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

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The discussion focuses on calculating the speed of a comet at the midpoint between two stars in a binary system, each with the mass of the sun and separated by 8.00 x 10^11 meters. The initial approach involved equating potential energy and kinetic energy, but the user received feedback indicating an error in their calculations. Clarification was provided that the correct value for 'r' should be half the distance between the stars, and the method used to derive the speed formula was deemed appropriate. The conversation emphasizes the importance of accurately determining the distance when applying gravitational equations. Overall, the thread seeks to resolve a misunderstanding in the application of physics principles to the problem.
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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!:confused:
 
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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.
 
Method looks fine to me, if r is the distance from midpoint to star.
 
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