EquatorGeodetic and Geocentric LatitudeFigure 1 Reference Ellipsoid representing the EarthGeodetic and Geocentric LatitudeASEN 3200George H. BornFigure 1 Reference Ellipsoid representing the EarthGeocentric 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. (2/2/)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 definition12/6/2001R+exyzbaCircumscribingCircleCross section of ellipse NorthObserverEquatorrReference : P.R. Escobal, “Method of Orbit Determination”, John Wiley & Sons, NY, 1965 # Page 24-29 and 135-136.Useful Equationssin=rz=222sin1sin1ee;sin=22cos1sinecos=rx=22sin1cose;cos=222cos1cos1eeIn terms of geocentric latitude, we havex = 222cos1cos1eeR, r = 22zx = )sin1(2 fRz = 222cos1sin1eeRWhere e is the eccentricity and f is the flattening of the ellipsoid. For the World Geodetic Survey (WGS-84)abaf, 2e = 22 ff , f = 25722.2980.1, e = 0.0818191In terms of geodetic latitude, we have2sin = 2222cos1sin)1(ee2cos = 2222cos1cos)1(eex = 22sin1coseR, z = 222sin1sin)1(eeR, r = 22zx 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 BateMueller and White).2The relation between and is given by tan =
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