# Period of a planet orbiting the Sun

**1. The problem statement, all variables and given/known data**

A planet P orbiting the Sun S is acted upon by a force F= -(mu*

**r**)/r

^{3}(itex won’t work here for some reason :S ) per unit mass where [itex]\mu[/itex] is a positive constant and

**r**is the vector [itex]\stackrel{\rightarrow}{SP}[/itex]

If the orbit of the planet is a circle of radius a, show that the period of the planet is [itex] \frac{2\pi a^{3/2}}{\mu ^{1/2}} [/itex]

The Earth and Mercury are orbiting the Sun.

The Earth is at a mean distance of approximately [itex] 1.5 * 10^{8} [/itex] km from the Sun and Mercury at approximately [itex] 5.8 * 10^{7} [/itex] km.

Given that the Earth’s period is about 365.25 days, find the period of Mercury.

**2. Relevant equations**

**3. The attempt at a solution**

Erm…. I really am not sure what to do.

I thought It would have something to do with centripetal force, and using [itex] ω=\frac{2\pi}{t} [/itex] but I can’t see how to use that to get the answer :S

Thanks

http://ift.tt/1dmUjUn

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