Hidden Oscillations in Planetary Motion: The Ef–FSI Framework

Gravitational waves are often regarded as rare signals from extreme cosmic events. This paper introduces the Ef–FSI framework, which demonstrates that their signature is continuously present in planetary orbits. The framework is built on two core quantities: the Foundational Energy Factor (Ef = vC), a constant energy-per-cycle per unit mass, and the Field Strength Index (FSI = v²C), which captures oscillatory Action–Reaction phases (perihelion = contraction, aphelion = expansion). Results confirm that Ef remains constant across perihelion, aphelion, and the mean orbital radius, with deviations typically <5%. FSI reveals systematic wave-like oscillations: Δ(+) > 1 at perihelion (Action) and Δ(–) < 1 at aphelion (Reaction). At the mean orbital radius, planetary FSIs converge to nearly identical values (~8.33 × 10²⁰ N·m/cycle/kg for Venus, Earth, and Mars), reflecting the symmetry of the solar field. Satellite systems (Jupiter and Saturn) also display internal convergence, confirming FSI as a system-level determinant. The framework reproduces Kepler’s laws directly, aligns with thermodynamics (Ef decreases systematically with radius), and extends naturally to the quantum scale, where Planck’s constant emerges as a special case of the cycle–energy law. Thus, planetary motion itself encodes continuous gravitational waves, making the Solar System a natural laboratory. Version notes (v2):This second version unifies notation, reduces redundancy, smooths section transitions, relocates Appendix A (moons) to Supporting Data, shortens the abstract, and adds figures illustrating Ef stratification and FSI oscillations.Project website (Ef–FSI Research Group):https://effsi.org