How to approximate trajectories and movement of two oppositely charged particles? Imagine a single, stationary charged atomic ion, say a Lithium anion or cation (Li+ or Li-).  Now imagine another a single free, oppositely charged particle--perhaps an electron or Hydrogen ion (H+)--passing by the first stationary atomic ion at a "classical" non-relativistic speed.  For simplicity, imagine they are both in a vacuum and both in zero gravity and free from outside electrical noise or other forces. 
What is a good equation to use to calculate the trajectories and/or movement of both of these particles, knowing the velocities and masses of each?
UPDATE:
While Ana V's answer below is very good, I'm really looking for an actual approximate answer of how close the two particles need to be to have measurable movement based on the forces. I'm not looking for a high level of accuracy.  Just trying to get a sense of the scale of impact on the trajectory of the moving particle and the movement (if any) of the stationary particle as you vary the closest distance between them.  Would they need to be very close to each other (say, less than a micron)?  Or would the stationary ion still exert enough force at macro-scale distances (say, a meter?) to measurably change the moving particle's trajectory and/or push away the stationary ion?  How close together do they need to be for the electrostatic forces to move one or both of them measurably?  Thank you!
 A: This may help your, it comes from Rutherford scattering by  which they determined that the atom has a hard core. It is positive alphas against positive nucleus, but the math is the same.


Determining the closest approach to the nucleus amounts to calculating the minimum distance for the hyperbolic orbit which is produced by the coulomb repulsive force. The expression for the closest approach as a function of the impact parameter b is given by: 

Which has a limit for back-scattering which is just determined by setting the initial kinetic energy equal to the final potential energy. This corresponds to stopping the projectile and sending it backward, so at its closest approach, all the energy is in electric potential energy.
If you are truly interested enter the values in the calculating entries of the  link and get hard numbers.
edit after edit
One has to realize that the Coulomb potential goes to infinity and a unique number cannot be given for a quantity that has a functional dependence.  In this case the momentum and the angle of scattering have to be defined to determine r_min, which makes for a complicated algebraically analysis dependent on the specific masses and momenta involved . 
