There is some work at Livermore (I think) that is indicating c is indeed not constant and is influenced by gravity and possibly other forces. If this turns out to be true it will turn physics on their ear. The other little tidbit is that it means Roddenberry style warp drive in probably possible if you can find the power to do it. My college physics went to his grave trying to prove that the "science" of Star Trek was all bunk. More and more it looks like he was wrong. Interesting.
So if M is fixed and the other two move around - -well that is just a mind blowing thing.