That's right. That's why when this experiment is actually done, the mirror is typically rigidly mounted to an optical bench, which is sitting on the surface of

That's right. That's why when this experiment is actually done, the mirror is typically rigidly mounted to an optical bench, which is sitting on the surface of a planet. If the mirror were freely floating in zero G, the outcome would be different. It is a worthwhile exercise to calculate how small the mass of the mirror would have to be before you would actually notice a difference in the results.