N-Body Problem Extension Hypothesis

: A system of mutually interacting point-mass objects is considered. All objects act on each other with mutual forces. A consistent relativity of motion based on the elimination of the observer is introduced. The center of inertia of the entire system is a common reference point. Central and mutual quantities are defined and the relationship between them is derived. A simple method of numerical approximation of the evolution of the central motion is presented. The scale invariance of the classical n-body problem is used to challenge the physical correctness of the problem formulation. Subsequently, a hypothesis is expressed about the extension of Coulomb’s law as well as Newton’s law of gravity. The consequences of the hypothesis are illustrated by the simulation of the helium-2 atom and the simulation of the motion of the stars S2, S4716 in the vicinity of the black hole in the core of our galaxy.