Equilibrium-Seeking Law as the Geometric Origin of Gravitation

This work proposes a unified physical interpretation of gravitational attraction based on the equilibrium-seeking behavior of physical systems. The central idea of this work is that all physical processes tend toward equilibrium states corresponding to minimum energy. Under central forces, minimum-energy configurations possess spherical symmetry. Therefore, spherical geometry is interpreted as the geometric proof of the equilibrium-seeking law of nature. The work proposes that gravitational attraction can be understood as motion toward a common equilibrium center. Two bodies attract because the system tends toward a shared equilibrium configuration. Mercury droplets provide a simple observable model of equilibrium-seeking behavior. When dispersed mercury is allowed to move, droplets merge and form a spherical shape, demonstrating motion toward equilibrium. The geometric origin of the inverse-square law is also discussed. Central symmetry naturally produces spherical geometry, leading to the 1/r² dependence of gravitational interaction. This conceptual framework and formulation are presented as original contributions by Erkin Atojonov and establish priority of authorship for the equilibrium-seeking interpretation of gravitation.