If the Milky Way galaxy is treated as a single body, what velocity would equation 1 predict it to have? Using the values from Wikipedia ( total mass: 1.2×10^12 solar masses, diameter: 1.1 kilo light years) gives a total velocity of 780 km/s. Measured value of rotation of stars in the outer edge is 254 km/s. As is observed in the the star chart, the calculated value is greater than the observed rotation presumably due to a large revolving velocity around some other structure.
Special Relativity states that as the velocity of an object increases so too does its mass ( Equation 3 in my notation). However, Equation 2 predicts that as the overall velocity of an object increases the velocity associated with mass and mass itself should decrease. I was puzzled by this dilemma; if both equations were correct how could they yield contradictory conclusions. It finally occurred to me how this could be so: only if both absolute velocity and mass are constant and unable to change. Locally, velocities can and do vary and relativistic effects may be observed.