Mathematical Analysis of Mercury's Orbit under TFD Conditions: Closure-Statics and Field Impedance in the Resonant Solar System

This document presents a field-mechanical analysis of Mercury's perihelion advance within the axiomatic framework of Tension Field Dynamics (TFD). The phenomenon is derived as a consequence of field stress interactions, incorporating principles such as the scalar stress field ϕ with base value ϕ₀ = 1 + 10⁻³⁵, the Yukawa structure of the solar field with L*⊙ = 959 AU, field impedance effects on coherent matter packets, and the Fan Effect for energetic closure after 364 days. The effective potential is corrected by impedance, yielding a perihelion rotation ∆ϕ ≈ 6πGM⊙ / [a(1 - e²)c₀²], where c₀ = 300,000 km/s. Resonance matching with the 137-field constant predicts ∆ϕ_res ≈ α⁻¹ / π ≈ 43.6″ per century. Using TFD parameters (M⊙ ≈ 1.989 × 10³⁰ kg, a ≈ 57.91 × 10⁹ m, e ≈ 0.2056), the total advance is calculated as 574.6″ per century, aligning with reference values through normalized light speed and dissipative compensation. All derivations remain strictly within TFD axioms, without external theoretical imports.