Mass Distribution, Rotation Curves and Gravity Theories
  {Comparison of mass density profiles of galaxies of varying sizes based on
some gravity theories from observed galaxy rotation curves and assessing the
need for dark matter.} We present an analysis of the rotation curves of five
galaxies of varying galactic radii: NGC6822 (4.8 kpc), Large Magellanic Cloud
(9 kpc), The Milky Way (17 kpc), NGC3198 (30 kpc) and UGC9133 (102.5 kpc). The
mass and mass density profiles of these galaxies have been computed using the
scientific computing s/w package MATLAB taking the already available velocity
profiles of the galaxies as the input, and without considering any Dark Matter
contribution. We have plotted these profiles after computing them according to
three different theories of gravity (and dynamics): Newtonian (black line),
Modified Newtonian Dynamics (MoND) (green line) and Vacuum Modified Gravity
(red line). We also consider how the profile due to the Newtonian theory would
modify if we take into account a small negative value of the Cosmological
Constant (5 x 10^-56 cm^-2 from theory) (blue line). Comparing these mass and
mass density profiles, we try to form an idea regarding what could be a
realistic theory of gravity and whether we need Dark Matter to explain the
results. Keywords : disk galaxy rotation curves, galaxy mass, mass density
profile, dark matter, Newtonian theory, MoND, Vacuum Modified Gravity, negative
cosmological constant
