You've checked your math and you are confident that you have the right
answer for the velocity of M31 using Hubble's law. You gleefully go to
your professor with the answer and the method you used to get the answer.
Unfortunately, he just shakes his head at you.
He then explains that although your general approach is theoretically
sound, it is only very distant objects that participate in "Hubble flow."
For closer galalaxies, such as M31, the effects of the expansion of the
Universe that give rise to Hubble's Law are swamped by the local effects of
gravity. In fact, M31 is part of the Milky Way's "local group," which
means that it is gravitationally bound to our own galaxy. And gravity has a
huge effect on M31's motion.
You'll just have to keep trying!
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