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Cartesian and ellipsoidal coordinates: Difference between revisions

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{{Article Infobox2
{{Article Infobox2
|Category=Fundamentals
|Category=Fundamentals
|Title={{PAGENAME}}
|Authors=J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain.
|Authors=J. Sanz Subirana, JM. Juan Zornoza and M. Hernandez-Pajares, University of Catalunia, Spain.
|Level=Basic
|Level=Basic
|YearOfPublication=2011
|YearOfPublication=2011
|Title={{PAGENAME}}
}}
}}
The <math>(x,y,z)</math> ECEF Cartesian coordinates of the above mentioned Terrestrial frames can be expressed in the associated ellipsoid as <math>(\lambda,\varphi, h)</math> ellipsoidal coordinates, where <math>\lambda</math> and <math>\varphi</math> are respectively the longitude and latitude from the ellipsoid, and <math>h</math> the height above it. Figure 1 illustrates the relation between Cartesian and ellipsoidal coordinates. The equations associated to this transformation are given in [[Ellipsoidal and Cartesian Coordinates Conversion]].
The <math>(x,y,z)</math> ECEF Cartesian coordinates of the above mentioned Terrestrial frames can be expressed in the associated ellipsoid as <math>(\varphi,\lambda, h)</math> ellipsoidal coordinates, where <math>\varphi</math> and <math>\lambda</math> are respectively the latitude and longitude from the ellipsoid, and <math>h</math> the height above it. Figure 1 illustrates the relation between Cartesian and ellipsoidal coordinates. The equations associated to this transformation are given in [[Ellipsoidal and Cartesian Coordinates Conversion]].




::[[File:Cartesian_Ellipsoid_Coord_coorenu.png|none|thumb|400px|'''''Figure 1:''''' Cartesian <math>(x,y,z)</math> and ellipsoidal <math>(\lambda, \varphi, h)</math> coordinates.]]
::[[File:Cartesian_Ellipsoid_Coord_coorenu.png|none|thumb|400px|'''''Figure 1:''''' Cartesian <math>(x,y,z)</math> and ellipsoidal <math>(\varphi, \lambda, h)</math> coordinates.]]




[[Category:Fundamentals]]
[[Category:Fundamentals]]
[[Category:GNSS Time Reference, Coordinate Frames and Orbits]]

Latest revision as of 11:53, 3 February 2013


FundamentalsFundamentals
Title Cartesian and ellipsoidal coordinates
Author(s) J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain.
Level Basic
Year of Publication 2011

The [math]\displaystyle{ (x,y,z) }[/math] ECEF Cartesian coordinates of the above mentioned Terrestrial frames can be expressed in the associated ellipsoid as [math]\displaystyle{ (\varphi,\lambda, h) }[/math] ellipsoidal coordinates, where [math]\displaystyle{ \varphi }[/math] and [math]\displaystyle{ \lambda }[/math] are respectively the latitude and longitude from the ellipsoid, and [math]\displaystyle{ h }[/math] the height above it. Figure 1 illustrates the relation between Cartesian and ellipsoidal coordinates. The equations associated to this transformation are given in Ellipsoidal and Cartesian Coordinates Conversion.


Figure 1: Cartesian [math]\displaystyle{ (x,y,z) }[/math] and ellipsoidal [math]\displaystyle{ (\varphi, \lambda, h) }[/math] coordinates.
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