Deriving Newton's G from a Single Star: A Minimal Algebraic Approach

This formal note isolates a minimal, purely algebraic derivation of Newton’s gravitational constant 𝐺 from stellar observables: mass (𝑀), radius (𝑅), and surface gravity (𝑎). No auxiliary models or empirical setups are required — only classical Newtonian mechanics. The formulation is so direct it may have remained overlooked for decades. Yet its implications are far-reaching: it enables the calculation of 𝐺 from direct astrophysical data, using nothing more than basic algebra — and from a single star. This derivation also lays the foundation for the broader photogravitational framework, in which radiation and gravity are unified into a single structural ratio. That direction, explored in a companion paper, builds directly upon this core result.