Question

An earth satellite $X$ is revolving around earth in an orbit whose radius is one-fourth of the radius of orbit of a communication satellite. Time period of revolution of $X$ is

• A. 3 hrs
• B. 6 hrs
• C. 4 days
• D. 72 days

Answer 1

Answer: (A)

Time period of a communication satellite $=24$ hours.
Using kepler's third law,
$T^2\propto r^3$
$\Rightarrow \frac{T_c}{T_x}={\left(\frac{r_c}{r_x}\right)}^{3/2}$
$\Rightarrow \frac{24}{T_x}=(4{)}^{3/2}$
$\Rightarrow T_x=\frac{24}{8}=3hrs$