Q. The time period of geostationary satellite at a height 36000 km is 24 h. A spy satellite orbits earth at a height 6400km. What will be the time period of sky satellite? (Radius of earth = 6400 km )
A) 5 h
B) 4 h
C) 3 h
D) 12 h
Explanation
(b) From Kepler’s third law of planetary motion
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T^{2} \propto R^{3}\ $
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{T_{2}^{2}}{T_{1}^{2}} = \frac{R_{2}^{3}}{R_{1}^{3}}$
$or\ \ \ \ \ \ \ \ \ \frac{T_{2}^{2}}{(24)^{2}} = \left( \frac{6400 + 6400}{36000 + 6400} \right)^{3}$
$or\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T_{2}^{2} = {(24)}^{2} \times \left( \frac{16}{53} \right)^{3}$
$\Longrightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ T_{2} = 4\ h$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.