A binary star system has two stars, each with the same mass as our sun, separated by 1.6x10^12 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? I'm confused as to how to approach this problem. I realized quickly that the potential energy of the comet at the midpoint is 0 because at that point the radius equals 0, so I wanted to use kinetic energy and work to figure the problem out, the only problem is that I don't know the distance over which the force is exerted. Also, I know the force that the stars are exerting on the comet using F_g=G*m_1*m_2/r^2. Well I guess it's more that I know the acceleration due to gravity that the comet experiences because I can cancel out the mass of the comet on both sides, which is necessary because the problem doesn't state the mass of the comet. I could then figure the problem out using the kinematic equation v^2=v_0^2+2aΔx, but I don't know the distance from the star system that the comet starts off at. Now that I think about it, there must be a maximum radius where the star system starts acting on the comet, and I can use that as my distance... actually if I can determine that I think I will just say that the initial potential energy=final kinetic energy and use that maximum radius as my "height." Specific Questions: Can I treat the star system as one source of gravitational force where the radius is the comet's distance from the center of mass of the two stars? Is there a specific method for solving this kind of problem that I'm not aware of? Is my last paragraph "Now that I think about it..." on the right track?