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Question

# Imagine a geo-stationary satellite of earth which is used as an intercontinental telecast station. At what height will it have to be established

A
103 m
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B
6.4×103 m
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C
35.94×106 m
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D
Infinity
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Solution

## The correct option is C 35.94×106 mWe know that the time period of a satellite in a circular orbit of radius r is given by T2=4π2r3GM At height h from surface, ⇒T2=4π2(R+h)3GM T=24 hrs; R=6400 km;G=6.67×10−11 Nm2/kg2;M=6×1024 kg Substituting the above, we get ⇒(24×60×60)2=4π2(6.4×106+h)36.67×10−11×6×1024 ⇒h=35,897 km=35.89×106 m Hence, option (c) is correct. Why this question: It is important to remember that the distance of a geostationary satellite from the center of the earth is equal to 36000 km.

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