The closer a satellite is to the Earth, the faster it moves. For a certain radius of orbit the satellite will move at such a speed that it is always over the same spot over the Earth's surface – actually above the equator. Such an orbit is called a geostationary or geosynchronous orbit.
We can find the radius of the orbit using, for a circular orbit, centripetal force = gravitational force.
There are equations for each of these forces.
The equation for the centripetal force is
The equation for the gravitational force is
=mass of satellite.
=Mass of Earth.
=radius of orbit
We can equate these to obtain
Simplifying gives
(1)
The satellite orbits the Earth, travelling a distance
(the circumference of the orbit) in a time
The equation
gives
hence
(2)
Equation (1) and (2) give
and from this we obtain
Hence
The radius of the Earth is about 637o km so the satellite is
above the Earth's surface.
The whole Earth's surface apart from the poles cam be covered using three geostationary satellites, as shown below.
