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  • A geostationary satellite has always to be at an altitude of (in kilometers) :  Option: 1 36000<div class='qna

A geostationary satellite has always to be at an altitude of (in kilometers) :

 

Option: 1

36000


Option: 2

24000


Option: 3

30000


Option: 4

20000


Answers (1)

best_answer

 As we know, the time period  

 

 

 For Geostationary and polar satellites is given by 

 

\begin{array}{l}{\text { } T=2 \pi \sqrt{\frac{r^{3}}{G M}}=2 \pi \sqrt{\frac{(R+h)^{3}}{g R^{2}}}} \\ \end{array}

By squaring and rearranging both sides

{\text { } \frac{g R^{2} T^{2}}{4 \pi^{2}}=(R+h)^{3}} \\ {\Rightarrow \quad h=\left(\frac{T^{2} g R^{2}}{4 \pi^{2}}\right)^{1 / 3}-R}

  So, put the value,  T = 24 h = 24\times60\times60 = 86400 s        

                               R = Radius\: o\! f \: the \: earth = 6400 km

                                  g =9.8\times10^{-3}\ km/s^2

    Substituting these values in the equation of the formula of height, we get-

                 h = (42400 - 6400) km = 36000 km

Posted by

sudhir.kumar

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