Question

Suppose you are at the earth's equator and observe a satellite passing directly overhead and moving from west to east in the sky. exactly 11.0 hours later, you again observe this satellite to be directly overhead. assume a circular orbit. how far above the earth's surface is the satellite's orbit?

Answer 1

If we are assuming a circular orbit and if it moves from west to east directly overhead you are on the equator. A satellite can move overhead west to east only above the equator. Now in 11 hours the Earth has rotated 11/24 of a revolution so the satellite has made 1 11/24 rev (which equals 35/24 rev) in that 11 hours. For a period of
 T=11(24/35)*3600 = 27154.29 sec.
 r^3 = T^2(GM)/4(pi)^2
 Earths mass (M) = 5.98 e24 kg
 G (a constant) = 6.673 e-11
 Earths surface radius (R) = 6.371 e6 meters
 r = satellite orbital radius in meters
 replacing and clearing r:
 r =  19533487.08 m (this is the distance from the center of the Earth) 
 h = r - R = 19533487.08 -  6.371 e6 =  13162487.08 m above the Earth's Surface