The time period $T$ of a satellite is related to the density $(\rho)$ of the plane which is orbiting close…
The time period $T$ of a satellite is related to the density $(\rho)$ of the plane which is orbiting close around the planet as.
$T \propto \rho^{1 / 2}$
$T \propto \rho$
$T \propto \rho^{-3 / 2}$
$T \propto \rho^{-1 / 2}$
Solution
According to Kepler's Law of orbits
$T^2 \propto R^3$
Density $\rho \propto \frac{M}{\left(\frac{4}{3} \pi R^3\right)} \Rightarrow \rho \propto R^{-3}$
$\Rightarrow T^2 \propto \frac{1}{\rho} \Rightarrow T \propto \rho^{\frac{-1}{2}}$