question_answer

A stationary satellite orbits the earth in the plane of the equator in a period of 24 hours. What is the orbital radius for this stationary satellite? Use the fact that a satellite close to the earth has an orbital radius of 1.025 R, where R is the earth's mean radius and in a time period of 88 minutes.

A)  8.6 R                                    

B)  6.6 R

C)  4.6 R                                    

D)  10.6 R

Correct Answer: B

Solution :

 

Closest satellite	Geostationary satellite
\[{{R}_{1}}=1.025\,R\]	\[{{R}_{2}}=?\]
\[{{T}_{1}}=88\,\,\min \]	\[{{T}_{2}}=24\,\,hrs=24\times 60\,\,mn\]

We know \[\frac{{{T}^{2}}}{{{R}^{3}}}=constent\Rightarrow \frac{{{R}_{2}}}{{{R}_{1}}}={{\left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)}^{\frac{2}{3}}}\] \[\Rightarrow {{R}_{2}}=1.025R\times {{\left( \frac{24\times 60}{88} \right)}^{\frac{2}{3}}}=6.6R\] The orbital radius is 6.6 times the earth mean radius.