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What is the radius of the circular orbit of a stationary satellite which remains motionless with respect to earth’s surface ?

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a
gR2T24π213
b
gR4π2T212
c
gRT2π13
d
gR2πT12

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detailed solution

Correct option is A

A satellite will appear motionless when its period of revolution is the same as that of earth that is T=24  hours. Let r be the radius of orbit from the centre of earth. Then dynamics of circular motionmω2r=GMmr2  ;  2πT2r3=GMr=GMT24π213=gR2T24π213∵GM=gR2

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