√
| gR² |
| r |
| 2πr |
| T |
and, solving for r, we get
r =
| gR²T² |
| 4π² |
| ⅓ |
Since we are interested in a synchronous satellite, T in this case will be 24 hours. We can now find r (using g = 32 feet per second per second and R = 3960 miles), and then obtain the distance r - R, which will be 22,300 miles. By using our previous formulas, we also can find the velocity of a satellite moving in this orbit, which will turn out to be v = 6870 miles per hour.
One possible method of using synchronous satellites. Signals from New York (N) to Paris (P) would go via satellite S₁; signals from New York to Calcutta (C) would go via satellites S₁ and S₂.