This document presents a complete numerical demonstration that acceleration is not an independent quantity, but emerges directly from a single invariant relation: ε = v² / (r · S) All calculations are performed using real measured values and without introducing additional formulas, external laws, or corrective coefficients. Two independent channels are resolved using the same relation: Earth orbital acceleration (29.78 km/s, 149,600,000 km) Earth surface acceleration (7.9 km/s, 6371 km) Both close numerically through the same structure and produce: Orbital acceleration ≈ 0.00593 m/s² Surface acceleration ≈ 9.80 m/s² The same method extends consistently to other planetary systems: Mars orbital acceleration ≈ 0.00254 m/s² Jupiter orbital acceleration ≈ 0.000219 m/s² In all cases: ε remains constant (~0.50) S is extracted from measured values acceleration satisfies both identities: a = v² / ra = ε · S This demonstrates that: acceleration is not an external law acceleration is already contained in the equilibrium relation different physical regimes (orbit, surface, planetary scale) are resolved by scale change only, not by different equations The document shows full step-by-step calculations, identity checks, and cross-scale closure, confirming that a single relation governs all evaluated systems.
Danijus Kazlauskas (2026) studied this question.