Question:
An artificial satellite is going round earth, close to the surface. What is the time taken by it to complete one round? (Radius of earth=6400km)
Answer:
(1) We know that Centripetal force required to keep the satellite in orbit = Gravitational pull acting on the satellite
Hence, mV2 / R = GMm / R2
which implies V2 = GM / R -----------(1)
(2) If g is the acceleration due to gravity on the surface of the earth, then g = GM / R2
So GM= gR2 ---------------- (2)
(3) Substitute (2) in (1), we get V2 = g R2 / R = gR
Given that R = 6.4 * 106 m
Time period = T = Distance travelled in one revolution / orbital velocity = 2 / V = 2 / (g R)1/2 = 2 (R / g)1/2
= 2 * 3.14 * [ (6.4 * 106 ) / 9.8 ]1/2 = 5.08 * 103 seconds = 84.6 min
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