Sci010 - Altitude calculation for Geosynchronous orbits

The angular velocity of a satellite orbiting the earth once every T seconds at v meters per second in a circle of radius r is

Thus the centrifugal force experienced by this satellite is

where is the mass of the satellite.

The gravitiaional force experienced by the satellite is given by

Here is the gravitational constastant, and is the mass of the earth.

For a stable circular orbit, the centrifugal force, which is directed outward radially must balance the gravitational force, which is directed inwardly. With simple algebra we can thus derive an expression relating the radius r and the period T of any satelite orbiting the Earth.

For a geosynchronous orbit we have , giving

The altitude of the satelite is r minus the radius of Earth (6370 km), which is 35,880 kilometers.





Luis Goddyn
Wed Nov 8 11:31:39 PST 1995