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Mechanics

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?

abhishek kumar singh

11 Years agoGrade

1 Answer

Sumit Majumdar

11 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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