Hidden Oscillations in Planetary Motion: The Ef–FSI Framework (v7)

Ef–FSI Framework (Version 7) presents a geometric–mechanical reinterpretation of orbital motion based on cycle-normalized invariants, without invoking force laws or mass as primary inputs. The framework is built upon two central quantities: the Foundational Energy FactorE_f = vCand the Field Strength Indexε = v²Cwhere C = 2πr is the instantaneous orbital cycle length. These quantities remain invariant within stable orbital systems and provide a unified description of orbital structure, phase balance, and scale stratification across planetary and sub-planetary regimes. Version 7 consolidates the framework into its most coherent and reviewer-ready form to date, with clarified scope, tightened derivations, and explicit separation between core results and interpretive extensions. New and expanded content in v7 includes: Field Reconstruction without Mass InputDemonstration that local accelerations (e.g. Earth surface gravity and lunar orbital acceleration) can be reconstructed from orbital data via ε, with mass inferred only after the field structure is established. Canonical Field Mechanics FormulationA unified treatment of inward–outward orbital phases, areal sweep invariance, and cycle normalization, presented as a mechanical field process rather than a force balance. Energy Stratification and Orbital LayeringExplicit articulation of how Ef governs the ordering of orbital shells, enabling comparison across planetary systems and serving as a structural analog to energy level organization. Macro–Micro Structural BridgeExtension of the invariant v²C logic toward atomic-scale organization, showing how orbital stratification and energy layering emerge from the same geometric constraints. Clarified ma–mv Relationship (Appendix)A dedicated appendix formalizing the relationship between force rate (ma), cumulative force (mv), energy transfer rate (½mv²/t), and cycle-based energy measures, without introducing new postulates. Improved Scope of Validity and Falsifiability ConditionsClear statements on where the Ef–FSI framework applies, how it may be tested against observational data, and under what conditions it would fail. This work is not proposed as a replacement for Newtonian mechanics, General Relativity, or Quantum Mechanics, but as a structural reinterpretation that reveals a deeper geometric order underlying orbital motion. Classical and relativistic quantities re-emerge as derived or normalized expressions once the field structure is reconstructed. Version 7 serves as the canonical reference for the Ef–FSI framework at its current stage of development and is intended as a foundation for further analytical, numerical, and comparative studies.