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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!