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Isometric Latitude

An authalic latitude which is directly proportional to the spacing of parallels of latitude from the equator on an ellipsoidal Mercator projection. It is defined by

psi=ln|tan(1/4pi+1/2phi)((1-esinphi)/(1+esinphi))^(e/2)|,
(1)

where the symbol tau is sometimes used instead of psi. The isometric latitude is related to the conformal latitude by

psi=lntan(1/4pi+1/2chi).
(2)

The inverse is found by iterating

phi=2tan^(-1)[exp(psi)((1+esinphi)/(1-esinphi))^(e/2)]-1/2pi,
(3)

with the first trial as

phi_0=2tan^(-1)(e^psi)-1/2pi.
(4)

See also

Latitude

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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. 15, 1987.

Referenced on Wolfram|Alpha

Isometric Latitude

Cite this as:

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

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