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Relativistic motion of gyroscopes and space gradiometry / E. Gill (1992)

Public Titre : Relativistic motion of gyroscopes and space gradiometry Type de document : Monographie Auteurs : E. Gill, Auteur ; Michael Soffel, Auteur ; H. Ruder, Auteur ; Monique Schneider, Auteur Editeur : Munich : Bayerische Akademie der Wissenschaften Année de publication : 1992 Collection : DGK - A Sous-collection : Theoretische Geodäsie num. 107 Importance : 82 p. Format : 21 x 30 cm ISBN/ISSN/EAN : 978-3-7696-8189-5 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie spatiale [Termes IGN] champ de gravitation [Termes IGN] corps céleste [Termes IGN] équation de Hamilton-Jacobi [Termes IGN] force d'inertie [Termes IGN] gradiométrie [Termes IGN] gyroscope [Termes IGN] linéarisation [Termes IGN] mécanique céleste [Termes IGN] métrique [Termes IGN] précession [Termes IGN] système Terre-Lune Index. décimale : 30.60 Géodésie spatiale Résumé : (Auteur) Relativistic effects in the motion of freely falling test particles moving along circular orbits in the exterior gravitational field of a spherically symmetric, slowly rotating or slightly oblate body are considered. To this end we solve the geodesic equation in the (parametrized) post-Newtonian metric, the linearized Kerr metric and the linearized Erez-Rosen metric, respectively. The main part of this article deals with the "pseudo-Newtonian resonances" found by MASHHOON and THEISS (1982-1986) in the motion of torque-free gyroscope axes, moving along inclined orbits in the gravitational field of a rotating mass. In relativistic spin motion and gradiometry these "resonances" should lead to new effects on time scales, comparable or large to the Fokker period. In this regime, it was argued, the usual post-Newtonian approximation should break down. However, solving the equations of parallel transport in the first post-Newtonian approximation, we show that the Mashhoon-Theiss "anomaly" appears already at this level and can be explained as arising from a simple interplay between Fokker (geodetic) and Schiff (Lense-Thirring) precession. For these reasons the Mashhoon-Theiss "anomaly" represents no new anomalous relativistic effect, but can be understood by means of the usual post-Newtonian formalism. Considering the motion of some torque-free gyroscope along circular orbits with small inclination in the gravitational field of an oblate body, where according to THEISS (1985b) similar relativistic resonances should appear, we show that no new interesting relativistic effects occur in that case. To investigate relativistic effects in space gradiometry we calculate the relativistic tidal forces in a local inertial system, using the previously derived results for geodesic and spin motion. According to the development of high precision superconducting satellite gradiometers the measurement of gravito-magnetic effects of the Earth's rotation may in principle be achieved in the near future. Analyzing the motion of the Earth-Moon system in the gravitational field of the rotating Sun, we find that gravito-magnetic effects can be neglected. Especially, taking into account the Newtonian precession of the Moon's orbit the Mashhoon-Theiss "anomaly" leads to a variation of the Earth-Moon distance with amplitude 0.4 /µm, in contrast to the results of Mashhoon and Theiss of 1.4 m (MASHHOON et al. 1986). Relativistic effects of the quadrupole moment of the central field can be neglected in satellite gradiometry and the motion of the Earth-Moon system, respectively. Numéro de notice : 40655 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Monographie Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=57824

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Code-barres	Cote	Support	Localisation	Section	Disponibilité
40655-01	30.60	Livre	Centre de documentation	Géodésie	Disponible