>a = 1/r^2
>
>Suppose that body A has velocity (1,0) along the x direction at
>(xA,yA) = (0, -0.5)
>and body B has velocity (-1,0) at
>(xB,yB) = (0,0.5)
>
>                       <-----B
>                             |
>                         ___ o ___
>                             |
>                             A----->
>at time t = 0.
>Those are you initial conditions.
>Now calculate the new positions at time t = t+ epsilon, where epsilon is
>some small number.
>First work out the new velocities in x and y,
>vxA, vYA, vxB, vyB
> then the new positions. That is,
>xA = xA+vxA*epsilon.
>When you get your program debugged, A and B should move (roughly) in  circle
>and you can plot that as it occurs. (scale as necessary, use different
>colours for A and B).
>Now play around with the value of epsilon and see what happens,
>also with the initial conditions and the masses.
>You may be surprised with the results.

Surely the curve will approach a circle more and more as the value of epsilon
is decreased.

I cannot see what you are getting at here. I think you left out the important
bit.
Getting late on a cold night, eh?