Page 146 - Satellite Communications, Fourth Edition

126 Chapter Five

assuming the earth station to be at mean sea level)

R cosl cosB (5.15a)
R x
R R cosl sinB (5.15b)
y
R R sinl (5.15c)
z
where B f f as defined in Eq. (3.8).
E
SS
The local gravity direction is r R. The coordinates for the direc-
tion of propagation k are
k R a GSO (5.16a)
x
x
k R y (5.16b)
y
R (5.16c)
k z z
Calculation of the polarization angle is illustrated in the following
example.

Example 5.1 A geostationary satellite is stationed at 105°W and transmits a ver-
tically polarized wave. Determine the angle of polarization at an earth station at
latitude 18°N longitude 73°W.
Solution Given data:
l 18°; f E 73°; f SS 105°; a GSO 42164 km; R 6371 km (spherical earth
of mean radius R assumed).
Eq. (3.8) gives:
B f E f SS 32°

Applying Eq. (5.15), the geocentric-equatorial coordinates for the earth station
position vector are:
R x R cosl cosB

6371cos18° cos32°
5138.48 km

R y R cosl sinB
6371cos18° sin32°

3210.88 km

R z R sinl
6371sin18°

1968.75 km