Page 97 - Satellite Communications, Fourth Edition

Chapter
3

The Geostationary Orbit

3.1 Introduction
A satellite in a geostationary orbit appears to be stationary with respect
to the earth, hence the name geostationary. Three conditions are
required for an orbit to be geostationary:
1. The satellite must travel eastward at the same rotational speed as
the earth.
2. The orbit must be circular.
3. The inclination of the orbit must be zero.
The first condition is obvious. If the satellite is to appear station-
ary, it must rotate at the same speed as the earth, which is constant.
The second condition follows from this and from Kepler’s second law
(Sec. 2.3). Constant speed means that equal areas must be swept out
in equal times, and this can only occur with a circular orbit (see Fig. 2.2).
The third condition, that the inclination must be zero, follows from
the fact that any inclination would have the satellite moving north
and south, (see Sec. 2.5 and Fig. 2.3), and hence it would not be geo-
stationary. Movement north and south can be avoided only with zero
inclination, which means that the orbit lies in the earth’s equatorial
plane.
Kepler’s third law may be used to find the radius of the orbit (for a
circular orbit, the semimajor axis is equal to the radius). Denoting the
radius by a GSO , then from Eqs. (2.2) and (2.4),

P 1/3
a GSO a 2 b (3.1)
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