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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