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Isometric Latitude

An isometric latitude is 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 Resource. https://mathworld.wolfram.com/IsometricLatitude.html

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