The Orbital Stability Constant of Celestial Bodies and the Unification of Single‑Body and Two‑Body Celestial Dynamical Systems

This paper employs the reference celestial body method as its fundamental research approach, investigating the actual force characteristics governing the orbital revolution of celestial bodies. It derives the first dedicated centripetal force formula for celestial orbits and establishes the first orbital stability constant formula coupling three variables: g, T, and R. Furthermore, the study deduces a constant relationship between orbital gravitational acceleration (g) and the orbital period (T). Through rigorous fundamental mechanical derivations, it systematically derives the formulations of both Kepler's constant and the law of universal gravitation. Ultimately, this work unifies the theoretical framework of celestial mechanics, achieving a complete reconstruction and logical closure of the foundational theories of classical celestial mechanics.This paper presents a unified theoretical description of single-body and two-body orbital kinematics, establishing a comprehensive computational framework and forming a new theoretical system for celestial mechanics. In essence, the revolution of all celestial bodies is the mutual motion of a two-body system; single-body orbital motion is merely a simplified special case of two-body motion under the condition where the companion star's mass is negligible.Typical orbital systems, including the Sirius binary system, the Earth-Moon system, and near-Earth space station orbits, were selected for numerical verification using observed orbital parameters. The results confirm that this theoretical system is mathematically self-consistent and mechanically sound.Grounded in the principles of circular kinematics and centered on the orbital stability constant, this theory establishes a novel theoretical and computational framework for celestial mechanics. It derives a series of orbital calculation formulas for single-body motion, two-body relative motion, and two-body motion relative to the center of mass. By combining the specialized centripetal force formula for celestial orbits with the universal law of gravitation, it enables the quantitative calculation of the comprehensive spatial perturbation coefficient and the holistic analysis of operational states.Furthermore, it introduces an in-orbit velocity verification formula for satellites, along with calculation methods for orbital design velocities, thereby establishing a new orbital validation approach. Yielding results that more accurately reflect actual force conditions, this theory is highly applicable to near-Earth orbit engineering, orbital parameter design, precise parameter validation, and operational state assessment. Ultimately, it represents a brand-new celestial mechanics theory that combines theoretical innovation with practical aerospace engineering value.