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Carpe Mori
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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?