Question

An artificial satellite is going around the earth. Find the time period of the

satellite if it is close to the surface of the earth. Radius of the earth = 6.4 x 106

m.​

Answer 1

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 *

second 84.6min