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Question

A satellite X is launched into a circular orbit of radius R around the earth while a second satellite Y is launched into an orbit of radius 4R. The ratio of the time periods of Y to X is what ?

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Solution

Given:
Radius of orbit of X is R1=R
Radius of orbit of Y isR2=4R
Time period of orbit of X be T1
Time period of orbit of Y be T2

According to Kepler's Third Law,
Time period TR32
where R : Radius of the orbit.

T2T1=R3/22R3/21
T2T1=(4RR)3/2=8
Abswer = 8

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