Question

On July 15, 2004, NASA launched the Aura spacecraft to study the earth's climate and atmosphere. This satellite was injected into an orbit 705 km above the earth's surface, and we shall assume a circular orbit.
(a) How many hours does it take this satellite to make one orbit?


(b) How fast (in km/s) is the Aura spacecraft moving?

Answer 1

On the earth surface g = GM/R^2
 And at the hieight h
 g" = GM/ [R+h] ^2
 g" = R^2/ [ R+h]^2 * g
 g" = {R/ [ R+h] }^2 * g
 g" = {6378/ 7083}^2 * 9.81 = 7.95 m/s^2
 --------------------------------------
T^2 = 4π^2 (R+h) /g"
T^2 = 4π^2 *7083 /7.95 
T = 187.54s = 0.052 hour.
 ========================
 Part B
 v = 2*π *[R+h] / T
 v = 2*π *[7.083] / 187.54s
 v = 0.24 km /s