Anomalous Perihelion Precession in a Refractive-Inertia Model: A Joint Four-Planet Determination of the Coupling β

A classical two-body model in which a moving body's inertia is dressed by a refractive index, n(r) = 1 + β·GM/(c²r), while the Newtonian potential acts on the bare mass, produces anomalous perihelion precession exactly linear in the single constant β, with no relativistic force term inserted by hand. Fitting β to the anomalous precessions of Mercury, Venus, Earth and Mars jointly gives β̂ = 2.9997829368146105 ± 0.006938166632503317 (χ² = 0.00048, 3 degrees of freedom), consistent with the frozen value β = 3 at 0.03 standard deviations. The same constant, carried frozen and untuned into observables it was never fitted to, splits the model: the S2 star's apsidal precession passes, while solar light deflection and the Shapiro delay fail by the factor 3/2 that separates the orbital coefficient from the light-propagation coefficient. One constant therefore serves the orbital sector of the model and cannot serve its light sector under the refractive reading. All statements are within the model; β is not claimed as a constant of nature.