A "New Hope" for Moon Formation: Presenting a Multiple Impact Pathway

The leading hypothesis for the origin of the Moon, that of a single giant impact, faces significant challenges. These include either the need for an impactor with a near-identical composition to Earth or an extremely high-mass or high-energy impact to achieve near-complete material mixing. In this paper we explore an alternative, the “multiple impact hypothesis”, which relaxes the compositional constraints on both the target and projectile, and allows for the consideration of more probable, less extreme impacts that steadily grow the Earth and Moon to their current size over several impact events. Using the hydrodynamical code SWIFT, we simulate “chains” of impacts and follow the growth of a moon around a planet analogous to our own. Our results demonstrate that chains of three or more impacts can produce systems comparable to the Earth-Moon system whilst achieving higher compositional similarities than the canonical giant impact scenario. This presents the multiple impact hypothesis as a promising alternative to the single large impact scenario for the origin of the Moon.

💡 Research Summary

The paper addresses two long‑standing challenges to the canonical single‑giant‑impact hypothesis for the origin of the Moon: (1) the near‑identical isotopic composition of Earth and Moon, which requires an impactor with a composition almost indistinguishable from Earth’s, and (2) the need to reproduce the present Earth‑Moon angular momentum without invoking unlikely high‑energy, high‑angular‑momentum collisions. To overcome these constraints, the authors propose a “multiple impact hypothesis” in which a series of moderate‑size collisions, each contributing a fraction of the final mass, gradually builds both the Earth and its satellite.

Methodology
The study uses a suite of smoothed particle hydrodynamics (SPH) simulations performed with the modern code SWIFT. Impact sequences (“chains”) consist of four successive collisions, and twelve independent chains are generated, yielding 48 individual impact events. The initial target mass for the first impact is set to 0.569 M⊕, reflecting the typical mass of a proto‑Earth when it first experiences moderate‑mass impacts in N‑body planet‑formation simulations (Carter et al. 2015). All targets are given a rapid three‑hour rotation period, roughly half of the breakup limit, to enhance the amount of material that can be lofted into orbit during an impact.

Impactors are drawn from a mass distribution derived from the same N‑body simulations, limited to masses ≥ 0.04 M⊕ because smaller bodies do not generate sufficient debris disks. Each impact is assigned the most probable geometry: a 45° impact angle (impact parameter 0.707) and a velocity equal to the mutual escape speed of the target‑impactor pair. This choice reduces the dimensionality of the parameter space while still representing realistic collisions.

Each simulation contains about 600 000 SPH particles, with a cubic‑spline kernel and a maximum smoothing length of 0.2 R⊕, giving a density floor of ~2.2 kg m⁻³. The target and impactor are built as two‑layer bodies (30 % iron core, 70 % forsterite mantle) using the Woma tool, with a temperature–density relation T ∝ ρ² and a surface temperature of 2000 K.

Post‑impact analysis proceeds by identifying the remnant planet’s centre (lowest gravitational potential), defining its radius where the smoothed density drops below 250 kg m⁻³, and separating particles into three categories: bound to the planet, unbound, or residing in a circumplanetary disk (periapsis larger than the planet’s radius). The disk’s total mass (M_d) and angular momentum (L_d) are computed, and the expected moonlet mass (M_moonlet) is estimated using the semi‑analytical relation of Salmon & Canup (2012), which links disk mass and angular momentum to the mass of a satellite forming at ~3.2 R⊕. An escaped‑mass fraction of 5 % of the disk is assumed. The moonlet is then inserted as a single massive particle on a circular orbit at 8 R⊕, interacting only gravitationally with the rest of the system. After each impact the planet’s spin is reset to the three‑hour period, and the next impact uses the updated planet mass and the same impact geometry.

Composition is tracked by tagging each particle with its origin (original target or one of the four impactors). Because the final Earth and Moon are mixtures of five distinct sources, the authors introduce a compositional “distance” d_c, defined as the Euclidean distance between the vectors of source fractions in the disk and in the planet. d_c = 0 indicates identical source contributions; the maximum possible value for N = 4 impactors is √N ≈ 2.

Results
Across the twelve chains, the final planetary masses range from 0.9 to 1.1 M⊕ (relative to the modern Earth) and the final moonlet masses from 0.8 to 1.2 M_Moon. The iron fraction of the disks (R_Fe) lies between 0.10 and 0.20, consistent with the Moon’s volatile‑depleted nature. The total angular momentum of the planet‑moon‑disk system after the fourth impact is typically 0.9–1.2 times the present Earth‑Moon angular momentum, despite the fact that angular momentum is not conserved between chain links (the spin is reset after each impact).

The compositional distance d_c averages 0.42, substantially lower than the ∼5 % isotopic deviation (δ_f) reported for single‑giant‑impact models. This demonstrates that multiple moderate collisions naturally blend material from several impactors, producing a Moon whose bulk composition closely matches that of the Earth without requiring the impactor to share Earth’s isotopic signature.

Interpretation
The authors argue that (i) a series of moderate impacts can cumulatively eject enough material into orbit to build a lunar‑mass satellite, (ii) the repeated mixing of material from different impactors reduces isotopic disparities, and (iii) the rapid initial rotation of the proto‑Earth enhances disk production, allowing the system to achieve the observed angular momentum without invoking extreme impact parameters. They acknowledge simplifications: fixed impact angle and speed, a constant spin reset, and the use of an analytic moonlet‑mass prescription rather than a full N‑body accretion model. Moreover, long‑term tidal evolution and the stability of the final Earth‑Moon configuration are not addressed.

Conclusion
The study presents a quantitative demonstration that a “multiple impact” pathway, involving as few as three to four moderate‑mass collisions, can reproduce the key dynamical and compositional properties of the present Earth‑Moon system. By relaxing the stringent compositional constraints of the canonical giant‑impact scenario and allowing more probable impact conditions, the multiple‑impact hypothesis emerges as a viable alternative. Future work should explore a broader range of impact angles, spin states, and post‑impact tidal evolution to fully assess the robustness of this pathway.