Generalized Newtonian force law and hidden mass

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Dark Matter, Dwarf Galaxies, Gravitation, Kinematics, Missing Mass (Astrophysics), Spiral Galaxies, Galactic Rotation, Mass Ratios, Particle Mass

Scientific paper

A generalized force is presented in resolution of the missing mass problem. The force appears as a closed form, two-parameter continuous function of interparticle displacement and is based on the exponential variation of the ratio of particle-mass to square displacement, in the small- and large-scale constant circular speed, in accord with observed halo galactic rotation and further, is in agreement with the infrared Tully-Fisher law. The variation in scale length is contained in a displacement-dependent exponential factor. A nondimensionalization scheme is introduced which permits present and previous generalized forces to be written as simple expressions of nondimensionalized acceleration and displacement. A graphical display of these nondimensionalized forces reveals very good agreement of the proposed force with related limiting forms in the two characteristic domains. When viewed with respect to a broad class of galaxy rotational data, it is found consistent with the present formulation to conclude that the separation from Newtonian gravitation occurs about the radius about 10 kpc.

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