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Basic equations for constructing geopotential models from the gravitational potential derivatives of the first and second orders in the terrestrial reference frame / M. Petrovskaya in Journal of geodesy, vol 86 n° 7 (July 2012)  

Public [article]  inJournal of geodesy > vol 86 n° 7 (July 2012) . - pp 521 - 530 Titre : Basic equations for constructing geopotential models from the gravitational potential derivatives of the first and second orders in the terrestrial reference frame Type de document : Article/Communication Auteurs : M. Petrovskaya, Auteur ; A. Vershkov, Auteur Année de publication : 2012 Article en page(s) : pp 521 - 530 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur terrestre [Termes IGN] gradient de gravitation [Termes IGN] harmonique sphérique [Termes IGN] modèle de géopotentiel [Termes IGN] repère de référence [Termes IGN] système de référence mondial Résumé : (Auteur) This research represents a continuation of the investigation carried out in the paper of Petrovskaya and Vershkov (J Geod 84(3):165–178, 2010) where conventional spherical harmonic series are constructed for arbitrary order derivatives of the Earth gravitational potential in the terrestrial reference frame. The problem of converting the potential derivatives of the first and second orders into geopotential models is studied. Two kinds of basic equations for solving this problem are derived. The equations of the first kind represent new non-singular non-orthogonal series for the geopotential derivatives, which are constructed by means of transforming the intermediate expressions for these derivatives from the above-mentioned paper. In contrast to the spherical harmonic expansions, these alternative series directly depend on the geopotential coefficients Cn,m and Sn,m . Each term of the series for the first-order derivatives is represented by a sum of these coefficients, which are multiplied by linear combinations of at most two spherical harmonics. For the second-order derivatives, the geopotential coefficients are multiplied by linear combinations of at most three spherical harmonics. As compared to existing non-singular expressions for the geopotential derivatives, the new expressions have a more simple structure. They depend only on the conventional spherical harmonics and do not depend on the first- and second-order derivatives of the associated Legendre functions. The basic equations of the second kind are inferred from the linear equations, constructed in the cited paper, which express the coefficients of the spherical harmonic series for the first- and second-order derivatives in terms of the geopotential coefficients. These equations are converted into recurrent relations from which the coefficients Cn,m and Sn,m are determined on the basis of the spherical harmonic coefficients of each derivative. The latter coefficients can be estimated from the values of the geopotential derivatives by the quadrature formulas or the least-squares approach. The new expressions of two kinds can be applied for spherical harmonic synthesis and analysis. In particular, they might be incorporated in geopotential modeling on the basis of the orbit data from the CHAMP, GRACE and GOCE missions, and the gradiometry data from the GOCE mission. Numéro de notice : A2012-356 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-011-0535-2 Date de publication en ligne : 31/12/2011 En ligne : https://doi.org/10.1007/s00190-011-0535-2 Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=31802 [article]

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Construction of spherical harmonic series for the potential derivatives of arbitrary orders in the geocentric Earth-fixed reference frame / M. Petrovskaya in Journal of geodesy, vol 84 n° 3 (March 2010)  

Public [article]  inJournal of geodesy > vol 84 n° 3 (March 2010) . - pp 165 - 178 Titre : Construction of spherical harmonic series for the potential derivatives of arbitrary orders in the geocentric Earth-fixed reference frame Type de document : Article/Communication Auteurs : M. Petrovskaya, Auteur ; A. Vershkov, Auteur Année de publication : 2010 Article en page(s) : pp 165 - 178 Note générale : Bibliographie Langues : Anglais (eng) Descripteur : [Vedettes matières IGN] Géodésie physique [Termes IGN] champ de pesanteur local [Termes IGN] coordonnées cartésiennes géocentriques [Termes IGN] déviation de la verticale [Termes IGN] Earth Gravity Model 2008 [Termes IGN] harmonique sphérique [Termes IGN] repère de référence [Termes IGN] trièdre local [Termes IGN] variance Résumé : (Auteur) The derivatives of the Earth gravitational potential are considered in the global Cartesian Earth-fixed reference frame. Spherical harmonic series are constructed for the potential derivatives of the first and second orders on the basis of a general expression of Cunningham (Celest Mech 2:207–216, 1970) for arbitrary order derivatives of a spherical harmonic. A common structure of the series for the potential and its first- and second-order derivatives allows to develop a general procedure for constructing similar series for the potential derivatives of arbitrary orders. The coefficients of the derivatives are defined by means of recurrence relations in which a coefficient of a certain order derivative is a linear function of two coefficients of a preceding order derivative. The coefficients of the second-order derivatives are also presented as explicit functions of three coefficients of the potential. On the basis of the geopotential model EGM2008, the spherical harmonic coefficients are calculated for the first-, second-, and some third-order derivatives of the disturbing potential T, representing the full potential V, after eliminating from it the zero- and first-degree harmonics. The coefficients of two lowest degrees in the series for the derivatives of T are presented. The corresponding degree variances are estimated. The obtained results can be applied for solving various problems of satellite geodesy and celestial mechanics. Copyright Springer Numéro de notice : A2010-155 Affiliation des auteurs : non IGN Thématique : POSITIONNEMENT Nature : Article nature-HAL : ArtAvecCL-RevueIntern DOI : 10.1007/s00190-009-0353-y Date de publication en ligne : 10/11/2009 En ligne : https://doi.org/10.1007/s00190-009-0353-y Format de la ressource électronique : URL article Permalink : https://documentation.ensg.eu/index.php?lvl=notice_display&id=30350 [article]

Exemplaires(1)

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266-2010031	SL	Revue	Centre de documentation	Revues en salle	Disponible