The time period T of the moon of planet mars (mass $\mathrm{M}_{\mathrm{m}}$ ) is related to its orb

Question

The time period T of the moon of planet mars (mass $\mathrm{M}_{\mathrm{m}}$ ) is related to its orbital radius $\mathrm{R}(\mathrm{G}=$ Gravitational constant) as\

Professor PC Thomas Classes · Answer

Time period $$ \begin{aligned} &=\frac{2 \pi \mathrm{r}}{\mathrm{v}_{\mathrm{o}}} \ & \mathrm{~T}=\frac{2 \pi \mathrm{R}}{\sqrt{\mathrm{GM}_{\mathrm{m}}}}\left(	herefore \mathrm{v}_{\mathrm{o}}=\sqrt{\frac{\mathrm{GM}}{\mathrm{R}}}ight) \ & \mathrm{T}^{2}=\frac{4 \pi^{2} \mathrm{R}^{3}}{\mathrm{GM}_{\mathrm{m}}} \end{aligned} $$