It is well known that dark matter was introduced to explain the orbits of stars in a galaxy. My main question is this: Were these calculations done using Newton or Einstein?
People I ask tell me that there's no difference because of small velocities and weak gravity, but my concern is that Newton cannot be right for large distances. In fact, if a star orbits the center of a galaxy in a distance of, say, 10.000 light years, then the star "sees" the gravitational center in the direction where it was 10.000 years ago. So for a circular orbit, the acceleration vector is not perpendicular to the velocity velocity, from which I would conclude that the speed of the star must be higher than in Newton's theory.
I wonder whether someone with more experience than I could run a simulation and tell me whether this makes any difference.