C 12A 2009 - Deriving Kepler's Third Law

[eku_girl83]

Two gravitaionally bound stars with equal masses m, separated by a distance d, revolve about their cneter of mass in circular orbites. Show that the period is proportional to d^3/2 and find the proportionality constant.

I know that in this case, F = mv^2/r and that F=Gm^2/d^2.

But where do I go from here??

Thanks for any help!

 

[Andrew Mason]

Two gravitaionally bound stars with equal masses m, separated by a distance d, revolve about their cneter of mass in circular orbites. Show that the period is proportional to d^3/2 and find the proportionality constant.
I know that in this case, F = mv^2/r and that F=Gm^2/d^2.
But where do I go from here??
Thanks for any help!

Equate the two forces (since centripetal force is supplied by gravity) and see what you get. (Note: r = d = distance between centres of mass).

AM