[Proj] Geocentric vs. Geodetic latitude

George Percivall percivall at gsfc.nasa.gov
Wed Apr 28 10:33:48 EDT 2004


The two definitions are consistent with my experience as well.

Coming from a background in satellite data I was familiar with "latitude" as
your geocentric latitude in contrast to your client's experience.  In the
case when you set the ellipsoid equal to a sphere, the two definitions
define the same angle.

During the development of ISO 19111 this was discussed. The editors of 19111
were geodesists and objected to my recommendation to include a geocentric
coordinate system.  The title of ISO 19111 is "Geographic Information -
spatial referencing by coordinates".

The OGC work to implement and extend ISO 19111 includes geocentric
coordinate reference systems.  The relevant OGC document is "OGC Abstract
Specification Topic 2."  Here is the latest public version:

Whether both angles should be "latitudes" may be a topic of discussion.  The
OGC document uses a spherical coordinate reference system with two angles
and a radius.  It does not specify that one of the angles is latitude:
omission or intentional?

George Percivall
- Principal Engineer, Geospatial Interoperability Office, NASA
   percivall at gsfc.nasa.gov
- Director, The Geospatial Interoperability Group, GST, Inc.
   percivall at gst.com

On 4/28/04 9:59 AM, "Frank Warmerdam" <warmerdam at pobox.com> wrote:

> Folks,
> I was recently suprised to encounter locations identified as being
> geocentric that were give as a latitude and longitude.  I had expected them
> to be x/y/z values in meters.
> A client of mine, better versed in such things explained that there is in
> fact a distinction between geocentric and geodetic lat/long.  He wrote:
>> "The angle L' is called "geocentric latitude" and is defined as the
>> angle between the equatorial plane and the radius from the geocenter.
>> The angle L is called "geodetic latitude" and is defined as the angle
>> between the equatorial plane and the normal to the surface of the
>> ellipsoid.  The word "latitude" usually means geodetic latitude.  This
>> is the basis for most of the maps and charts we use.  The normal to the
>> surface is the direction that a plumb bob would hang were it not for
>> local anomalies in the earth's gravitational field."
> I need to implement some code to convert geocentric latitude to geodetic
> latitude.  I think I can do from the above description, but I am wondering
> if anyone can confirm the above description, provide a forumla or most
> importantly provide some sample latitudes in both systems I can check my
> work against.
> Best regards,

More information about the Proj mailing list