- #1

autodidude

- 333

- 0

## Homework Statement

From K&K's 'Intro to Mechanics'

Find the shortest possible period of revolution of two identical gravitating solid spheres which are in circular orbit in free space about a point midway between them.

## Homework Equations

## The Attempt at a Solution

So I figured the gravitational force exerted on each sphere by the other would be

[tex]F=\frac{2mg}{r^2}[/tex]

according to Newton's law of gravitation (m being each sphere's mass). This force would be providing the centripetal acceleration that's keeping them going in a circle so the angular velocity can't exceed a certain value and this is related to the period of revolution.

[tex]F_c=\frac{2mG]{r^2}=m\frac{v^2}{r}[/tex]

∴[tex](\frac{2G}{r})^{1/2}=v[/tex]

So plugging that into [tex]T=\frac{\omega}{2\pi}[/tex] gives me [tex]T=(\frac{G}{2\pi^2r^3})^{1/2}[/tex]

Is this correct? If not, am I at least on the right track?

Thanks in advance