Page 107 - Satellite Communications, Fourth Edition

The Geostationary Orbit 87

In the calculations leading to d, a spherical earth of mean radius
6371 km may be assumed and earth-station elevation may be ignored,
as was done in the previous section. The value obtained for will be
sufficiently accurate for initial alignment and fine adjustments can
be made, if necessary. Calculation of the angle of tilt is illustrated in
Example 3.3.

Example 3.3 Determine the angle of tilt required for a polar mount used with an
earth station at latitude 49° north. Assume a spherical earth of mean radius 6371
km, and ignore earth-station altitude.

Solution Given data:

l E 49°; a GSO 42164 km; R 6371 km; b l E = 49°.
Equation (3.11) gives:
2
2
d 26371 42164 2 6371 42164 cos 49
> 38287 km
From Eq. (3.12):

El arccosa 42164 sin 49 b
38287
> 33.8°
90° 33.8° 49°
> 7°

3.4 Limits of Visibility
There will be east and west limits on the geostationary arc visible from
any given earth station. The limits will be set by the geographic coor-
dinates of the earth station and the antenna elevation. The lowest ele-
vation in theory is zero, when the antenna is pointing along the
horizontal. A quick estimate of the longitudinal limits can be made by
considering an earth station at the equator, with the antenna pointing
either west or east along the horizontal, as shown in Fig. 3.6. The lim-
iting angle is given by

a E

arccos
a GSO
6378
arccos
42164
81.3