The mass of a planet that has a moon whose time period and orbital radius are $T$ and $R$ respectively can be written as
The mass of a planet that has a moon whose time period and orbital radius are $T$ and $R$ respectively can be written as
$4{\pi ^2}{R^3}{G^{ - 1}}{T^{ - 2}}$
$8{\pi ^2}{R^3}{G^{ - 1}}{T^{ - 2}}$
$12{\pi ^2}{R^3}{G^{ - 1}}{T^{ - 2}}$
$16{\pi ^2}{R^3}{G^{ - 1}}{T^{ - 2}}$
The mass of a planet that has a moon whose time period and orbital radius are $T$ and $R$ respectively can be written as
$m{\omega ^2}R = \frac{{GMm}}{{{R^2}}}\, \Rightarrow \,{\left( {\frac{{2\pi }}{T}} \right)^2}R = \frac{{GM}}{{{R^2}}}$$ \Rightarrow \,M = \frac{{4{\pi ^2}{R^3}}}{{G{T^2}}}$
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