Page 98 - Satellite Communications, Fourth Edition

78 Chapter Three

The period P for the geostationary is 23 h, 56 min, 4 s mean solar time
(ordinary clock time). This is the time taken for the earth to complete
one revolution about its N–S axis, measured relative to the fixed stars
(see Sec. 2.9.4). Substituting this value along with the value for given
by Eq. (2.3) results in

42164 km (3.2)
a GSO
The equatorial radius of the earth, to the nearest kilometer, is

a 6378 km (3.3)
E
and hence the geostationary height is

h GSO a GSO a E
42164 6378 (3.4)
35786 km

This value is often rounded up to 36,000 km for approximate calculations.
In practice, a precise geostationary orbit cannot be attained because
of disturbance forces in space and the effects of the earth’s equatorial
bulge. The gravitational fields of the sun and the moon produce a shift
of about 0.85°/year in inclination. Also, the earth’s equatorial ellipticity
causes the satellite to drift eastward along the orbit. In practice, station-
keeping maneuvers have to be performed periodically to correct for
these shifts, as described in Sec. 7.4.
An important point to grasp is that there is only one geostationary
orbit because there is only one value of a that satisfies Eq. (2.3) for a
periodic time of 23 h, 56 min, 4 s. Communications authorities
throughout the world regard the geostationary orbit as a natural
resource, and its use is carefully regulated through national and inter-
national agreements.

3.2 Antenna Look Angles
The look angles for the ground station antenna are the azimuth and ele-
vation angles required at the antenna so that it points directly at the
satellite. In Sec. 2.9.8 the look angles were determined in the general
case of an elliptical orbit, and there the angles had to change in order
to track the satellite. With the geostationary orbit, the situation is much
simpler because the satellite is stationary with respect to the earth.
Although in general no tracking should be necessary, with the large earth
stations used for commercial communications, the antenna beamwidth
is very narrow (see Chap. 6), and a tracking mechanism is required