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Earth Ellipsoid Coordinates (Topic)

Earth Ellipsoid Coordinates

The Earth is more accuratley modelled as an oblate ellipsoid of revolution. If the symmetry axis is taken as $OZ$ the Cartesian equation with respect to its center is

$\displaystyle \frac{X^2}{a^2} + \frac{Y^2}{a^2} + \frac{Z^2}{b^2} = 1, \,\,\,\,\, a > b .$ (1)

The definition of longitude $\lambda$ is exactly the same as on the sphere. The geodetic latitude $\phi$, which we will siomply call latitude, is the angle at which the normal at $P$ intersects the equatorial plane $(Z = 0)$.


\begin{tikzpicture} \begin{axis}[hide axis\htmladdnormallink{,unit vector}{https... ...0] ({a*cos(x)*cos(y)},{b*sin(x)*cos(y)},{c*sin(y)}); \end{axis}\end{tikzpicture}

Bibliography

This article is a derivative work of the creative commons share alike with attribution in [1].

[1]Osborne, Peter. The Mercator Projections. Zenodo, 2013. https://doi.org/10.5281/zenodo.35392.



"Earth Ellipsoid Coordinates" is owned by bloftin.
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Also defines:  geodetic latitude

Cross-references: domain, function, unit vector, latitude, longitude

This is version 5 of Earth Ellipsoid Coordinates, born on 2025-12-04, modified 2025-12-04.
Object id is 1027, canonical name is EarthEllipsoidCoordinates.
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Physics Classification: 91.10.By (Mathematical geodesy; general theory)
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