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Question

# A geostationary satellite is orbiting the earth at a height of 7R above the surface of the earth, where R is the radius of the earth. What will be the time period of another satellite at a height 5R from the surface of the earth?

A
9 hours
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B
6 hours
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C
93 hours
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D
63 hours
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Solution

## The correct option is C 9√3 hoursTime period of geostationary satellite, T1=24h Radius of orbit of the satellite, R1=7R+R=8R Radius of orbit of new satellite, R2=5R+R=6R Let the time period of the new satellite be T2 According to Kepler’s third law, T2∝r3⇒(T2T1)2=(R2R1)2⇒(T2T1)2=(6R8R)3⇒(T224)2=(6R8R)3⇒(T2)2=(68)3×(24)2⇒T2=9√3h Hence, the correct answer is option (c).

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