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Question

EARTH SATELLITE
A synchronous satellite goes around the earth once in every 24 h. What is the radius of orbit of the synchronous satellite in terms of the earth's radius? (Given: Mass of the earth, ME=5.97×1024kg, radius of the earth, RE=6.37×106m, universal constant of gravitation, G=6.67×1011Nm2kg2)

A
2.4RE
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B
3.6RE
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C
4.8RE
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D
6.6RE
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Solution

The correct option is C 6.6RE
The time period of satellite is T=2πr3GME
Squaring both sides, we get T2=4π2r3GME

r3=T2GME4π2r=(T2GME4π2)1/3

Here, T=24h=24×60×60s

G=6.67×1011Nm2kg2

ME=5.98×1024kg

r=((24×60×60)2×6.67×1011×5.98×10244×(3.14)2)1/3

=42.1×106m

rRE=42.1×1066.37×106=6.6r=6.6RE

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