Question

# The time period of an earth satellite in a circular orbit of radius R is 2 days and its orbital velocity is vo. If time period of another satellite in a circular orbit is 16 days then

A
its radius of orbit is 4R and orbital velocity is vo.
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B
its radius of orbit is 4R and orbital velocity is vo2.
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C
its radius of orbit is 2R and orbital velocity is vo.
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D
its radius of orbit is 2R and orbital velocity is vo2.
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Solution

## The correct option is B its radius of orbit is 4R and orbital velocity is vo2.According to the Kepler's third law T2∝R3∴T1T2=(R1R23/2) or R2=(R1)(T2T1)3/2=(R1)(162)2/3=4R1=4R (given R1=R) ....(i)Orbital velocity, vo=√GMR∴vo2vo1=√R1R2=√R14R1=12 ....(using (i))or vo2=12vo1=12vo

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