I've forgotten to mention a (literally!) side effect.
Since the starfield is rotating now, there will be some black spaces, depending on the rotation angle. If the angle is 45 degrees (or 135, 225, 315), there are four opposite black triangles in the corners. At angles of 90 and 270 degrees, there are two black sidebars. You'll need to remember the position of those stars as well. (A star might be able to rotate out and into the screen.)
The distance which you'll need to remember is sqr(2) * (longest side of your screen). In this case no black shapes will show at even square screens.