  In a recent paper McGaugh, Lelli, and Schombert showed that in an empirical
plot of the observed centripetal accelerations in spiral galaxies against those
predicted by the Newtonian gravity of the luminous matter in those galaxies the
data points occupied a remarkably narrow band. While one could summarize the
mean properties of the band by drawing a single mean curve through it, by
fitting the band with the illustrative conformal gravity theory with fits that
fill out the width of the band we show here that the width of the band is just
as physically significant. We show that at very low luminous Newtonian
accelerations the plot can become independent of the luminous Newtonian
contribution altogether, but still be non-trivial due to the contribution of
matter outside of the galaxies (viz. the rest of the visible universe). We
present a new empirical plot of the difference between the observed centripetal
accelerations and the luminous Newtonian expectations as a function of distance
from the centers of galaxies, and show that at distances greater than 10 kpc
the plot also occupies a remarkably narrow band, one even close to constant.
Using the conformal gravity theory we provide a first principles derivation of
the empirical Tully-Fisher relation.
