- #1

Vitani11

- 275

- 3

## Homework Statement

Three identical stars, each with mass m, form the verticies of an equilateral triangle with side length d and rotate in a circular orbit due to their mutual gravitation. What is the period τ of their rotation?

I set up the FBD for each star and am now trying to figure out what to do from there. I know how to get period into the equation from circular motion, but is that all there is to it? The FBD gives different equations for each mass so when I solve I get different periods for each star. What should I be doing here?

Force equations

Star at bottom left point:

x: Fcosθ+F = ma

_{x}

y: Fsinθ = ma

_{y}

Star at bottom right:

x: -(Fcosθ+F) = ma

_{x}

y: Fsinθ = ma

_{y}

Star at top:

y: -2F = ma

_{y}(or should this be -2Fcos(θ/2)?)

x: forces cancel to 0

If you draw an equilateral triangle you will see what I'm talking about and then how I oriented my axes around the stars.