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Question

A geostationary satellite orbits around the earth in a circular orbit of radius 36000km. Then, the time period of a spy satellite orbiting a few hundred kilometers above the earth's surface will approximately be ( Given: REarth=6400 km )

A
12h
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B
1h
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C
2h
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D
4h
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Solution

The correct option is A 2h
For a satellite of mass m moving with a velocity v in a circular orbit of radius r around the earth of mass M, we have,
mv2r=GMmr2 or v=GMr
But v=2πrT.
Thus 2πrT=GMr or Tr32
T2T1=(r2r1)32 ...................(1)
Given r2=6400 km and r1=36000 km. For a geostationary satellite T1=24 h. Using these values in (1), we have get,
T2=24×(64360)32=1.8 hours.
Hence the closest choice is (c).

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