**Author:**

Franco-Rodriguez, Jorge Adalberto

**Category:**

Research Papers

**Sub-Category:**

Mathematical Physics

**Date Published:**

December 26, 2019

**Keywords:**

Center of Mass, Sub-Center of Mass, Two-Body Problem, Three-Body Problem, Four-Body Problem, N-body problem, Newton’s Laws, Universal Law of Gravitation, Gravitational Force, Central Force.

**Abstract:**

On the basis that all bodies attract each other according to Newton’s Law of Gravitation, from observation of the universe it was concluded that it can be modeled as a simple structure composed by single objects (particles, celestial bodies, galaxies, etc.) and basic units (BUP) of P gravitational objects (P ≥ 2) that can be also reduced each to a single point of mass located at their Subcenter of Mass (SoM). It is apparent that the P objects of a BUP move elliptically or circularly at the same angular speed (SAS) around their SoM. Although parabolic and hyperbolic are also solutions of stable motions, for simplicity, in this model of an ordered universe, only the elliptical and circular movements were considered. The basic units were detected as hierarchical constituents of gravitational systems transmitting their gravitational effects (central forces) through their SoM to the other objects. By reducing any BUP first to a Two-Body problem and later to the One-Body formulation, equal forces exerted from their SoM, equal moments, equal angular momenta and equal angular speeds for each object were demonstrated in such BUP. With this optic, combinations of the BUP among them and with other single objects recreate all the possible configurations that any gravitational system can exhibit (the N-body Problem) and therefore can be easily solved.Finally, the always used “Superposition principle of central forces” for N > 2 was shown false through the analysis of a simple BU3.

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