Kepler's Third Law and centripetal acceleration

[Shackleford]

I'm not getting very far with these problems. Don't know what my problem is.

Given a circular orbit, the centripetal acceleration is given by the gravitational force between the two stars. I chose the center to be halfway between the stars d/2.

http://i111.photobucket.com/albums/n149/camarolt4z28/2010-09-13225621.jpg?t=1284437088

http://i111.photobucket.com/albums/n149/camarolt4z28/2010-09-13225642.jpg?t=1284437089

 

[vela]

Try writing v in terms of d and τ.

 

[Shackleford]

Try writing v in terms of d and τ.

pi*d = vt

(1/t)*pi*d = v

v = pi*d*τ

That doesn't get me anywhere.