Circular Motion and Gravitation of a star

[Carpe Mori]

Homework Statement

Two equal-mass stars maintain a constant distance apart of 8.0 x10^10 m and rotate about a point midway between them at a rate of one revolution every 12.6 yr
(a) why don't the two stars crash into one another due to the gravitational force between them
(b) what must be the mass of the stars

Homework Equations

F = G*m1*m2/r^2
F(r) = ma(r)
a(r) = v^2/r
v = 2*pi*r/T

The Attempt at a Solution

part b i said m1 = m2 = m
F = ma(r)
F(12) = m*(2*pi*r/T)^2 / r
F(12) = G*m^2 / r^2

substitution and solving for m gave me

m = ((2*pi*r)^2 * r )/ (G*T^2)

substituting i got 2.4 *10^26 kg

answer in book is like 9.6*10^26 kg

can someone point out my error(s) to account for this discrepancy?

 

[Carpe Mori]

anyone?

 

[Carpe Mori]

oh snaps i figured it out

if anyone cares...

my mistake was that in the equation for graviational attractive force (F = G*m1*m2/r^2) the r is actual distance between the two center of masses and my mistake was that i thought it was half of that distance (the radius)

so yeah...cheers?