Modified Gravity (MOG) fits to observed radial acceleration of SPARC
  galaxies
  The equation of motion in the generally covariant modified gravity (MOG)
theory leads, for weak gravitational fields and non-relativistic motion, to a
modification of Newton's gravitational acceleration law. In addition to the
metric $g_{\mu\nu}$, MOG has a vector field $\phi_\mu$ that couples with
gravitational strength to all baryonic matter. The gravitational coupling
strength is determined by the MOG parameter $\alpha$, while parameter $\mu$ is
the small effective mass of $\phi_\mu$. The MOG acceleration law has been
demonstrated to fit a wide range of galaxies, galaxy clusters and the Bullet
Cluster and Train Wreck Cluster mergers. For the SPARC sample of rotationally
supported spiral and irregular galaxies, McGaugh et al. [24] (MLS) have found a
radial acceleration relation (RAR) that relates accelerations derived from
galaxy rotation curves to Newtonian accelerations derived from galaxy mass
models. Using the same SPARC galaxy data, mass models independently derived
from that data, and MOG parameters $\alpha$ and $\mu$ that run with galaxy
mass, we demonstrate that adjusting galaxy parameters within $\pm 1$-sigma
bounds can yield MOG predictions consistent with the given rotational velocity
data. Moreover, the same adjusted parameters yield a good fit to the RAR of
MLS, with the RAR parameter $a_0=(5.4\pm .3)\times 10^{-11}\,{\rm m/s^2}$.
