ERRORS IN STELLAR STRUCTURE THEORY. The Size of the Sun Under A. Eddington's Model

ABSTRACTBackground: The mainstream model of stellar structure, originating from Arthur Eddington's 1926 work, asserts that gravitational compression supplies the required force to overcome the Coulomb barrier and ignite thermonuclear fusion within a star's core.Methods: This paper executes a mathematical and historical audit of the gravitational confinement paradigm. By equating the required Coulomb repulsion force of two interacting nuclei to the available Newtonian gravitational force of a star with solar mass, we compute the critical radius R where such a process becomes mechanically viable.Results: Numerical calculations demonstrate that for proton-proton fusion to be driven exclusively by gravity, the entire mass of the Sun must be confined within a sphere of radius R ≈ 4.958 · 10-5 meters (less than 1 mm), yielding an impossible density of ~1042 kg/m³.Conclusions: The extreme dimensional discrepancy mathematically invalidates the hypothesis of gravitationally induced thermonuclear fusion in real stars. It is concluded that stars utilize an alternative, non-gravitational mechanism for nuclear reaction generation, conceptually proven by terrestrial self-regulated systems.