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Question

# Imagine a geostationary satellite of earth which is used as an inter continental telecast station. At what height will it have to be established ?(Take G=6.67×10−11 Nm2kg−2 and mass of earth, M=6×1024 kg).

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

## The correct option is B 35.94×106 m Time period for a geostationary satellite is 24 hour, so T=24 hour. We know that time period of a satellite in a circular orbit is given by, T2=4π2(R+h)3GMWhere, M is mass of the earth and R is radius of the earth. h is the height of the satellite above the earth's surface. Given, R=6400 km G=6.67×10−11 Nm2kg−2 M=6×1024 kg. Substituting the values, we get (24×60×60)2=4π2(64×105+h)36.67×10−11×6×1024 ⇒h=35786×103 m ⇒h=35786 km Hence, the above value is approximately equals to that of option (c). 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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