Question

A geostationary satellite orbits around the earth in a circular orbit of radius $36000km$. Then, the time period of a spy satellite orbiting a few $100km$ above the earth's surface $R_{earth}=6400km$ will approximately be

• A. $\frac{1}{2}h$
• B. $1h$
• C. $2h$
• D. $4h$

Answer 1

Answer: (C)

$2h$

$T^2\propto R^3$
$T^2=K{R}^3\Rightarrow (24{)}^2=K(36000{)}^3$
$K=\frac{1}{9\times {10}^4\sqrt{10}}$
$T^{\prime }=\frac{1}{9\times {10}^4\sqrt{10}}(6400{)}^{3/2}=2h$