The two-body problem with pushing force, what ll be their speed in t=infinity?

malrf

Hi!

I want to solve the following: I have 2 particles p1, p2, with given m1,m2,v1 , p2 stands still in the origin(x,y,z=0).
Between them there is only 1 force F=1/(d^2), the force is pushing the particles away from each other.
I start p1 from infinite distance with given speed, and i know it's equation of motion without the pushing force, and i want to know what ll be it's speed after infinite time. (p1 is closing to p2 and p1's line of motion without the force is not crossing p2)

After searching google i found that there might be a closed form expression solving the 2-body problem, but those expression only true if the course of the particles is an ellipse, so i don't know how to solve my problem.

Thanks for helping!