Question

A satellite moves in a circular orbit around the earth. The radius of this orbit is one half that of the moon's orbit. Find the time in which the satellite completes one revolution.

• A. $\frac{1}{2}$ lunar month
• B. $\frac{2}{3}$ lunar month
• C. $2^{-3/2}$ lunar month
• D. $2^{3/2}$ lunar month

Answer 1

Answer: (C)

$2^{-3/2}$ lunar month

Time period of revolution of moon around the earth
= 1 lunar month.
$\frac{T_s}{T_m}={\left(\frac{r_s}{r_m}\right)}^{3/2}={\left(\frac{1}{2}\right)}^{3/2}⟹T_s=2^{-3/2}$ lunar month.