Basic HTML Version
144
TELE-satellite International — The World‘s Largest Digital TV Trade Magazine
— 06-07-08/2012
— www.TELE-satellite.com
The satellites
Satellites have to remain in their posi-
tion relative to the surface of the earth
so that transmissions from them can be
used commercially – they have to be
positioned geo-stationary so that a fixed
antenna can receive signals. Therefore,
satellites have to meet the following con-
ditions:
1. The have to rotate above the equa-
tor.
2. The have to move in the same direc-
tion as the earth.
3. The have to be positioned at a dis-
tance from the earth that allows them to
take 24 hours for one full rotation (pre-
cisely 23
h
56
m
04
s
).
In order to fulfil these conditions
Kepler’s third law of planetary motion
has to be applied:
The
of the
of a
planet is directly
to the
of the
of its orbit.
According the Kepler’s first law of plan-
etary motion the orbit is an ellipse. In
our case the ellipse comes very close to
a circle. The great elliptic axis a is thus
replaced by the radius R, and the sat-
ellite’s mass m can be neglected when
compared to the earth’s mass M. Apply-
ing Kepler’s third law we thus arrive at
the following constants:
U = 23
h
56
m
04
s
= 86 164 sec
U = rotation time
G = 6,668.10
-11
N.m
2
.kg
-2
G = gravitation constant
M = 5,976.10
24
kg
M = earth’s mass
Fig.2
The speed of the satellite is this:
(The satellites are positioned at 42,160
– 6,378 km = approx. 36,000 km above
the equator)
Polar mount antennas
If we were able to install a motor-
ised antenna on the north pole or at the
centre of the earth it would be possible
to receive signals from all geo-stationary
satellites – at least in theory. However,
this would not be realistic even on the
north pole as all satellites are below the
horizon and therefore cannot be received.
From this it follows that the reception
range of an antenna that is directed
towards the south and aligned towards
the east or west is largest at the equa-
tor and gradually decreases the more we
move north. At a northern and southern
latitude of 80 degrees the range is zero.
Calculations we will perform at a later
stage will provide a scientific framework
for this statement. As antennas realisti-
cally can only be set up on the earth’s
surface the proportions and relations of
figure 3 apply.
The antenna is installed at a certain
position P on the earth, with a northern
latitude φ. If we now align the antenna to
face precisely south, for example point-
ing to satellite S1 and rotate it around
the axis PP’ that has a pole-to-pole
alignment until it points to satellite S2
it will not be able to exactly meet it as
the antenna’s radius is smaller than the
distance PS2. It meets the equator plane
at point S2’, i.e. somewhat lower. This in
turn suggests that the elevation (see fig.
5) of the antenna has to be increased.
The bigger the deviation from a pre-
cise southern direction, the bigger the
margin of error. A check calculation was
performed to find out of this margin of
error that needs to be taken into account
in practice: At the geographic latitude of
47 degrees and a ω value of 60 degrees
the error is -0.41 degrees, which is neg-
ligible.
Fig. 3
M = centre of the earth
R = radius of the earth (6,371 km)
P = location of the antenna
φ = northern latitude of P
S1 = southern direction
S1 and S2 are satellites (fictitious)
MS1 = MS2 = radius of the satellites’
orbit ( 42,160 km)
PS1 = PS2` = radius of the motorised
dish
If a spectator stands at location P
and ‘looks’ in the direction of the satel-
lites, what he sees appears to be similar
to Fig. 4a. A satellite that is positioned
in the exact south appears higher and
those satellites that are located to the
east or west appear closer to the horizon
until they disappear below the horizon.
Because of the earth’s gravity spectators
see the horizon as a horizontal line (see
also Fig. 8).
Fig. 4
A very different situation emerges
when we deal with a polar mount
antenna, as it rotates around the polar
axis and ‘sees’ satellites next to each
other in a straight line (which is why
polar mount antennas are used in the fist
place). However, when the dish rotates
the distance to the horizon changes, as
Fig. 4b illustrates. Naturally, the antenna
cannot perform an arc-like movement,
because it only rotates around a single
axis, which is aligned in parallel to the
pole-to-pole line.
What we have learned so far clearly
highlights the advantages of a motorised
polar mount antenna when it comes to
receiving a multitude of satellites and
their respective channels. Such a set-up
is not even very complex, with the single
biggest issue probably being a suitable
location to install the antenna. What you
also need is a receiver which is capa-
ble of controlling a motor, as an extra
device for motor control does not make
sense. If you are computer-literate and
both your receiver and your PC feature
an RS-232 interface even the tiresome
task of organising thousands of channels
becomes manageable quite easily and if