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Parametric Latitude


An auxiliary latitude also called the reduced latitude and denoted eta or theta. It gives the latitude on a sphere of radius a for which the parallel has the same radius as the parallel of geodetic latitude phi and the ellipsoid through a given point. It is given by

 eta=tan^(-1)(sqrt(1-e^2)tanphi).
(1)

In series form,

 eta=phi-e_1sin(2phi)+1/2e_1^2sin(4phi)-1/3e_1^3sin(6phi)+...,
(2)

where

 e_1=(1-sqrt(1-e^2))/(1+sqrt(1-e^2)).
(3)

See also

Authalic Latitude, Conformal Latitude, Ellipsoid, Geocentric Latitude, Isometric Latitude, Latitude, Oblate Spheroid, Rectifying Latitude, Sphere, Spheroid

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References

Adams, O. S. "Latitude Developments Connected with Geodesy and Cartography with Tables, Including a Table for Lambert Equal-Area Meridional Projections." Spec. Pub. No. 67. U. S. Coast and Geodetic Survey, 1921.Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, p. 18, 1987.

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Parametric Latitude

Cite this as:

Weisstein, Eric W. "Parametric Latitude." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ParametricLatitude.html

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