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a planet of mass m is revolves aroud the sun in circular orbit with velocity v .what is the time period of revolution of the planet?

a planet of mass m is revolves aroud the sun in circular orbit with velocity v .what is the time period of revolution of the planet?

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1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
9 years ago
Dear student,
The gravitational force acting on the planet would be given by:
F_{G}=\frac{GMm}{r^{2}}
The centripetal force acting on the planet would be given by:
F_{C}=\frac{Mv^{2}}{r}
Now, the Gravitational force and the centripetal force would be equal to each other:
\frac{GMm}{r^{2}}=\frac{mv^{2}}{r}\Rightarrow v=\sqrt{\frac{GM}{r}}\Rightarrow \frac{2\pi r}{T}=\sqrt{\frac{GM}{r}}\Rightarrow T^{2}=\frac{4\pi^{2}r^{3}}{GM}
Hence the time period of revolution would be given by:
T=\sqrt{\frac{4\pi^{2}r^{3}}{GM}}
Regards
Sumit

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