Why does the Mapping Toolbox documentation confuse the 'WGS84' and 'GRS80' reference ellipsoids?

The "Geoid and Ellipsoid" section of the Mapping Toolbox documentation states that the default reference ellipsoid is based on the 1980 Geodetic Reference System, which is the same as that of the 1984 World Geodetic System. However the flattening coefficients of the two reference ellipsoids are slightly different.

 <http://www.mathworks.com/access/helpdesk/help/toolbox/map/geogeom3.html>

Answer 1

[MathWorks Support Team]

This is an error in the Mapping Toolbox documentation. It is unlikely to be numerically significant for applications.

In R2006a, the Mapping Toolbox added the 1984 World Geodetic System (WGS84) reference ellipsoid to the function almanac. There is only a minor difference between the WGS84 and the GRS80 ellipsoids.

To illustrate the differences, you can excute the following code in Matlab (R2006a or later):

wgs84=almanac('earth','wgs84','meter')

 wgs84 =

1.0e+006 *

    6.3781    0.0000

grs80=almanac('earth','grs80','meter')

 grs80 =

1.0e+006 *

    6.3781    0.0000

wgs84 - grs80

 ans =

1.0e-009 *

         0   -0.2002

The sentence in the documentation, "It is also the reference ellipsoid for the 1984 World Geodetic System (WGS84)" is incorrect. However, as the discrepency is only about 0.1 mm along the semiminor axis, it is of little practical consequence.