Page 83 - Satellite Communications, Fourth Edition

Orbits and Launching Methods 63

TABLE 2.4 Azimuth Angles
Azimuth (degrees)
r S r E
a
180° a
− 180° a
− 360° a

The antenna elevation angle is
Z
El 5 arcsin (2.48)

The antenna azimuth angle is found from
Z Z
E
5 arctan (2.49)
Z Z
S
The azimuth depends on which quadrant a is in. With a in degrees
the azimuth is as given in Table 2.4.

Example 2.20 The IJK range vector components for a certain satellite, at GST
240°, are as given below. Calculate the corresponding range and the look angles
for an earth station the coordinates for which are—latitude 48.42°N, longitude
89.26°W, height above mean sea level 200 m.
Solution Given data: r I 1280 km; r J 1278 km; r K 66 km; GST 240°;
l E 48.42°; f E 89.26°; H 200 m

The required earth constants are a E 6378.1414 km; e E 0.08182

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
2
z SNQ1 e E R HT sin l E
2
[6390.121 (1 0.08182 ) 0.2] 0.74803
4748.151 km