How do we know that Galaxies aren't smaller and therefore require less "dark matter" to hold them together?

 

What factors are taken into account?

 

Distance (redshift)

angle subtended (is that the correct term)

 

How much stronger (percentage wise) would gravity have to be to not require dark matter?

The measurements of galaxy size are calculated with the subtended angle and the distance. The first distance mesurement where done on nearby galaxies having a particular type of stars, the Cepheide. The distance to some Cepheide in our galaxy can be measured by paralaxe (change of apparent position 6 moth appart). The Cepheide stars are variable star, their brigthness go cycle up and down. Knowing there distances they saw that the cycle period is related to the absolute brigthness variation. So by measuring brigthness variation of Cepheide in other galaxie they know the absolute magnitude (brigthness). With the absolute magnitude and the apparent magnitude they calculated the distance. The subtended angle is directly measured.

That was a proof that the galaxies where other universe island.

We cannot discern individual Cepheide star in distant galaxie.

Then Hubble discovered that the spectrum of galaxies where redshifted. The more distant galaxies where the most redshifted. So the redshift is used by extrapolation to mesure the distant of the farest galaxies.

The mass of galaxies are evaluated with the surface brigthness and the hydrogen cloud mesure by 21cm H line.

If I remember right the evalutation of how mass is needed to hold a galaxie tougether is ten time the visible mass. The force of gravity is proportional to the mass a naive guess would be ten time stronger ???

The measurements of galaxy size are calculated with the subtended angle and the distance.........................................................................................................If I remember right the evalutation of how mass is needed to hold a galaxie tougether is ten time the visible mass. The force of gravity is proportional to the mass a naive guess would be ten time stronger ???

 

So is the subtended angle corrected for the presumed hubble expansion (which would exagerrate the subtended angle) that is at right angles to the hubble expansion that causes the redshift?

 

And the difference in diameter required to explain the discrepancy on it's own would a factor of roughly 3 then? (square root of 10)

 

Is the missing matter (percentage wise) constant with distance?