Commercial GEOs provide fixed satellite service (FSS) in the C and Ku bands of the radio
spectrum. Some GEOs use the ku band to provide certain mobile service (mss).
A constellation is a group of similar satellites moving together in partnership to provide a
network of useful services
.
For geometric consideration, a satellite can also be explained as a body that moves around
another body (of greater mass) under the influence of gravitational force between them. The
force F required to keep a satellite in a circular orbit can be expressed as:
F = M
s
W
2
r (N)
Where W = angular velocity of the satellite in red/sec
R = radius of the orbit, m
R = Re + h
o
13

r is the distance of a synchronous satellite from the centre of the earth. ho is the orbit altitude,
that is the height above the sub satellite point on the earth terminal.
The gravitational force Fg acting on the satellite of mass Ms at distance r from the centre of the
earth is
Fg = M
s
g
(N)
g = acceleration due to gravity at the surface of the earth (9.8 m/s
2
)
Re = radius of the earth
Re at the equator = 6378.39km
Re at the pole = 6356.91km
Consequently, for a satellite in a stable circular orbit around the earth,
F = Fg
:. M
s
g
= M
s
W
2
r
r
3
=
The period of the orbit, ts, that is the time taken for one complete revolution (360
o
or 2
radian)
can be expressed as
t
s
=
=
seconds.
If we assume a spherical homogenous earth, a satellite will have an orbital velocity represented
by
14

V = Re
(m/s)
SECTION SIX
COVERAGE AREA
The amount of coverage is an important feature in the design of earth observation satellites.
Coverage depends on altitude and look angles of the equipment, among several factors. Consider
the angle of view from the satellite to the earth terminal as α; then the apex angle is 2
.
The view angle has a mathematical physical function given by
=
15

Using empirical values (Re = 6,378km), r = 42162km) the apex angle 2α equals 17.33
, the polar
angle beamwidth. It follows that an “earth coverage” satellite antenna must have a minimum
beamwidth
BW
of 17- 33
. In practice, an antenna of 18
or 19
beam width used to allow for directional
misalignment.
The beam width of the satellite antenna determines the area of the earth serviced or covered. The
beam width required directly determines the antenna gain and, for a given operating frequency,
the physical size of the antenna aperture.
The coverage area can be expressed as
A
cor
= 2πRe
2
(1-
)
Where
is the central angle, the apex angle required at the satellite to produce a given coverage
A
cor
must satisfy
16
Satellite
Orbit
Coverage area
An illustration of coverage area and apex angle
2
Rs
Equator

2πRe
2
(1-
) =
However, for small angles, that is,
, we can approximate the global beam width to
2
where d
cov
is the coverage area diameter
SECTION SEVEN
GEOMETRIC DISTANCES
By considering the geometry of the geosatellites orbit in its orbit plane, we will be able to
calculate
1.
The distance between the satellite and the earth station, called the slant range; Rs
2.
The azimuth and elevation angles, collectively called the look angles. The look angles are
the coordinates to which an earth station antenna must be pointed to communicate with a
17

satellite. The azimuth angle a

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- Winter '19
- Ezemma
- communications satellite, Geosynchronous orbit