Central Forces, Spherical Symmetry and the Origin of the Inverse-Square Law of Gravitation

This work presents a geometric and physical interpretation of the inverse-square law of gravitation based on central forces and equilibrium-seeking behavior of physical systems. It is proposed that under central forces the minimum-energy configuration possesses spherical symmetry. Central interactions naturally produce spherical distributions of influence. Since a sphere of radius r has surface area: S = 4πr² the intensity of a central interaction decreases proportionally to 1/r². This work provides a geometric explanation of the inverse-square law and develops the equilibrium-seeking interpretation of gravitation proposed in: Erkin Atojonov (2026)The Equilibrium-Seeking Law: Geometric Origin of Gravitationhttps://doi.org/10.5281/zenodo.18807421 and Erkin Atojonov (2026)Why Two Bodies Attract Each Otherhttps://doi.org/10.5281/zenodo.18810650 The main conclusion is that central forces naturally produce spherical symmetry, and spherical symmetry leads to the inverse-square law of gravitation. This conceptual framework is presented as an original contribution by Erkin Atojonov and establishes priority for the geometric interpretation of the inverse-square law.

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