CU-Boulder ASEN 3200 - Geodetic and Geocentric Latitude (3 pages)

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Geodetic and Geocentric Latitude



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Geodetic and Geocentric Latitude

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Pages:
3
School:
University of Colorado at Boulder
Course:
Asen 3200 - Orbital Mechanics/Attitude Dynamics and Control
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2 6 2001 Geodetic and Geocentric Latitude ASEN 3200 George H Born z North Observer Circumscribing Circle r b y Equator x a Cross section of ellipse Figure 1 R e 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 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 definition 1 Reference P R Escobal Method of Orbit Determination John Wiley Sons NY 1965 Page 24 29 and 135 136 Useful Equations sin cos 1 e 2 sin z r 1 e 2 sin 2 sin cos x cos 1 e 2 sin 2 r sin 1 e 2 cos 2 1 e 2 cos 1 e 2 cos 2 In terms of geocentric latitude we have x z R 1 e 2 cos 1 e cos 2 2 r x2 z2 R 1 f sin 2 R 1 e 2 sin 1 e 2 cos 2 Where e is the eccentricity and f is the flattening of the ellipsoid For the World Geodetic Survey WGS 84 f a b a 2 e2 2 f f f 1 0 298 25722 e 0 0818191 In terms of geodetic latitude we have sin 2 1 e 2 sin 2 1 e 2 cos 2 cos 2 1 e 2 cos 2 1 e 2 cos 2 x R cos 1 e 2 sin 2 z R 1 e 2 sin 1 e 2 sin 2 r x2 z2 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 2 The relation between and is given by tan tan 1 f 2 3


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