Question

The period of satellite in circular orbit of radius R is T. What is the period of another satellite in a circular orbit of radius 4R

Answer 1

Dear Student ,
Here in this case from the Kepler's third law of planetary motion we get ,
$$\begin{gathered} \frac{T{\text{'}}^2}{T^2}=\frac{64R^3}{R^3}=\frac{1}{64} \\ \Rightarrow T{\text{'}}^2=64T^2 \\ \Rightarrow T\text{'}=8T \end{gathered}$$

Regards