Isn't there a lot of uncertainty about the mass of the milky way? I think if you are going to use something as a unit you really need an accurate figure.
There is indeed lots of uncertainty, and all Milky Way mass estimates are model dependent. Also, the ~10^12 solar mass figure referred to above is an estimate of the total galaxy + dark matter halo mass. Stellar or baryonic mass estimates are closer to ~6 x 10^10 solar masses. I'm using "~" to mean uncertainty to within a factor of 2 or so.
