useful to understand the physics of the problem and also to check numerical procedures. We rediscover and
discuss the Love’s solutions and obtain new analytical solutions for the tangential displacement. We extend these analytical
results to some geodetic responses of the Earth to tidal forces such as the perturbation of the surface gravity field, the
tilt and the deviation of the vertical with reference to the Earth’s axis. |
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| Keywords: | body tides elasto-gravitational deformations Love numbers |
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