Page 108 - Satellite Communications, Fourth Edition

88 Chapter Three

a GSO Θ Θ a GSO
a E

Figure 3.6 Illustrating the limits of visibility.

Thus, for this situation, an earth station could see satellites over a geo-
stationary arc bounded by 81.3° about the earth-station longitude.
In practice, to avoid reception of excessive noise from the earth, some
finite minimum value of elevation is used, which will be denoted here
by El min . A typical value is 5°. The limits of visibility will also depend
on the earth-station latitude. As in Fig. 3.2b, let S represent the angle
subtended at the satellite when the angle
min 90° El min . Applying
the sine rule gives

S arcsina R sin
b (3.17)
a GSO min

A sufficiently accurate estimate is obtained by assuming a spherical
earth of mean radius 6371 km as was done previously. Once angle S is
known, angle b is found from

S (3.18)
b 180
min
From Eq. (3.9):

B arccosa cos b b (3.19)
cos l E

Once angle B is found, the satellite longitude can be determined from
Eq. (3.8). This is illustrated in Example 3.4.