Geocentric Latitude

An Auxiliary Latitude given by

$\begin{displaymath} \phi_g=\tan^{-1}[(1-e^2)\tan\phi]. \end{displaymath}$

The series expansion is

$\begin{displaymath} \phi_g=\phi-e_2\sin(2\phi)+{\textstyle{1\over 2}}{e_2}^2\sin(4\phi)+{\textstyle{1\over 3}}{e_2}^3\sin(6\phi)+\ldots, \end{displaymath}$

where

$\begin{displaymath} e_2\equiv {e^2\over 2-e^2}. \end{displaymath}$

See also Latitude

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, pp. 17-18, 1987.