Question

​The time period of a satellite revolving in a circular orbit of radius r is T. Time period of another satellite revolving in the circular orbit of radius 4r will be

Answer 1

Dear Student ,
As we know that , from the Kepler's third law of planetary motion ,
$$\begin{gathered} T^2\propto R^3 \\ Now,\frac{{T_1}^2}{{T_2}^2}=\frac{r^3}{64r^3} \\ \Rightarrow \frac{T^2}{{T_2}^2}=\frac{1}{64} \\ \Rightarrow {T_2}^2=64T^2 \\ \Rightarrow T_2=8T \end{gathered}$$
Regards