Page 99 - Satellite Communications, Fourth Edition

The Geostationary Orbit 79

to compensate for the movement of the satellite about the nominal
geostationary position. With the types of antennas used for home recep-
tion, the antenna beamwidth is quite broad, and no tracking is neces-
sary. This allows the antenna to be fixed in position, as evidenced by the
small antennas used for reception of satellite TV that can be seen fixed
to the sides of homes.
The three pieces of information that are needed to determine the look
angles for the geostationary orbit are
1. The earth-station latitude, denoted here by l E
2. The earth-station longitude, denoted here by f E
3. The longitude of the subsatellite point, denoted here by f SS (often this
is just referred to as the satellite longitude)
As in Chap. 2, latitudes north will be taken as positive angles, and lat-
itudes south, as negative angles. Longitudes east of the Greenwich
meridian will be taken as positive angles, and longitudes west, as neg-
ative angles. For example, if a latitude of 40°S is specified, this will be
taken as 40°, and if a longitude of 35°W is specified, this will be taken
as 35°.
In Chap. 2, when calculating the look angles for low-earth-orbit (LEO)
satellites, it was necessary to take into account the variation in earth’s
radius. With the geostationary orbit, this variation has negligible effect
on the look angles, and the average radius of the earth will be used.
Denoting this by R:

R 6371 km (3.5)

The geometry involving these quantities is shown in Fig. 3.1. Here,
ES denotes the position of the earth station, SS the subsatellite point,
S the satellite, and d is the range from the earth station to the satel-
lite. The angle
is an angle to be determined.
There are two types of triangles involved in the geometry of Fig. 3.1,
the spherical triangle shown in heavy outline in Fig. 3.2a and the plane
triangle of Fig. 3.2b. Considering first the spherical triangle, the sides
are all arcs of great circles, and these sides are defined by the angles
subtended by them at the center of the earth. Side a is the angle
between the radius to the north pole and the radius to the subsatel-
lite point, and it is seen that a 90°. A spherical triangle in which
one side is 90° is called a quadrantal triangle. Angle b is the angle
between the radius to the earth station and the radius to the sub-
satellite point. Angle c is the angle between the radius to the earth
station and the radius to the north pole. From Fig. 3.2a it is seen that
c 90° l .
E