Catalogue en ligne IGN

Zur Theorie des Normalsphäroides der Erde ; Die theoretische Lösung des gesamten Problemes der Erdfigur / K. Ledersteger (1960)

Public

Titre :	Zur Theorie des Normalsphäroides der Erde ; Die theoretische Lösung des gesamten Problemes der Erdfigur
Titre original :	[Pour la théorie du sphéroïde normal de la Terre ; La solution théorique du problème entier de la figure de la Terre]
Type de document :	Monographie
Auteurs :	K. Ledersteger, Auteur
Editeur :	Munich : Bayerische Akademie der Wissenschaften
Année de publication :	1960
Collection :	DGK - A
Sous-collection :	Höhere Geodäsie num. 036
Importance :	30 p.
Format :	21 x 30 cm
Note générale :	Bibliographie
Langues :	Allemand (ger)
Descripteur :	[Vedettes matières IGN] Géodésie physique [Termes IGN] ellipsoïde de Clairaut [Termes IGN] figure de la Terre [Termes IGN] sphèroïde
Index. décimale :	30.40 Géodésie physique
Résumé :	(Auteur) A solution if possible free of hypotheses of the problem of the earth figure on a strictly physical basis requires the simultaneous determination of the normal spheroid and the geoïd undulations. The normal spheroid is defined to be that one-parametric figure of equilibrium, which has in common with the real earth the velocity of rotation, the mass, the moments of inertia (and thus the rotation-impulse) and finally the mass-function of fourth order, D. Since the real vertical gradient of the gravity outside the earth's body is not known accurately enough, the interposition of an artificial geoïd, the so-called free-air geoïd, is necessary, which has the same potential value as the geoïd and whose determination is based on the Theorem of Stokes-Poincaré. The gravity distribution and the indirect effect for that free-air geoïd can be derived with great accuracy without any presumption of certain mass-displacements. It coincides with the geoïd on the oceans and rises on the continents to about 9 m above the geoïd. For 1000 m above sea-level these elevations amount to only 114 mm. The pertaining equipotential spheroid is either an outer level-surface or the free surface of the normal spheroid that has to be determined. The adjustment of the free-air gravity values renders the theoretical gravity on the equipotential spheroid and Helmert's equation system yields with an approximative value of the axis quite excellent approximations for the flattening of the equipotential spheroid, for the parameter £ and for the elevations ft < 0 of the equipotential spheroid above its coaxial ellipsoid of revolution. Subsequently, Stokes' Integral furnesheg from jhe free-air gravity anomalies the heights N of the free-air geoïd above its equipotential spheroid, which being gravimetrical heights are free of an error occurring in the assumed axis. Now four surfaces exist: the geoïd, the free-air geoïd, the pertaining equipotential spheroid and its coaxial ellipsoid of revolution. From the elevations z = (N + h c) of the actual geoïd above this ellipsoid, the ,,absolute adjustment of the deflections of the vertical" wherein the relative deflections of one or two continental triangulation nets, computed on the above mentioned ellipsoid, are adjusted to the absolute deflections of the vertical as derived from the geoïdal elevations z renders the correction of the axis together with the absolute location of the net, besides the relative position of the continents, separated by the oceans. Based on the fact; that the form-parameter has a maximum value on the surface of any figure of equilibrium, it can be confirmed that the equipotential spheroid obtained is already identical with the normal spheroid, otherwise the vertical distances d between the normal spheroid and the equipotential spheroid which convert the geoïdal elevations z into the absolute undulations £ = (z + d) can be determined from the already found potential difference. The obtained formula for the theoretical gravity on the normal spheroid is easy to be transformed by means of the free-air gradient onto the coaxial ellipsoid of revolution, i. e. the mean earth ellipsoid. The main advantages of this strictly physical procedure are the elimination of the fictitious equipotential-ellipsoid and an exact connection, based on potential theory, of the gravity anomalies and the geoïdal undulations with the mass-irregularities in the earth's crust.
Numéro de notice :	39831
Affiliation des auteurs :	non IGN
Thématique :	POSITIONNEMENT
Nature :	Monographie
Permalink :	https://documentation.ensg.eu/index.php?lvl=notice_display&id=63808

Exemplaires(1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
39831-01	30.40	Livre	Centre de documentation	Géodésie	Disponible

IGN

Centre de documentation
scientifique

Accueil

Sélection de la langue

Adresse

Se connecter

Actualité

L'actu ! Horaires du CDOS

Informations pratiques

Exemplaires(1)

IGN / ENSG

L'IGN a pour vocation

Accès directs

2014 -2024 IGN

IGN

Centre de documentationscientifique

Accueil

Sélection de la langue

Adresse

Se connecter

Actualité

L'actu ! Horaires du CDOS

Informations pratiques

Exemplaires(1)

IGN / ENSG

L'IGN a pour vocation

Accès directs

2014 -2024 IGN

Centre de documentation
scientifique