In a question here Ron Maimon comments that "relativistic mass makes gravity, not rest mass."

If so, does that mean that the faster that stars orbit the galaxy the larger the relativistic mass of the galaxy therefore more gravity therefore the stars orbit even faster therefore the gravity gets even more therefore the stars keep on getting faster ...

So the speed of stars and mass of galaxy would be correlated with age and history of the galaxy or galaxy clusters and that's why calculations of galaxies' masses don't add up.

  • $\begingroup$ People approximate a central-blackhole's mass from the linear speed of the edge of its galaxy. Then the galaxy center must be moving relativistic. $\endgroup$ – huseyin tugrul buyukisik Aug 31 '12 at 15:12

It doesn't quite work like that. For one thing, stars' orbital speeds, while reasonably fast by human standards (often hundreds of km/s), are (in most cases) incredibly slow by relativistic standards - in other words, they are miniscule fractions of the speed of light. So the difference between the "relativistic mass" (or energy, as I would call it) and the rest mass is entirely negligible for all except perhaps a few stars in any given galaxy. Certainly there's no way it could account for the missing mass attributed to dark matter.

Besides, it's not the case that the stars' orbital speeds steadily increase over time in response to increased gravity. Instead, there is going to be some equilibrium at which the effects of the increased orbital speed balance out the effects of the increased gravity. The stars will quickly reach that equilibrium during the galaxy's formation, and then, simply speaking, they will remain at that speed, so the entire galaxy exists in a steady state of orbital motion. There would be no further correlations of orbital speed with age beyond this point.

And anyway, the models that people used to determine the presence of dark matter do take this effect into account (in the sense that they have determined that it has no noticeable effect on the calculations).

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    $\begingroup$ As an addendum, the region of the galaxy where dark matter is most critical to explain the motions of the stars is also the region of the galaxy where relativistic effects on the motion of the stars is the smallest--dark matter seems to dominate MOST in the Newtonian regime, not the other way around. $\endgroup$ – Jerry Schirmer Aug 31 '12 at 17:37

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