Geodetic and Geocentric LatitudeASEN 3200

George H. Born

Figure 1 Reference Ellipsoid representing the Earth

Geocentric Latitude – The acute angle measured perpendicular to the equatorial

plane and a line joining the center of the earth and a point on the surface of the reference

ellipsoid. ( )

Geodetic Latitude – The acute angle between the equator and a line drawn

perpendicular to the tangent of the reference ellipsoid. Map coordinates are given as

longitude and geodetic latitude.

Reduced Latitude – See figure 1 for definition

Reference : P.R. Escobal, “Method of Orbit Determination”, John Wiley & Sons, NY,

1965 # Page 24-29 and 135-136.

1

2/6/2001

R+

xy

z

b

a

CircumscribingCircle

Cross section of ellipse

NorthObserver

Equator

Useful Equations

= = ; =

cos = = ; =

In terms of geocentric latitude, we have

x = , r = =

z =

Where e is the eccentricity and f is the flattening of the ellipsoid.

For the World Geodetic Survey (WGS-84)

, = , = , e = 0.0818191

In terms of geodetic latitude, we have

=

=

x = , z = , r =

Note that if we wish to find x and z for a tracking station located at height H above the

reference ellipsoid we must add (H cos ) to x and (H sin ) to z (see Eqn. 2.8-7 in Bate

Mueller and White).

The relation between and is given by

2

=

3