Geocentric Latitude

New in version 5.0.0.

Convert from Geodetic Latitude to Geocentric Latitude (in the forward path).

Alias geoc
Domain 2D
Input type Geodetic coordinates
Output type Geocentric angular coordinates

The geodetic (or geographic) latitude (also called planetographic latitude in the context of non-Earth bodies) is the angle between the equatorial plane and the normal (vertical) to the ellipsoid surface at the considered point. The geodetic latitude is what is normally used everywhere in PROJ when angular coordinates are expected or produced.

The geocentric latitude (also called planetocentric latitude in the context of non-Earth bodies) is the angle between the equatorial plane and a line joining the body centre to the considered point.

Geocentric latitude

Note

This conversion must be distinguished fom the Geodetic to cartesian conversion which converts geodetic coordinates to geocentric coordinates in the cartesian domain.

Mathematical definition

The formulas describing the conversion are taken from [Snyder1987] (equation 3-28)

Let \(\phi'\) to be the geocentric latitude and \(\phi\) the geodetic latitude, then

\[\phi' = \arctan \left[ (1 - e^2) \tan \left( \phi \right) \right]\]

The geocentric latitude is consequently lesser (in absolute value) than the geodetic latitude, except at the equator and the poles where they are equal.

On a sphere, they are always equal.

Usage

Converting from geodetic latitude to geocentric latitude:

+proj=geoc +ellps=GRS80

Converting from geocentric latitude to geodetic latitude:

+proj=pipeline +step +proj=geoc +inv +ellps=GRS80

Parameters

+ellps=<value>

See proj -le for a list of available ellipsoids.

Defaults to “GRS80”.