Question

A satellite moves in a circle around the earth. The radius of this circle is equal to one-half of the radius of the moon's orbit. The satellite completes one revolution is

• 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)

The period of revolution of a satellite at a height $h$ from the surface of earth is given by
$T=2\pi \sqrt{\frac{(R_e+h{)}^3}{g{R}_e^2}}$
Given $T_m=1$ lunar month,
$=T_{\text{sat}}=2\pi \sqrt{\frac{{\left(R+\frac{h}{2}\right)}^2}{g{R}^2}}$
$\Rightarrow T_{\text{sat}}\approx \frac{1}{2^{3/2}}$
$T_{\text{moon}}=2^{-3/2}$ lunar month