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

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 (v4): This version updates and expands the framework with the following key additions: Quantum Bridge (revised): clarified derivation linking Ec=mvC with Planck’s h=mvλ, including closure to Newton’s Fd. Bohr–Ef–FSI Bridge (new section): demonstrates that the 2N² electron shell law arises directly from the field invariant (v²C), with tables comparing planetary and atomic systems. Complete numerical tables: added baseline constants (planetary and hydrogen), stepwise calculations (Ef, v, C, ne, ee), and normalization to show invariant patterns. Symbols and notes: appended additional symbol table and explanatory notes for new variables (N, ne, ee, ne/S). References updated: now include DOI links for all prior versions (v1, v2, v3), with v4 established as the canonical English release. Readers can immediately see how Version 4 strengthens the macro–micro bridge, adding full quantitative evidence for orbital stratification in both planetary and atomic domains.Note: In Version 3, the cover page mistakenly displayed ‘v2’. This has been corrected in Version 4.Version v5: • Added section "Mechanical Interpretation of Ec" — introducing the relationship between field-supplied energy and the mass-per-particle ratio, explaining why outer planets formed from lighter matter. • Revised numerical tables (Ef, FSI, Δ+, Δ−) with corrected values consistent with NASA’s Fact Sheet (2025). • Clarified the distinction between apparent velocity (vC) and normalized foundational energy (Ec = v). • Updated diagrams for orbital sector plots and equal-area validation. • Added bilingual release (English and Thai) in a single record. (This record contains both English and Thai versions of the Ef–FSI Framework, v5.)Version v6 (Trilingual edition):This version preserves the same verified data and theoretical content as Version 5.The only addition is a complete Chinese translation, making the framework trilingual (Thai, English, and Chinese) for wider international accessibility.Readers who have downloaded Version 5 need not re-download, as the scientific content remains identical. งานวิจัย Ef–FSI Framework (กรอบพลังงานและดัชนีความแรงสนาม)นำเสนอแบบจำลองทางฟิสิกส์ที่เชื่อมโยงพลังงาน สนาม และสสารภายใต้กลไกเดียวกันตั้งแต่มหภาค (การเคลื่อนที่ของดาวเคราะห์)จนถึงระดับจุลภาค (โครงสร้างอะตอม)โดยใช้แนวคิด “พลังงานพื้นฐานของสสาร” (Ef)และ “ดัชนีความแรงสนาม” (FSI) เพื่อแสดงว่าธรรมชาติทั้งหมดอยู่ภายใต้กลไกเดียวกันของสนามที่มีตัวตนจริง คำสำคัญ: พลังงานพื้นฐานของสสาร, ดัชนีความแรงสนาม, กลศาสตร์สนาม, ทฤษฎีเอกภาพ, Ef–FSI Framework 中文摘要:本研究 Ef–FSI 框架 提出了一种从宏观 (行星运动) 到微观 (原子结构) 的统一物理模型。该模型通过 “场强指数” (Field Strength Index, ε) 与 “物质基础能量” (Foundational Energy of Matter, Ef)描述能量与物质在同一力学机制下的连续转换关系。研究强调空间并非空无,而是具有质量特性的场介质 (field substance),它决定了所有运动的能量分布与反应过程。 关键词: 场强指数, 物质基础能量, 统一场理论, 场力学, Ef–FSI 框架 日本語概要:本研究 Ef–FSI Framework は、場の強さ指数 (Field Strength Index, ε) および物質の基礎エネルギー (Foundational Energy of Matter, Ef) を用いて、マクロスケール (惑星運動) からミクロスケール (原子構造) まで、エネルギーと物質の統一的な力学モデルを提案する。この枠組みは、力学的場の圧力を重視し、空間を単なる背景ではなく、運動を支配する実体的な媒体として再定義するものである。 キーワード: 場の強さ指数, 物質の基礎エネルギー, 統一場理論, 力学的場, Ef–FSI Framework Mirror record available on Figshare:https://doi.org/10.6084/m9.figshare.30281686 Project website (Ef–FSI Research Group):https://effsi.org Follow me on LinkedIn: www.linkedin.com/comm/mynetwork/discovery-see-all?usecase=PEOPLE_FOLLOWS&followMember=surakit-tobanleng-5a7829384