In Figure 1 we depict a cross-section of the spheroid through the poles. The point O is the center of the earth. B is the North Pole. The major (equatorial) axis, OA, of the meridional ellipse has length , the minor (polar) axis, OB has length . A point on the ellipse has coordinates where the angle is called the reduced or parametric latitude. The point is the point on the circumscribing circle (of radius ) the same distance from the polar axis as P. The angle is called the geocentric latitude.
However, the latitude used in navigation and geodesy is the geodetic or astronomical latitude, which is defined to be the angle between the northerly horizon at P and the polar axis. It is equal to the angle in Figure 1.
Longitude, , is defined in exactly the same way on the spheroid as on the sphere, namely as the angle between the meridian and the prime meridian. We use here the standard convention of North longitudes and East latitudes as positive.
In three dimensional Cartesian coordinates, points on the spheroid have coordinates .
There are alternative ways of specifying the dimensions of the
spheroid other than by its major and minor radii and . The
flattening, , is defined by , and the eccentricity by
. For the WGS84 spheroid, km and
. The eccentricity and flattening are thus