How Fast Will the Comet Travel at the Midpoint Between Two Stars?

[rebeldiiamond]

ok so here's the problem
A binary star system has two stars, each with the same mass as our sun, separated by 8.00 x 10^11 . A comet, far away from both stars is essentially at rest. Slowly but surely, gravity pulls the comet toward the stars. Suppose the comet travels along a straight line that passes through the midpoint between the two stars.
What is the comet's speed at the midpoint?

here's what i tried (but it was wrong)
pe initial(comet)= ke intial = 0
pe final (comet)= ke final= -GMsun/r
since 2 masses --> 2(GMsun/r)


ke = 1/2mvr^2---> v= sqrt(4(GMsun/r))
it says i have the wrong answer...
Is my method completely wrong? What can I do to fix it? Any help is greatly appreciated!

 

[kamerling]

why do you have 1/2mvr^2 for the kinetic energy? You do end up with the correct expression for v. What did you use for r? r is half the distance between the stars.

 

[JimChampion]

Method looks fine to me, if r is the distance from midpoint to star.