Sergey P. Babailov* and P. A. Stabnikov
Only one gravitational interaction is not enough to explain the anomalous high speeds of rotation of stars on the outskirts of galaxies. Therefore, several approaches have been proposed by various authors, including the existence of dark matter, deformation of the gravitational interaction itself at ultra-long distances, modifications of Newton's classical laws, the introduction of additional additive potentials that are weaker than the gravitational interaction, but which decrease with distance relatively "slower" than the actual gravitational interaction. All these approaches make it possible to explain the experimental data on the velocities of stars, but within the limits of the size of the galaxy. For even more distant distances, the accelerated expansion of the Universe is established. So, to explain this, the concept of dark energy was introduced earlier. The approaches proposed earlier cannot fully explain all the features of the motion of galaxies relative to each other. At the same time, the introduction of two additional potential interactions (with the forces δMm/R and -βMm/Rn) formally makes it possible to explain most of the experimentally found features of the motion of stars at sub galactic and intergalactic distances.
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