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Question

A geostationary satellite is orbiting the earth at a height of 6R above the surface of the earth; R being the radius of the earth. What will be the time period of another satellite at a height 2.5 R from the surface of the earth?


A

62 hours

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B

62.5 hours

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C

63 hours

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D

12 hours

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Solution

The correct option is A

62 hours


The time period of satellite orbiting at a distance r from the centre of the earth is given by T2=4π2r3GM where M is the mass of the earth. Therefore, the ratio of the time periods of two satellites at distance r1 and r2 respectively from the centre of the earth is
T1T2=(r1r2)32T2=T1(r2r1)32
For the geostationary satellite, T1=1 day = 24 hours and r1=6R+R=7R.
For the other satellite, r2=2.5R+R=3.5R
Therefore, T2=24×(3.5R7R)32=24×(12)32=62 hours
Hence, the correct choice is (a).


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