Download Satellite orbits

Satellite orbits
Satellites are kept in orbit around the Earth by the centripetal force due to the gravitational
attraction between the Earth and the satellite. The following explanation shows how this is
possible without the satellite having an engine.
Imagine that you go up a high mountain and fire a shell horizontally. If there was no pull of
gravity the shell would travel off in a straight line at a steady speed following path A.
In actual fact the Earth pulls it down and it follows path B.
A
C
B
Remember that the gun exerts no force on the shell once it has left the gun barrel.
If we now fire the shell faster it will follow path C and come down further away. Faster still
and it will land even further away from the gun.
However if the ground falls away beneath the path of the shell (rather like the hill below a ski
jumper) then the shell will hit the ground a lot further away (path D). (Long jump pits have to
have the sand exactly the same level as the take off board if they are to be legal and be able
to be used for record attempts)
A
D
Now imagine what will happen if we look at the movement from a long distance away so that
we can see the whole Earth. If a shell is fired fast enough it will not fall to the ground at all but
come back to the mountain top. It will have ORBITED the Earth. The next diagram shows
this.
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Of course, actual satellites are much higher up, there is
no air resistance up there and because they are a long
way away they don’t have to go round so fast. One
example are communication satellites that have a period
of one day.
To get a shell to orbit the Earth if it was fired from a
mountain as high as Snowdon (roughly 1000 m high)
would need a launch velocity of roughly 8000 m/s or
nearly 20 000 m.p.h.
C
Remember that the centre of a satellite’s orbit is the
centre of the Earth and is not measured from its surface.
The first Earth satellites launched towards the end of the twentieth century had obits around
300 km above the Earth’s surface.
Geostationary satellites
Communication satellites used for television, radio and telephone orbit the Earth at a distance
of just over 42 000 km! These orbits are in the same plane as the equator of the Earth. They
are called GEOSTATIONARY ORBITS and satellites in these orbits stay above the same
point on the Earth.
You can work out the radius of the orbit using Kepler’s Third Law and knowing the distance
of the Moon and the time it takes to orbit the Earth.
The Moon orbits the Earth at a distance of 384 000 km from its centre in 27.3 days. We need
to work out the orbit radius form a satellite with a period of 1 day.
Using Kepler’s Third Law: Rs3/Ts2 = Rm3/Tm2 where Rs and Rm are the orbit radii of the
satellite and the Moon and Ts and Tm are their orbit times.
This gives the radius of the orbit for a communication satellite as 42 400 km or about 6½
Earth radii.
Satellites that are used to monitor the weather, crops or for military use are often put in low
orbits above the poles. As the satellites move in their orbit the Earth spins below then and so
they can see different parts of the planet during an orbit.
How long does it take a planet to orbit the Sun?
The planets all move at different speeds, being held in their orbit by the gravitational
attraction between the Sun and the planet. For a given sized planet this force is greater the
closer the planet is to the Sun.
Foe example Mercury (the closest planet to the Sun) moves rapidly round the Sun taking
only 88 days to make one orbit. It travels at about 89.2 km/s. The Earth is further away taking
1 year to make one orbit, travelling at 29 9 km/s. Pluto, at the outer reaches of the Solar
System moves at only 4.7 km/s and takes almost 250 years to travel once round the Sun.
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