Ratio of time period of satellites orbiting around earth at a distance of about 9r and 4r from earth surface is : ( where r is the radius of earth)

We know, $T^{2}=\frac{4 \pi^{2}}{9 M} R^{3}$

$\Rightarrow T^{2} \alpha R^{3}$

Lit $T_{s}^{\prime}$ be the time period of a satellite orbiting around the earth at a distance

$g_{r}=R^{\prime}$

$T_{s}^{\prime \prime}$ be the time period of satellite orbiting from earth surface, $4 n=R^{\prime \prime}$

$\begin{array}{l} \therefore\left(\frac{T_{s}{ }^{\prime}}{T_{s^{\prime \prime}}}\right)^{2}=\left(\frac{R^{\prime}}{R^{\prime \prime}}\right)^{3} \\ \Rightarrow \frac{T_{s}^{\prime}}{T_{s^{\prime \prime}}}=\left(\frac{9 r}{4 r}\right)^{3 / 2} \\ \Rightarrow \frac{T_{s^{\prime}}}{T_{s^{\prime \prime}}}=\left(\frac{27}{8}\right) \end{array}$

The ratio of time period is (27:8)