Geostationary Orbits

If a satellite is in a geostationary orbit, it would appear to remain in a fixed position in the sky. This happens when the satellite rotates at the same angular velocity as the Earth, i.e. once a day. It must also be on the equatorial plane, or else it would move up and down the equator. It must be circular as well, or the angular velocity can vary.

Geostationary orbits are useful for satellites that need to transmit communication signals to the other side of the world. Then it would help if the satellite is always there to send or receive the signal from the ground.

Recall that the gravitational force = the centripetal force for a circular orbit. So GMm/r2 = mv2/r, where M is the mass of the Earth, m the mass of th esatellite, v its velocity, and r its distance from the centre of the Earth.

Lets write v in terms of the circumference 2πr and period T of the orbit. So v = 2πr/T. Substituting, we get GMm/r2 = m(2πr/T)2/r. Simplifying, we find r3 = GMT2/4π2.

Since we know that T is one day, we can find r if we know the mass of the Earth. Alternatively, recall the acceleration of free fall g = GM/R2, where R is the radius of the Earth. Rearranging, GM = gR2.

Then the orbit radius is r3 = gR2T2/4π2. If you remember that R is 6400 km and g is 9.81 m/s2, you can use this to find r.


Copyright 2010 by Kai Hock. All rights reserved.
Last updated: 28 September 2010.