Derivation of the Gravitational Constant and the Photogravitational Ratio from Single-Star Observables

This document introduces a new method for deriving Newton’s gravitational constant (G) from a single star's observed parameters—luminosity (L), mass (M), radius (r), and surface acceleration (a)—without relying on orbital mechanics or two-body systems. The approach centers on the photogravitational ratio (Φ = L / M·a), reflecting each star’s radiation-gravity balance. From this, G is computed directly as G = (L·r²)/(Φ·M²). Applied to the Sun, this yields a near-exact match to the known value of G. The model offers a fresh radiative view of gravity as an emergent property of luminous structure, with implications for dark matter, field geometry, and quantum gravity.