mathematics - Kepler orbit : get position on the orbit over time

I'm developing a space-simulation related game, and I am having some trouble implementing the movement of binary stars, like this:

The two stars orbit their centroid, and their trajectories are ellipses.

I basically know how to determine the angular velocity at any position, but not the angular velocity over time. So, for a given angle, I can very easily compute the stars position (cf. http://en.wikipedia.org/wiki/Orbit_equation).

I'd want to get the stars position over time. The parametric equations of the ellipse works but doesn't give the correct speed : { X(t) = a×cos(t) ; Y(t) = b×sin(t) }.

Is it possible, and how can it be done?

Answer

Following a few links from the Wikipedia page you reference leads to Position as a function of time.