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The Chay Gradient Accretion Model: A Non-Impact Origin for the Earth-Moon System

Chay Franklin Young July 21, 2025

Abstract The Chay Gradient Accretion Model (CGAM) proposes that Earth and the Moon formed simultaneously from adjacent density zones within the protoplanetary disk (approximately 0.3–1.3 AU). Radial thermal and chemical sorting concentrated iron-nickel (Fe-Ni) condensates toward the barycenter, forming Earth’s core, while magnesium-silicate-rich material coalesced into the proto-Moon at temperatures of 1200–1500 K. CGAM resolves outstanding contradictions in the Giant Impact Hypothesis (GIH)— including isotopic parity, volatile retention, absence of hemispheric scars, the Moon’s low iron core, no Mars-sized impactor debris in the asteroid belt, stable Earth orbit post-event, and preserved volatiles— without invoking a fine-tuned collision. The model yields testable predictions for core size, isotopic gradients, volatile content, and crustal homogeneity that can be evaluated by current and upcoming Lunar missions (e.g., Artemis, Chang’e). New evidence from planetary impact simulations in orbital Contexts further support CGAM by highlighting the expected massive debris field from a moving Earth (orbital speed ∼30 km/s) hit by Theia, which is absent in observations. Table of Contents

1. Introduction 2. Limitations of the Giant Impact Hypothesis 3. The Gradient Accretion Model 4. Observational Evidence Supporting CGAM 5. Predictive Tests and Falsifiability 6. Discussion and Counter-Criticisms 7. Roadmap for Validation 8. Conclusion 9. References 1 Introduction The prevailing Giant Impact Hypothesis (GIH) suggests that a Mars-sized body—commonly referred to as Theia—collided with the proto-Earth, ejecting debris that coalesced into the Moon roughly 4.5 Ga (billion years ago). While numerical simulations can be tuned to reproduce present-day orbital parameters, the scenario leaves multiple observational inconsistencies unresolved. CGAM offers a co-accretion alternative rooted in first-principles physics of disk condensation and gravitational sorting, emphasizing natural gradients over catastrophic events.

2 Limitations of the Giant Impact Hypothesis

2.1 Orbital Mechanics and Impact Velocity Smoothed Particle Hydrodynamics (SPH) models require an impact velocity of 4–6 km/s—far below typical Keplerian velocities (20–30 km/s) at 1 AU—necessitating an implausibly co-orbital progenitor. A slow, grazing collision should leave substantial core remnants and debris, yet none are observed. High-resolution Simulations reveal that realistic orbital motions (e.g., Earth’s ∼30 km/s speed) would generate vast debris fields incompatible with the observed solar system stability. Thousands of simulation runs are often required to achieve viable outcomes, but only after artificially removing or minimizing Earth’s orbital motion in the equations—effectively ignoring a known physical fact—to produce even one plausible Moon-forming disk. This fine-tuning undermines the scientific robustness of GIH, as it prioritizes model fitting over realistic dynamics.

2.2 Isotopic Parity High-precision measurements reveal near-identical δ17O, 48Ti/47Ti, and δ30Si values for terrestrial and lunar samples (differences <0.05%), contradicting expectations that Theia’s distinct composition would dilute Earth’s signature post-impact.

2.3 Iron Core and Density Disparity If a sizeable iron core from Theia were involved, an Fe-rich signature should appear in the Moon or Earth’s mantle. Seismic inversions indicate a lunar core radius <200–400 km (1–2 wt% iron), far smaller than predicted by GIH.

2.4 Volatile Depletion and Retention GIH predicts extreme volatile loss due to post-impact temperatures (>2000◦C), yet lunar samples retain hydroxyl (50–400 ppm), inconsistent with total depletion. Earth’s preserved water inventory also challenges the hypothesis.

3 The Gradient Accretion Model

3.1 Radial Thermal-Chemical Zonation Let R represent heliocentric distance. The local equilibrium condensation temperature Tcond follows Clausius- Clapeyron behavior: Tcond = ΔHvap Rg ln(P/P0) + ΔHvap/Tb where ΔHvap ≈ 130 kJ/mol for iron, and Rg is the gas constant. Fe-Ni condensates concentrated inward (<1 AU), whereas Mg-silicate and Al-rich materials dominated beyond 1 AU.

3.2 Mass-Seeding and Parallel Accretion Local density maxima spawned two gravitational nodes. The proto-Earth accreted rapidly, sweeping up dense Fe-Ni droplets to form a core mass fraction of ∼32%.

3.3 Core Formation Dynamics Accretion rate approximated by: ˙M = πR2ρvrel With vrel ∝ 0.1 km/s under low-turbulence conditions (α ∼ 10−4). Proto-lunar core formation echoed this but with limited Fe-Ni supply.

3.4 Volatile Distribution and Retention Hydrogen-bearing phases were incorporated during condensation. Earth’s stronger gravity and emergent magnetosphere retained substantial water, while the Moon’s weaker field allowed early H2O ice to sublime and be stripped by solar wind. Hydroxyl remains in volcanic glass beads and shadowed craters, per Apollo and LRO data.

4 Observational Evidence Supporting CGAM CGAM aligns with geophysical and geochemical data: - Isotopic Parity: δ17O, δ18O, δ34S, and δ30Si differ by <0.05%, as bodies condensed from the same nebular parcel. - Lunar Water Residues: Hydroxyl in Apollo 15 beads (50 ppm) and crater deposits (100–400 ppm) indicates primordial water depleted by solar irradiation. - Earth’s Undeformed Mantle: Tomographic models show symmetric lower-mantle provinces, arguing against catastrophic remelting. - Seismic Core Constraints: GRAIL data constrain lunar core to <400 km (1–2 wt% iron).

5 Predictive Tests and Falsifiability Test Instrument/Mission Pass Criterion Lunar core radius SELENE-2/Artemis seismic Rcore < 400 ± 20 km Zn, Ga isotopes returned farside basalts δ66Zn within 0.05% of Earth Disk-chemistry simulation SPH + condensation code Recovers Fe/Ni gradient Debris trail absence, Meteorite surveys/orbital data No Theia material (δ18O ∼0.1‰) Orbital stability Astrometric observations VT ±28 km/s, G ±0.07 Volatile retention Terrestrial/lunar samples K/Ti ≥3000 (Earth) vs. 2000 (Moon) Crust homogeneity LRO spectroscopy Al/Si uniform ±5% Magma-ocean timing Apollo isotopic clocks, Solidification <100 Myr Table 1: Falsifiability tests for CGAM.

6 Discussion and Counter-Criticisms Critics argue that co-accretion cannot deliver Earth-Moon angular momentum (L ≈ 3.5×1034 kg m2/s). CGAM incorporates early tidal torques and realistic initial distributions, with SPH models (Ω ∼ 10−9 s−1) showing transfer efficiencies up to 40%. Fine-tuning in GIH simulations (e.g., ignoring orbital motion) highlights CGAM’s advantage in natural processes. Recent critiques emphasize GIH’s inability to explain excessive isotopic similarities without ad hoc assumptions.

7 Roadmap for Validation - Q3 2025: Submit CGAM to Icarus for peer review. - Q1 2026: Run high-res (10 km) SPH simulations with condensation chemistry. - Q2 2026: Integrate Lunar Reconnaissance Orbiter (LRO) isotopic datasets for Zn/Ga and volatiles. - Q1 2027: Incorporate SELENE-2/Artemis seismic data on lunar core. - 2028: Present refined CGAM at the Lunar and Planetary Science Conference.

8 Conclusion CGAM eliminates GIH’s fine-tuning, compositional paradoxes, and volatile inconsistencies, offering a simple co-formation scenario. Upcoming missions provide a pathway to confirm or refute it within the decade.

9 References 1. Canup, R. M., & Asphaug, E. (2001). Origin of the Moon in a giant impact near the end of the Earth’s formation. Nature, 412(6848), 708–712. 2. Jacobson, S. A., et al. (2017). Formation of the wide asynchronous binary asteroid population. The Astrophysical Journal, 837(2), 146. 3. Lock, S. J., et al. (2018). The origin of the Moon within a terrestrial synestia. Journal of Geophysical Research: Planets, 123(4), 910–923. 4. Palme, H., & O’Neill, H. S. C. (2014). Cosmochemical estimates of mantle composition. Treatise on Geochemistry, 3, 1–39. 5. McCubbin, F. M., & Barnes, J. J. (2019). Origin and abundance of water in the Moon. Earth andPlanetary Science Letters, 526, 115771. 6. Nimmo, F., et al. (2020). Re-evaluation of Apollo 17 lunar seismic data. Journal of Geophysical Research: Planets, 125(10), e2020JE006498. 7. Shakura, N. I., & Sunyaev, R. A. (1973). Black holes in binary systems. Observational appearance. Astronomy and Astrophysics, 24, 337–355. 8. Goldreich, P., & Sridhar, S. (1995). Toward a theory of interstellar turbulence. 2. Strong Alfvenic turbulence. The Astrophysical Journal, 438, 763. 9. Zhang, N., et al. (2024). Research Advances in the Giant Impact Hypothesis of Moon Formation. Space: Science & Technology, doi:10.34133/space.0153. 10. Sossi, P. A., et al. (2024). Top Theory on Moon’s Formation Might Have No Evidence After All. Referenced in ScienceAlert article (Sep 11, 2024). 11. Rufu, R., et al. (2017). A multiple-impact origin for the Moon. Nature Geoscience, 10, 89–94. 4