Finite Non-Equilibrium Force Theory for Real-Time Satellite Orbit Control

We present a finite non-equilibrium force formulation that enables real-time satellite orbit calculation and control using only instantaneous orbital distance. The theory explicitly incorporates mass, finite size, orbital distance, and non-equilibrium force within a single closed-form expression. Unlike conventional differential or potential-based approaches, the present formulation is based on finite differences and remains non-vanishing even in the infinite-distance limit. The force directly satisfies Newton’s equation of motion with the inertial mass identified as the mass parameter appearing in the force itself. As a result, both forward orbit prediction and inverse orbit control become algebraically tractable and computationally lightweight, enabling practical implementation on low-power devices such as smartphones.