The Saeidi Gravitational Oscillation Framework A Dimensionless Gravitational–Orbital Phase Correspondence of Earth

This paper introduces the Saeidi Gravitational Oscillation Framework, a phenomenological gravitational–orbital scaling model based on the characteristic acceleration-defined time scale (Tg = c/g), where (c) is the speed of light and (g) is the surface gravitational acceleration of a celestial body. The associated characteristic gravitational length and acceleration-rate scale are defined as (g = c²/g) and (g = g/c), respectively. Using the orbital period (T ₎ₑ₁), the study introduces the dimensionless gravitational–orbital parameter (R = gT ₎ₑ₁/c = g T ₎ₑ₁). In the present interpretation, (R) measures the accumulated acceleration-defined gravitational phase scale over one complete orbital period. A preliminary comparison across selected Solar System planets shows that Earth satisfies the near-unity condition (R_ 1. 03), indicating that Earth’s orbital period is numerically close to its characteristic gravitational time scale (Tg = c/g). The framework is further connected to two broader theoretical contexts. First, the length scale (g = c²/g) is interpreted through the weak-field gravitational redshift relation, where it appears naturally as a characteristic redshift length. Second, the acceleration-rate scale (g = g/c) is shown to possess a structural correspondence with the Unruh acceleration scale, providing a possible thermodynamic and relativistic context for the proposed parameter. The work does not claim a confirmed resonance, a new gravitational law, or a replacement for standard gravitational theory. Instead, it presents a compact dimensionless gravitational–orbital phase correspondence that may motivate broader investigations across planets, moons, dwarf planets, and exoplanetary systems, as well as future tests involving uncertainty analysis, statistical null models, and comparative studies of potentially habitable environments.