A satellite is orbiting the Earth of mass M in equatorial plane in a circular orbit having radius 2R and same sense of rotation as that of the Earth. Find duration of time for which a man standing on

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A satellite is orbiting the Earth of mass M in equatorial plane in a circular orbit having radius 2R and same sense of rotation as that of the Earth. Find duration of time for which a man standing on the equator will be able to see the satellite continuously. Assume that the man can see the satellite when it is above horizon. Take Earth's angular velocity = ω .

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Ans. GM ​ ( 2 2 ​ + 3 3 ​ ) 2 π R 3/2 ( 6 6 ​ ) ​ mb ​ Let ω 0 ​ be the angular velocity of the satellite, then ω 0 ​ = 8 R 3 GM ​ ​ relative angular velocity of satellite, ω r ​ = ω 0 ​ − ω e ​ range of angle for which statellite can be seen by the man, ​ α = 20 = 2 [ cos − 1 2 R R ​ ] = 3 2 π ​ ​ h ere f ore time, t = 3 ω r ​ 2 π ​ = 3 [ 8 R 3 GM ​ − ω e ​ ​ ] 2 π ​

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