# How many geosynchronous satellites does it take to cover all earth surface?

Geosynchronous satellites orbit at an altitude of 35,786 km, directly above the Equator, and assume that earth is a perfect sphere. Please any hints or detail computation would be really appreciated. Thanks

-
You can simplify the problem by thinking in terms of the equatorial plane: represent the equator as the circle $x^2+y^2=R_e^2$ where $R_e$ is the equatorial radius of the Earth. Then put a satellite at $(d+R_e,0)$, where $d$ is the height above the surface. Now draw a line from this point which is tangent to the circle at the point of intersection. What is the point of intersection? –  dls Mar 7 '12 at 5:27