The planet Mars has two satellites-Phobus and Deimos. The former is at a distance of $R_{1}=9600 \ma

Question

The planet Mars has two satellites-Phobus and Deimos. The former is at a distance of $R_{1}=9600 \mathrm{~km}$ from the centre of Mars and the later at distance of $R_{2}=2400 \mathrm{~km}$. The ratio of the periods of revolution of these satellites around Mars is\

Professor PC Thomas Classes · Answer

$\mathrm{T}_{\mathrm{ph}}^{2} \propto \mathrm{R}_{1}^{2} \quad \mathrm{~T}_{\mathrm{De}} \propto \mathrm{R}_{2}^{2}$\ $\frac{\mathrm{T}_{\mathrm{ph}}^{2}}{\mathrm{~T}_{\mathrm{De}}^{2}}=\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}ight)^{3}=\left(\frac{9500}{2400}ight)^{3}=64$\ $\frac{\mathrm{T}_{\mathrm{ph}}}{\mathrm{T}_{\mathrm{De}}}=8$\