Page 80 - Satellite Communications, Fourth Edition

60 Chapter Two

With the height of the earth station above mean sea level denoted by
H, the geocentric coordinates of the earth station position are given in
terms of the geodetic coordinates by (Thompson, 1966)
a E
N 5 2 2 (2.39)
21 e sin l E
E
R 5 (N H) cos l cos LST
E
I
5l cos LST (2.40)
R 5 (N H) cos l sin LST
J
E
5l sin LST (2.41)
2
R 5 SNQ1 e R HT sin l E
E
K
5 z (2.42)
Example 2.19 Find the components of the radius vector to the earth station at
Thunder Bay, given that the latitude is 48.42°, the height above sea level is 200
m, and the LST is 167.475°.
Solution With all distances in km, H 0.2 km
a E
N 5
2 2
21 e E sin l E
6378.1414
5
2
2
21 0.08182 sin 48.42
6390.121 km
l (N H) cos l E
6390.321 0.66366
4241.033 km
R I lcos(LST)

4241.033 ( 0.9762)
4140.103 km

R J lsin(LST)
4241.033 (0.216865)
919.734 km

2
R K [N(1 e E ) H] sin l E