We describe gravitational N-body simulations to investigate whether various non-Newtonian interactions between the stars of a system could explain the flat rotational curves which are characteristic of actual isolated spiral galaxies. It is shown that replacing the standard Newtonian interaction by the models of Sanders (1984), Kuhn and Kruglyak (1987) and Milgrom (1983), no massive halo (or dark matter) is required to produce the flat rotational curves of the systems under consideration. All models also generate the exponential surface mass density distribution which is in agreement with that observed in disk-shaped galaxies. In relation to the spiral structure of galaxies, we present the evidence that the non-Newtonian interactions can reproduce the multiple armed patterns in stellar disks without dark matter.
