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Cited by 50Astro and Planetary SciencePlanetary Science and ExplorationHistory and Developments in Astronomy

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Immediate Origin of the Moon as a Post-impact Satellite

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Kegerreis, J. A., Ruiz-Bonilla, S., Eke, V. R., Massey, R. J., Sandnes, T. D., Teodoro, L. F. A.·2022·The Astrophysical Journal Letters
DOI 10.3847/2041-8213/ac8d96
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Abstract

The Moon is traditionally thought to have coalesced from the debris ejected by a giant impact onto the early Earth. However, such models struggle to explain the similar isotopic compositions of Earth and lunar rocks at the same time as the system’s angular momentum, and the details of potential impact scenarios are hotly debated. Above a high resolution threshold for simulations, we find that giant impacts can immediately place a satellite with similar mass and iron content to the Moon into orbit far outside Earth’s Roche limit. Even satellites that initially pass within the Roche limit can reliably and predictably survive, by being partially stripped and then torqued onto wider, stable orbits. Furthermore, the outer layers of these directly formed satellites are molten over cooler interiors and are composed of around 60% proto-Earth material. This could alleviate the tension between the Moon’s Earth-like isotopic composition and the different signature expected for the impactor. Immediate formation opens up new options for the Moon’s early orbit and evolution, including the possibility of a highly tilted orbit to explain the lunar inclination, and offers a simpler, single-stage scenario for the origin of the Moon.

Overview

CoChat Summary

TL;DR

High-resolution SPH simulations show giant impacts can immediately place Moon-like satellites into wide orbits, with some surviving Roche-limit passage via tidal stripping. This single-stage scenario can produce satellites with Moon-like mass and iron content, outer layers rich in proto-Earth material, and potentially inclined orbits.

Key findings

  • At resolutions above >10^6.5 particles, stable outer satellites form reliably; one example satellite has mass 0.69 M☾ and periapsis 7.1 R⊕, far outside the Roche limit of ∼2.9 R⊕.
  • Satellites that pass inside the Roche limit can survive partial stripping and be torqued outward; survival fraction fits a simple prediction scaling with the cube of initial periapsis, with initial periapses as low as ∼2.4 R⊕ surviving at ≥10% initial mass. One example loses about one-third of its mass, ending at 1.1 M☾ with periapsis raised to 3.1 R⊕.
  • Immediate satellites typically have 30%–40% proto-Earth material in bulk; the outer ∼10% by radius can exceed 60% proto-Earth, and the outer 30% by radius (∼2/3 by mass) averages 40%–50%. Iron content ranges from ∼0.1% to 3%, comparable to the ∼1% lunar core; outer layers are molten at at least 4000 K while deeper interiors are only a few hundred kelvin above near-solidus.
  • A misaligned target spin can produce an inclined satellite; one example has mass 1.4 M☾, periapsis 3.1 R⊕, and inclination 32°.

Methods

  • ∼400 impact simulations using the SWIFT smoothed particle hydrodynamics code, up to 10^8 particles. Base scenario: impact angle β = 45°, contact speed v_c = 1 v_esc (∼9 km s⁻¹), target mass M_t = 0.887 M⊕, impactor mass M_i = 0.133 M⊕, no pre-impact spins; fine suite covers β = 43°–48° and v_c = 0.98–1.04 v_esc, with angular momenta 1.19–1.37 L_EM.
  • Varied impactor mass (0.100 and 0.067 M⊕), pre-impact spins, surface temperatures (1000, 2000, 3000 K), and resolution (10^4–10^8 particles), plus modified SPH schemes.
  • Satellites identified with a friends-of-friends algorithm using linking length 0.017 R⊕ and a minimum of 50 particles; results compared with analytic torque and tidal-stripping predictions.

Limitations

  • Stated: The exact particle-number threshold for resolving satellite formation is left for future work; final satellite masses and orbits are not perfectly converged, and multistage collisions/stripping are chaotic, so small initial changes can have larger consequences.
  • Stated: Long-term evolution is not modeled; bespoke future studies are required to extrapolate outputs to the present day, and the authors did not explore the full variety of initial spins or systematically sample all parameter space.
  • Evident from text: Simulations stop at 90–180 ks (25–50 hr) after impact, so only immediate post-impact evolution is simulated; the varied-mass/spin/temperature suites are described as coarse rather than complete, and Table 1 tabulates only the single most massive satellite, with some scenarios not yet progressed to later re-impact or stripping events.

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Integrity signals

Registry

Crossref · 10.3847/2041-8213/ac8d96

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Figures

Figure 1 Illustrative snapshots from an impact simulation where a satellite is placed directly onto a wide orbit, in this example with the lowest fi nal eccentricity. In the middle panels, the particles that will form the satellite and inner remnant are highlighted in purple and green. The black lines show the estimated orbit. Gray and orange show the proto-Earth ' s core and mantle material, respectively, and brown and yellow the same for Theia. The color luminosity varies slightly with the internal energy. The annotated time is measured from fi rst contact, so the simulation began at -1 hr. An animation is available at http: // icc.dur.ac.uk / giant_impacts / moon_ wide_orbit_slice.mp4, and with the same data rendered in 3D at http: // icc.dur.ac.uk / giant_impacts / moon_wide_orbit_houdini.mp4.
Figure 1 Illustrative snapshots from an impact simulation where a satellite is placed directly onto a wide orbit, in this example with the lowest fi nal eccentricity. In the middle panels, the particles that will form the satellite and inner remnant are highlighted in purple and green. The black lines show the estimated orbit. Gray and orange show the proto-Earth ' s core and mantle material, respectively, and brown and yellow the same for Theia. The color luminosity varies slightly with the internal energy. The annotated time is measured from fi rst contact, so the simulation began at -1 hr. An animation is available at http: // icc.dur.ac.uk / giant_impacts / moon_ wide_orbit_slice.mp4, and with the same data rendered in 3D at http: // icc.dur.ac.uk / giant_impacts / moon_wide_orbit_houdini.mp4.CC-BY · From the PDF
Figure 2 The categorically distinct behavior of outer-satellite formation emerges consistently for resolutions above a threshold of > 10 6.5 particles. Each panel shows a snapshot from simulations of the same scenario at the same time 3.6 hr after impact using different numbers of particles. 10 4 and 10 4.5 particles ( not shown ) behave similarly to 10 5 .
Figure 2 The categorically distinct behavior of outer-satellite formation emerges consistently for resolutions above a threshold of > 10 6.5 particles. Each panel shows a snapshot from simulations of the same scenario at the same time 3.6 hr after impact using different numbers of particles. 10 4 and 10 4.5 particles ( not shown ) behave similarly to 10 5 .CC-BY · From the PDF
Figure 3 The change in mass, periapsis, and orbital eccentricity of satellites that pass through a periapsis near or inside the Roche limit and retain at least 10% of their initial mass, which tends to result in a signi fi cantly wider fi nal orbit following partial tidal stripping. Diamonds and circles show the pre- and post-periapsis satellites, respectively.
Figure 3 The change in mass, periapsis, and orbital eccentricity of satellites that pass through a periapsis near or inside the Roche limit and retain at least 10% of their initial mass, which tends to result in a signi fi cantly wider fi nal orbit following partial tidal stripping. Diamonds and circles show the pre- and post-periapsis satellites, respectively.CC-BY · From the PDF
Figure 4 The convergence and uncertainty of the mass of the initial satellite ( or larger single remnant ) and the periapsis of the fi nal satellite that form in different-resolution simulations of the impact scenario in Figure 2, as a function of the number of particles. The error bars show the standard deviations across eight reoriented repeats, with points for the individual 10 7.5 - and 10 8 -particle simulations.
Figure 4 The convergence and uncertainty of the mass of the initial satellite ( or larger single remnant ) and the periapsis of the fi nal satellite that form in different-resolution simulations of the impact scenario in Figure 2, as a function of the number of particles. The error bars show the standard deviations across eight reoriented repeats, with points for the individual 10 7.5 - and 10 8 -particle simulations.CC-BY · From the PDF
Figure 5 The inclined satellite produced by an impact onto a spinning protoEarth misaligned to Theia ' s orbital angular momentum, shown as in Figure 1. The z ˜ -direction is set as the orientation of the post-impact planet ' s spin angular momentum, which is estimated simply as the total over all particles within 2 R ⊕ . The results are not sensitive to this choice, as using 1.5 R ⊕ or 2.5 R ⊕ only changes the inferred satellite inclination by < 0.5 ° .
Figure 5 The inclined satellite produced by an impact onto a spinning protoEarth misaligned to Theia ' s orbital angular momentum, shown as in Figure 1. The z ˜ -direction is set as the orientation of the post-impact planet ' s spin angular momentum, which is estimated simply as the total over all particles within 2 R ⊕ . The results are not sensitive to this choice, as using 1.5 R ⊕ or 2.5 R ⊕ only changes the inferred satellite inclination by < 0.5 ° .CC-BY · From the PDF
Figure A1. The initial conditions for an impact scenario, to scale, in the protoEarth target ' s rest frame. The angle and speed at fi rst contact, β and v c , are set neglecting any tidal distortion before the collision. The initial separation is set such that the time to impact is 1 hr, as detailed in Kegerreis et al. ( 2020, Appendix A ) , with the velocity at contact in the -x -direction.
Figure A1. The initial conditions for an impact scenario, to scale, in the protoEarth target ' s rest frame. The angle and speed at fi rst contact, β and v c , are set neglecting any tidal distortion before the collision. The initial separation is set such that the time to impact is 1 hr, as detailed in Kegerreis et al. ( 2020, Appendix A ) , with the velocity at contact in the -x -direction.CC-BY · From the PDF
Figure A2. The early orbital evolution of the forming satellite and inner remnant highlighted in matching colors in Figure 1. The panels show the radial distances of the bodies from the central planet, the tangential component of the force from the inner body on the satellite, the change in each body ' s angular momentum and the prediction for that of the satellite from the tangential force ( dashed line ) , the satellite ' s periapsis, and its eccentricity.
Figure A2. The early orbital evolution of the forming satellite and inner remnant highlighted in matching colors in Figure 1. The panels show the radial distances of the bodies from the central planet, the tangential component of the force from the inner body on the satellite, the change in each body ' s angular momentum and the prediction for that of the satellite from the tangential force ( dashed line ) , the satellite ' s periapsis, and its eccentricity.CC-BY · From the PDF
Figure A3. Illustrative snapshots of the fi rst periapsis passage after the satellite-forming initial impact, from a simulation where the fi nal satellite ends up on a stable orbit. Colors and annotations are the same as in Figure 1, except here purple and green highlight the material that will end up in the fi nal satellite and that will be stripped from the initial body, respectively. The dashed line indicates the Roche limit. An animation is available at http: // icc.dur.ac.uk / giant_impacts / moon_strip_ orbit_slice.mp4, and with the same data rendered in 3D at http: // icc.dur.ac.uk / giant_impacts / moon_strip_orbit_houdini.mp4.
Figure A3. Illustrative snapshots of the fi rst periapsis passage after the satellite-forming initial impact, from a simulation where the fi nal satellite ends up on a stable orbit. Colors and annotations are the same as in Figure 1, except here purple and green highlight the material that will end up in the fi nal satellite and that will be stripped from the initial body, respectively. The dashed line indicates the Roche limit. An animation is available at http: // icc.dur.ac.uk / giant_impacts / moon_strip_ orbit_slice.mp4, and with the same data rendered in 3D at http: // icc.dur.ac.uk / giant_impacts / moon_strip_orbit_houdini.mp4.CC-BY · From the PDF
Figure A4. The orbital evolution of the material that survived and that was stripped from the initial satellite in the periapsis passage illustrated in Figure A3, presented as in Figure A2.
Figure A4. The orbital evolution of the material that survived and that was stripped from the initial satellite in the periapsis passage illustrated in Figure A3, presented as in Figure A2.CC-BY · From the PDF
Figure A5. The positions and orbits of the satellites produced by eight reoriented repeats of the same scenario as in Figures 2 and 4 with 10 7 particles, at the same times before ( solid lines and diamonds ) and after ( dashed lines and circles ) the fi rst periapsis tidal-stripping event. The inner and outer gray circles indicate the planet ' s radius and the Roche limit at about 1 and 2.9 R ⊕ , respectively.
Figure A5. The positions and orbits of the satellites produced by eight reoriented repeats of the same scenario as in Figures 2 and 4 with 10 7 particles, at the same times before ( solid lines and diamonds ) and after ( dashed lines and circles ) the fi rst periapsis tidal-stripping event. The inner and outer gray circles indicate the planet ' s radius and the Roche limit at about 1 and 2.9 R ⊕ , respectively.CC-BY · From the PDF
Figure A6. Diagrams for estimating the stripping of material when a satellite passes through periapsis within the Roche limit. Top: notation for the mass lost ( hatched region ) from the tidal force at a distance r from the center of a satellite with radius R and initial mass mi , at a distance d from a planet with mass M . Bottom: notation for the time spent inside the Roche limit, R Roche ( gray circle ) , by a satellite on an orbit ( black ellipse ) with a semimajor axis a , eccentricity e , and periapsis r p < R Roche . f is the complement to the true anomaly, and E is the eccentric anomaly. The dotted line shows the auxiliary circle.
Figure A6. Diagrams for estimating the stripping of material when a satellite passes through periapsis within the Roche limit. Top: notation for the mass lost ( hatched region ) from the tidal force at a distance r from the center of a satellite with radius R and initial mass mi , at a distance d from a planet with mass M . Bottom: notation for the time spent inside the Roche limit, R Roche ( gray circle ) , by a satellite on an orbit ( black ellipse ) with a semimajor axis a , eccentricity e , and periapsis r p < R Roche . f is the complement to the true anomaly, and E is the eccentric anomaly. The dotted line shows the auxiliary circle.CC-BY · From the PDF
Figure A7. The fractional change in mass of satellites that are partially stripped through periapsis. The black line is the predicted power law of / µ m m r f i p 3 , scaled in magnitude to fi t the slow-spinning initial satellites. The crosses show the model predictions for each simulation using Equations ( 1 ) and ( A2 ) .
Figure A7. The fractional change in mass of satellites that are partially stripped through periapsis. The black line is the predicted power law of / µ m m r f i p 3 , scaled in magnitude to fi t the slow-spinning initial satellites. The crosses show the model predictions for each simulation using Equations ( 1 ) and ( A2 ) .CC-BY · From the PDF

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Metadata

Authors
Kegerreis, J. A., Ruiz-Bonilla, S., Eke, V. R., Massey, R. J., Sandnes, T. D., & Teodoro, L. F. A.
Affiliations
  • Ames Research Center (US)
  • Durham University (GB)
Corresponding author
Kegerreis, J. A.
ORCID
Venue
The Astrophysical Journal Letters
Publisher
American Astronomical Society
Published
2022-10-01
Volume
937
Issue
2
Pages
L40
ISSN
  • 2041-8205 (ISSN-L)
  • 2041-8213
DOI
10.3847/2041-8213/ac8d96
OpenAlex
W4301395651
Cited by
50
References
53
Citations by year
2026: 13 · 2025: 12 · 2024: 18 · 2023: 7
FWCI
4.16
Type
journal article
Language
en
Open access
Licence
Locations
  • The Astrophysical Journal Letters (publishedVersion, cc-by)
  • ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam) (acceptedVersion, cc-by-sa)
  • arXiv (Cornell University) (submittedVersion)
  • Durham Research Online (Durham University) (submittedVersion, cc-by)
  • arXiv (Cornell University)
Funders
UKRI ∣ Science and Technology Facilities Council (ST/P000541/1, ST/T000244/1, ST/N001494/1, ST/T002565/1, ST/P006744/1, ST/T506047/1, ST/V506643/1, ST/K00042X/1, ST/P002293/1, ST/R002371/1, ST/S002502/1, ST/R000832/1)
Topics
  • Physical Sciences › Earth and Planetary Sciences › Space and Planetary Science › Astro and Planetary Science
  • Physical Sciences › Earth and Planetary Sciences › Space and Planetary Science › Planetary Science and Exploration
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › History and Developments in Astronomy
Keywords
Moon formation, giant impact hypothesis, Roche limit, impactor composition

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Kegerreis, J. A., Ruiz-Bonilla, S., Eke, V. R., Massey, R. J., Sandnes, T. D., & Teodoro, L. F. A. (2022). Immediate Origin of the Moon as a Post-impact Satellite. The Astrophysical Journal Letters. https://doi.org/10.3847/2041-8213/ac8d96

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