# Gravitational Potential Energy question

1. Jul 21, 2007

### neo982

The problem statement, all variables and given/known data
A binary star system has two stars, each with the same mass as our sun, separated by 1.00×10^12 m. A comet is very far away and 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?

The attempt at a solution

I know that this is supposed to use the K_f +U_f = K_i + U_i formula because energy is conserved. But the hard part to this problem is the reasoning behind it. I thing that the final potential energy (U_F) should be zero there fore giving me the eq. K_f = K_i + U_i.....but then I start to wonder if the K_i should be zero also because it says the velocity is essentially at zero. When trying some of these ideas I end up with a radius (for the potential energy formula) -Gmm/r also I am not sure how to factor in the mass of both the planets and the radius between them, I initially thought that I should treat them as one big planet with total mass. Im close, but just need help with the conceptual part of this problem.

2. Jul 21, 2007

### rootX

Last edited: Jul 21, 2007
3. Jul 21, 2007

### neo982

Thanks I got it.. K_f + U_f = 0 ..therefore v_f = sqrt([2*G(2*mass of planet)/r]) where radius is 1/2 of the value the question gives..which is the diameter...which is 32,586 m/s

Thanks.