The Dynamic Equilibrium of the Solar System: A Semiclassical Unification of Orbital Scales

We apply the Dynamic Equilibrium Principle to the solar system, demonstrating that planetary orbital radii form a discrete, anchored, logarithmic hierarchy. Two fundamental constants are identified from the data: the characteristic length scale L0 = 0.387 AU (Mercury's orbital radius) and the systemic specific angular momentum Z ≈ 1.57 × 10¹³ m²/s. The inner planets (Mercury through Mars) occupy the range ∼ 1.8–3.9 L0; the outer planets (Jupiter through Neptune) occupy the range ∼ 13–78 L0. The Frost Line at ∼ 5.2 AU is derived analytically from the Shell Capacity equation S(r) = √GM⊙ r²/M(r) with threshold Scrit ≈ 4.1 × 10⁻² kg⁻¹ m² s. The Kuiper Belt and Oort Cloud are interpreted as a distinct dynamical regime where coherent solar gravity gives way to external perturbations. The eccentricity distribution is shown to be consistent with asymmetric relaxation: outward displacement decays more slowly than inward displacement. Application to the TRAPPIST-1 system provides an independent test: its closely packed terrestrial planets at r < 0.06 AU are identified as a migrated system frozen in resonance, confirming that the Shell Capacity equation can detect disequilibrium between composition and orbital position. The analysis suggests that the same structural principles governing atomic and molecular systems may extend to planetary architectures, though this remains a hypothesis requiring further testing.