Question

A satellite is revolving around earth in a circular orbit. The radius of orbit is half of the radius of theorbit of moon. Satellite will complete one revolution in.

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

Answer 1

The correct option is A $1/2^{3/2}$lunar month

Using Kepler's 3rd law: $T^2\propto R^3$

Let $T_1$ be the time taken by moon to complete one revolution around earth which is called lunar month and $R$ be the radius of orbit.

$\frac{T_2}{T_1}=[\frac{R^{\prime }}{R}{]}^{3/2}$

For $R^{\prime }=\frac{R}{2}$ $\frac{T_2}{T_1}=[\frac{\frac{R}{2}}{R}{]}^{3/2}$

$⟹T_2=\frac{1}{2^{3/2}}{T}_1$