Lunar Formation by Triple Phase Transition in the Differentiating Proto-Earth

Michel DEBAILLEUL 

The origin of the Moon remains one of the open questions of planetary science. The canonical giant impact model (Theia collision) predicts neither the near-isotopic identity of Earth and Moon, nor the crustal dichotomy, nor the ≈ 300 Myr delay of the terrestrial dynamo. The synestia model faces the same limitations. This work is conceptually distinct from both: it requires no external impactor, no synestia, and no free parameter — only the inevitable physical consequences of terrestrial accretion.
The starting point is thermodynamic and non-negotiable: the gravitational energy released during accretion exceeds the mantle fusion energy by a factor of 155. The proto-Earth is therefore necessarily a fully molten, rapidly rotating magma sphere (T_rot ≈ 5 h), without a stabilizing satellite, evolving in a permanently out-of-equilibrium Hadean environment. The unique driving force — progressive Fe-Ni segregation — orchestrates three coupled transitions constituting the Triple Phase Transition (TPT): (1) Rheological — the silicate melt acquires a yield stress (Bingham-Herschel law, τ_y ∈ [10², 10⁴] Pa) and organises a Coherent Magmatic Torus (CMT) in the Hadean intertropical belt |φ| < 30° of the co-rotating body frame — not the geographic equator; (2) Mechanical — elliptical parametric resonance (Malkus 1968; Kerswell 2002; Lacaze et al. 2004) drives the CMT to bifurcation velocity U_crit ≈ 9.8 km/s in ≈ 32 hours, entirely determined by the Maclaurin flattening f = 0.107 — no free parameter — producing N = 2–3 cohesive ejection episodes in 3–4 weeks; (3) Magnetic — the terrestrial dynamo ignites 290–360 Myr after ejection, consistent with Jack Hills zircon palaeomagnetic data. The CMT mass (M_TMC ≈ 2.3 × 10²² kg) is internally constrained from the observed radius of the first accretion layer. The crustal dichotomy emerges as a direct mechanical consequence of the asymmetric second episode. The apparent paradox between a 3–4 week formation and a 40 Myr Fe-Ni segregation is resolved by two distinct physical timescales: global segregation (τ_seg ≈ 40 Myr) charges the system; local Stokes redistribution within the CMT (τ_Stokes ≈ 257 s, fully derived) stamps each ejection episode with a chemically distinct signature.
A native WebGL interactive simulation illustrates the full dynamics in real time with adjustable parameters (ε, Ω, α, f_cap, N, T-Tauri intensity).
The model formulates ten quantitative and falsifiable predictions. The central prediction — seismic interface at d ≈ 200–315 km, impedance contrast |R| ∈ [0.01; 0.04] — will be directly tested by the Chang'e 7 broadband seismometer at the lunar south pole in August 2026, a mission specifically designed to probe lunar internal structure and seismic stratigraphy. A pre-existing Fe enrichment detected by Lunar Prospector at the south pole (P3b) constitutes an independent observational convergence with the TPT stratigraphic prediction. The geochemical predictions — Fe/Si depth gradient, Hf-W chronometry at 4.467 Ga, formation age > 4.45 Ga — are testable by Artemis III (2028–2029), which will collect mantle samples exposed by the South Pole-Aitken basin, the deepest and oldest impact structure on the Moon. This deposit pre-registers all ten predictions prior to these mission data.