Intrinsic Gravitational Signature Metric and the Quantification of the Universal Gravitational Signature Threshold

This paper introduces a novel mathematical framework to quantify the orbital independence and gravitational captivity of celestial bodies within planetary systems. Under this framework, a unique metric termed the Intrinsic Gravitational Signature (S) is defined as the product of the Universal Gravitational Constant (G) and the local gravitational acceleration (g) of a celestial body. By solving this function concurrently with Newtonian classical field equations, a fundamental structural equation, S = (G^2× m)/r^2 , is derived. This manuscript establishes the dimensional validity of this new metric and validates it using empirical data from major planets and satellites within the Solar System. The empirical validation establishes a baseline constant named the Universal Gravitational Signature Threshold, hereinafter referred to as the Signature Threshold (S_t = 2.0 x 10^(-10) m^4/(kg .s^4)). The numerical value of this threshold is derived via statistical regression and boundary-layer optimization of empirical solar system data, isolating the precise inflection point which mathematically bifurcates independently orbiting bodies from gravitationally captive satellites.