Page 103 - Satellite Communications, Fourth Edition

The Geostationary Orbit 83

From Eq. (3.8):

b arccos(cos B cos l E )
36.23°
From Eq. (3.9):
sin ZB Z
A 5 arcsina b
sin b
17.1°

By inspection, l E > 0 and B < 0. Therefore, Fig. 3.3c applies, and

A z 180° A
162.9°

Applying the cosine rule for plane triangles to the triangle of Fig. 3.2b
allows the range d to be found to a close approximation:

2
d 2R a 2 GSO 2Ra GSO cos b (3.11)
Applying the sine rule for plane triangles to the triangle of Fig. 3.2b
allows the angle of elevation to be found:

a
El arccosa GSO sin bb (3.12)
d
Example 3.2 Find the range and antenna elevation angle for the situation spec-
ified in Example 3.1.

Solution R 6371 km; a GSO 42164 km, and from Example 3.1, b 36.23°.
Equation (3.11) gives:
2
2
d 26371 42164 2 6371 42164 cos 36.23
> 37215 km

Equation (3.11) gives:

El arccosa 42164 sin 36.23 b
37215
> 48°

Figure 3.4 shows the look angles for Ku-band satellites as seen from
Thunder Bay, Ontario, Canada.