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I have seen explanations elsewhere that stars' relativistic velocities in a Galaxy would not account for the missing mass of what we call "dark matter", but in order to get a total relativistic mass of everything in a Galaxy, wouldn't one have to account for the velocity and rest mass of every single particle in that Galaxy?

Have we a way of approximating this for huge systems like galaxies?

Or is my mistake failing to realize that the "mass" of something like a star already accounts for the relativistic velocities of all of its component particles?

If that is so, wouldn't the measurement of the sum of the relativistic masses of all of the particles be different when the frame of reference is the galactic center rather than the center of the star?

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The vast majority of the normal matter in a galaxy moves at non-relativistic speed. For example the Sun moves at a speed of 240 km/s about the galactic centre, which gives a correction of only 1 in 1.4 million to the rest mass.

https://www.universetoday.com/133414/distance-speed-suns-orbit-around-galactic-centre-measured/

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    $\begingroup$ one should point out that dark matter needed to explain galactic rotation curves is about five times normal matter $\endgroup$
    – anna v
    Mar 11 '18 at 17:18
  • $\begingroup$ Seems obvious then that relativistic mass cannot explain dark matter. Does rest mass of something huge like a star already account for all the relativistic masses of each atom within it? $\endgroup$
    – Joe Bakhos
    Mar 12 '18 at 17:29

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