Question

# Which graph best represents the variation of radius r of a circular orbit of a satellite against its time period T?

A
1
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B
2
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C
3
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D
4
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Solution

## The correct option is C 3Consider a satellite of mass M revolving in a circular orbit around the earth, which is located at the center of its orbit. If a satellite is at height h above earths surface the radius of the orbit r=Re th where Re is radius of earth. The gravitational force between Me and M provides the centripetal force for circular motionGMem(Re+h)2=mV2Re+hor V2=GMeRe+hV=√GMeRe+hHence orbital velocity depends on height of the satellite above earth's surface. Time period if satellite is time taken to complete one revolution.T=2πrV=2π(Re+h)√Re+h/GMeT2=4π2(Re+h)3GMe where r=Re+hSo, option (C) −3 is time.

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