# 10.1 Satellite Communication Systems

Today’s world is connected by a vast communication network that provides a wide array of voice, data, and video services to both fixed and mobile terminals (Fig. 10-1). The viability and effectiveness of the network are attributed in large measure to the use of orbiting satellite systems that function as relay stations with wide area coverage of Earth’s surface. From a geostationary orbit at 35,786 km above the equator, a satellite can view over one-third of Earth’s surface and can connect any pair of points within its coverage (Fig. 10-2). The history of communication satellite engineering dates back to the late 1950s when the U.S. Navy used the moon as a passive reflector to relay low-data-rate communications between Washington D.C. and Hawaii. The first major development involving artificial Earth satellites took place in October of 1957 when the Soviet Union launched Sputnik I and used it for 21 days to transmit (one-way) telemetry information to a ground receiving station. This was followed by another telemetry satellite, Explorer I, launched by the United States in January, 1958. An important development took place in December of that year when the United States launched the Score satellite and used it to broadcast President Eisenhower’s Christmas message, marking the first instance of two-way voice communication via an artificial satellite.

# Figure 10-1 Elements of a satellite communication network.

# Figure 10-2 Orbits of geostationary satellites.

(a) Geostationary satellite orbit

(b) Worldwide coverage by three satellites spaced 120° apart

These achievements were followed by a flurry of space activity, leading to the development of operational communication satellites by many countries for both commercial and governmental services. This section describes satellite communications links with emphasis on transmitter–receiver power calculations, propagation aspects, frequency allocations, and antenna design considerations.

A satellite is said to be in a geostationary orbit around the Earth when it is in a circular orbit in a plane identical with Earth’s equatorial plane at an altitude where the orbital period is identical with Earth’s rotational period, thereby appearing stationary relative to Earth’s surface. A satellite of mass M s in circular orbit around Earth (Fig. 10-3) is subject to two forces: the attractive gravitational force F g and the repelling centrifugal force F c. The magnitudes of these two forces are given by

F g=G M s M e R 0 2, (10.1)
F c=M s u s 2 R 0=M s ω 2 R 0, (10.2)

where G=6.67×10−11 N·m 2/k g 2 is the universal gravitational constant, M e=5.98×10 24 kg is Earth’s mass, R 0 is the distance between the satellite and the center of Earth, and u s is the satellite velocity. For a rotating object, u s=ω R 0, where ω is its angular velocity. In order for the satellite to remain in orbit, the two opposing forces acting on it have to be equal in magnitude, or

G M s M e R 0 2=M s ω 2 R 0, (10.3)

which yields a solution for R 0 given by

R 0=G M e ω 2 1/3. (10.4)

# Figure 10-3 Satellite of mass m s in orbit around Earth. For the orbit to be geostationary, the distance R 0 between the satellite and Earth’s center should be 42,164 km. At the equator, this corresponds to an altitude of 35,786 km above Earth’s surface.

Figure 10 3 Full Alternative Text

To remain stationary with respect to Earth’s surface, the satellite’s angular velocity has to be the same as that of Earth’s own angular velocity around its own axis. Thus,

ω=2 π T, (10.5)

where T is the period of one sidereal day in seconds. A sidereal day, which takes into account Earth’s rotation around the sun, is equal to 23 hours, 56 minutes, and 4.1 seconds. Using Eq. (10.5) in Eq. (10.4) gives

and upon using the numerical values for T, M e, and G, we obtain the result R 0= 42,164 km. Subtracting 6,378 km for Earth’s mean radius at the equator gives an altitude of h=35,786 km above Earth’s surface.

From a geostationary orbit, Earth subtends an angle of 17.4°, covering an arc of about 18,000 km along the equator, which corresponds to a longitude angle of about 160°. With three equally spaced satellites in geostationary orbit over the Earth’s equator, it is possible to achieve complete global coverage of the entire equatorial plane with significant overlap between the beams of the three satellites. Concerning coverage toward the poles, a global beam can reach Earth stations up to 81° of latitude on either side of the equator.

Not all satellite communication systems use spacecraft that are in geostationary orbits. Indeed, because of transmitter power limitations or other considerations, it is sometimes necessary to operate from much lower altitudes. In this case, the satellite is placed in a highly elliptical orbit (to satisfy Kepler’s law) so that for part of the orbit (near its perigee) it is at a range of only a few hundred kilometers from Earth’s surface. Whereas only three geostationary satellites are needed to provide near-global coverage of Earth’s surface, a much larger number is needed when the satellites operate from highly elliptical orbits. A good example of the latter is the Global Positioning System (GPS) described in Technology Brief 5.