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And now for the reverse problem   
   

     


   This is the way a lot of galaxies look in dimensionless form.  Like airplanes,  they follow the same rules for dynamics regardless of size.  Star formation however depends on density (not SMD) and friction or impact effects of some sort.  The measured and computed speeds are identical in this plot.

     Dimensionless terms are:
md  = (mass inside r)/ (total mass)
ln(rhod)= ln(rho / rhoav)
rd  = r / rmax
ln(SMDd) = ln(SMD/SMDav)
SMDav = (total mass)/(total area)
vd = v/( Kepler v at rim)

   
NGC 3198 dimensionless results.
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