A Suggested Alternative to Dark Matter in Galaxies: I. Theoretical
  Considerations
  Dark matter is the generally accepted paradigm in astrophysics and cosmology
as a solution to the higher rate of rotation in galaxies, among many other
reasons. But since there are still some problems encountered by the standard
dark matter paradigm at the galactic scale, we have resorted to an alternative
solution, similar to Milgrom's Modified Newtonian dynamics (MOND). Here, we
have assumed that: (i) either the gravitational constant, G, is a function of
distance (scale): G = G(r), or, (ii) the gravitational-to-inertial mass ratio,
mg/mi, is a function of distance (scale): f(r). We have used a linear
approximation of each function, from which two new parameters appeared that
have to be determined: G1, the first-order coefficient of gravitational
coupling, and C1, the first-order coefficient of gravitational-to-inertial mass
ratio. In the current part of this research, we have generated simplified
theoretical rotation curves for some hypothetical galaxies by varying the
parameters. We have concluded that our model gives a qualitatively and
quantitatively acceptable behavior of the galactic rotation curves for some
values of these parameters. The values of the 1st-order coefficients that give
quantitatively acceptable description of galactic rotation curves are: G1
between around 10^-31 to 10^-30 m^2 s^-2 kg^-1; and, C1 between 10^-21 to
10^-20 m^-1. Furthermore, our model implies the existence of a critical
distance at which the MOND effects become significant rather than a critical
acceleration. In fact, Milgrom's MOND converges with our model if the critical
acceleration is not a constant but a linear function of the galactic baryonic
mass.
