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
related by:

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2002-03-21