Q. The mass of a planet that has a moon whose time period and orbital radius are $T$ and $R$ respectively can be written as
A) $4\pi^{2}R^{3}G^{- 1}T^{- 2}$
B) $8\pi^{2}R^{3}G^{- 1}T^{- 2}$
C) $12\pi^{2}R^{3}G^{- 1}T^{- 2}$
D) $16\pi^{2}R^{3}G^{- 1}T^{- 2}$
Explanation
(a) $m\omega^{2}R = \frac{GMm}{R^{2}} \Rightarrow \left( \frac{2\pi}{T} \right)^{2}R = \frac{GM}{R^{2}} \Rightarrow M = \frac{4\pi^{2}R^{3}}{GT^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.