A geostationary satellite is orbiting the earth at a height 6R above the earth's surface, where R is radius of earth. The time period of another satellite at a height 2.5R from earth's surface would be:
24h
62.5h
256h
6√2h
A
62.5h
B
6√2h
C
256h
D
24h
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Solution
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The correct option is D6√2h
For geostationary satellite : r1=R+6R=7RT1=24h
For second satellite : r2=R+2.5R=3.5R
Time period of satellite : T=2π√r3GM where, r is the radius of orbit
⟹T2T1=
⎷r32r31
∴T224=√(3.5R)3(7R)3=12√2
⟹T2=242√2=6√2h
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