## Geostationary or Geosynchronous Orbit

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 obtainSimplifying gives(1)

The satellite orbits the Earth, travelling a distance(the circumference of the orbit) in a timeThe equationgiveshence(2)

Equation (1) and (2) giveand from this we obtain

Hence

The radius of the Earth is about 637o km so the satellite isabove the Earth's surface.

The whole Earth's surface apart from the poles cam be covered using three geostationary satellites, as shown below.