How a Synchronous Satellite Would Work
For our purposes, we will not be concerned with all the problems of launching a synchronous satellite into its proper orbit. But you may be curious why we know that this orbit must be 22,300 miles high. It can be calculated by using two basic formulas from elementary physics.
From Newton’s Law of Gravitation we know that the velocity, v, of a satellite moving in a circular orbit[5] will be
v = √
| gR² |
| r |
where R is the radius of the earth, r is the distance from the center of the earth to the satellite, and g is the acceleration due to gravity (see [diagram above]).
We also know that this velocity must be
v =
| 2πr |
| T |
since the distance the satellite travels to complete an orbit is 2πr, and T is the time of one complete revolution. Thus we have the equality