# 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.

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

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
```