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Reconstructing the late-accretion history of the Moon


The importance of highly siderophile elements (HSEs; namely, gold, iridium, osmium, palladium, platinum, rhenium, rhodium and ruthenium) in tracking the late accretion stages of planetary formation has long been recognized. However, the precise nature of the Moon’s accretional history remains enigmatic. There is a substantial mismatch in the HSE budgets of the Earth and the Moon, with the Earth seeming to have accreted disproportionally more HSEs than the Moon1. Several scenarios have been proposed to explain this conundrum, including the delivery of HSEs to the Earth by a few big impactors1, the accretion of pebble-sized objects on dynamically cold orbits that enhanced the Earth’s gravitational focusing factor2, and the ‘sawtooth’ impact model, with its much reduced impact flux before about 4.10 billion years ago3. However, most of these models assume a high impactor-retention ratio (the fraction of impactor mass retained on the target) for the Moon. Here we perform a series of impact simulations to quantify the impactor-retention ratio, followed by a Monte Carlo procedure considering a monotonically decaying impact flux4, to compute the impactor mass accreted into the lunar crust and mantle over their histories. We find that the average impactor-retention ratio for the Moon’s entire impact history is about three times lower than previously estimated1,3. Our results indicate that, to match the HSE budgets of the lunar crust and mantle5,6, the retention of HSEs should have started 4.35 billion years ago, when most of the lunar magma ocean was solidified7,8. Mass accreted before this time must have lost its HSEs to the lunar core, presumably during lunar mantle crystallization9. The combination of a low impactor-retention ratio and a late retention of HSEs in the lunar mantle provides a realistic explanation for the apparent deficit of the Moon’s late-accreted mass relative to that of the Earth.

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The data that support the findings of this study are available from the corresponding author on request.

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  1. 1.

    Bottke, W. F. et al. Stochastic late accretion to Earth, the Moon, and Mars. Science 330, 1527–1530 (2010).

  2. 2.

    Schlichting, H. E., Warren, P. H. & Yin, Q.-Z. The last stages of terrestrial planet formation: dynamical friction and the late veneer. Astrophys. J. 752, 8–16 (2012).

  3. 3.

    Morbidelli, A. et al. A sawtooth-like timeline for the first billion years of lunar bombardment. Earth Planet. Sci. Lett. 355-356, 144–151 (2012).

  4. 4.

    Neukum, G., Ivanov, B. A. & Hartmann, W. K. Cratering records in the inner solar system in relation to the lunar reference system. Space Sci. Rev. 96, 55–86 (2001).

  5. 5.

    Day, J. M. D. & Walker, R. J. Highly siderophile element depletion in the Moon. Earth Planet. Sci. Lett. 423, 114–124 (2015).

  6. 6.

    Day, J. M. D. et al. Osmium isotope and highly siderophile element systematics of the lunar crust. Earth Planet. Sci. Lett. 289, 595–605 (2010).

  7. 7.

    Elkins-Tanton, L., Burgess, S. & Yin, Q. Z. The lunar magma ocean: reconciling the solidification process with lunar petrology and geochronology. Earth Planet. Sci. Lett. 304, 326–336 (2011).

  8. 8.

    Borg, L. E. et al. Chronological evidence that the Moon is either young or did not have a global magma ocean. Nature 477, 70–72 (2011).

  9. 9.

    Morbidelli, A. et al. The timeline of the lunar bombardment: revisited. Icarus 305, 262–276 (2018).

  10. 10.

    Canup, R. M. Forming a Moon with an Earth-like composition via a giant impact. Science 338, 1052–1055 (2012).

  11. 11.

    Cuk, M. & Stewart S. T. Making the Moon from a fast-spinning Earth: a giant impact followed by resonant despinning. Science 338, 1047–1052 (2012).

  12. 12.

    Jones, J. H. & Drake, M. J. Core formation and Earth’s late accretionary history. Nature 323, 470–471 (1986).

  13. 13.

    Morgan, J. W., Walker, R. J., Brandon, A. D. & Horan, M. F. Siderophile elements in Earth’s upper mantle and lunar breccias: data synthesis suggests manifestations of the same late influx. Meteorit. Planet. Sci. 36, 1257–1275 (2001).

  14. 14.

    Walker, R. J. Highly siderophile elements in the Earth, Moon and Mars: update and implications for planetary accretion and differentiation. Chem. Erde Geochem. 69, 101–125 (2009).

  15. 15.

    Warren, P. H., Jerde, E. A. & Kallemeyn, G. W. Prisitine Moon rocks: Apollo 17 anorthosites. Proc. Lunar Planet. Sci. Conf. 21, 51–61 (1991).

  16. 16.

    Ryder, G. Mass flux in the ancient Earth-Moon system and benign implications for the origin of life on Earth. J. Geophys. Res. 107 (E4), 5022 (2002).

  17. 17.

    Kraus, R. G. et al. Impact vaporization of planetesimal cores in the late stages of planet formation. Nat. Geosci. 8, 269–272 (2015).

  18. 18.

    Artemieva, N. A. & Shuvalov, V. V. Numerical simulation of high-velocity impact ejecta following falls of comets and asteroids onto the Moon. Sol. Syst. Res. 42, 329–334 (2008).

  19. 19.

    Elbeshausen D. et al. The transition from circular to elliptical impact crater. J. Geophys. Res. 118, 2295–2309 (2013).

  20. 20.

    Le Feuvre, M. & Wieczorek, M. A. Nonuniform cratering of the Moon and a revised crater chronology of the inner solar system. Icarus 214, 1–20 (2011).

  21. 21.

    Shoemaker, E. M. in Physics and Astronomy of the Moon (ed. Kopal, Z.) 283–359 (Academic, 1962).

  22. 22.

    Holsapple, K. A. & Housen, K. R. A crater and its ejecta: an interpretation of deep impact. Icarus 191, 586–597 (2007).

  23. 23.

    Wieczorek, M. A. et al. The crust of the Moon as seen by GRAIL. Science 339, 671–675 (2013).

  24. 24.

    Norman, M. D. et al. Chronology, geochemistry, and petrology of a ferroan noritic anorthosite clast from Descartes breccia 67215: clues to the age, origin, structure, and impact history of the lunar crust. Meteorit. Planet. Sci. 38, 645–661 (2003).

  25. 25.

    Kleine, T. et al. Hf-W chronology of the accretion and early evolution of asteroids and terrestrial planets. Geochim. Cosmochim. Acta 73, 5150–5188 (2009).

  26. 26.

    Borg, L. E. et al. A review of lunar chronology revealing a preponderance of 4.34–4.37 Ga ages. Meteorit. Planet. Sci. 50, 715–732 (2015).

  27. 27.

    Nemchin, A. et al. Timing of crystallization of the lunar magma ocean constrained by the oldest ziron. Nat. Geosci. 2, 133–136 (2009).

  28. 28.

    Rubie, D. C. et al. Highly siderophile elements were stripped from Earth’s mantle by iron sulfide segregation. Science 353, 1141–1144 (2016).

  29. 29.

    Miljković, K. et al. Excavation of the lunar mantle by basin-forming impact events on the Moon. Earth Planet. Sci. Lett. 409, 243–251 (2015).

  30. 30.

    Neumann, G. A. et al. Lunar impact basins revealed by Gravity Recovery and Interior Laboratory measurements. Sci. Adv. 1, e1500852 (2015).

  31. 31.

    Frey, H. in Recent Advances and Current Research Issues in Lunar Stratigraphy Vol. 477 (eds Ambrose, W. A. & Williams, D. A.) 53–75 (Geological Society of America, 2011).

  32. 32.

    Kamata, S. et al. The relative timing of lunar magma ocean solidification and the late heavy bombardment inferred from highly degraded impact basin structures. Icarus 250, 492–503 (2015).

  33. 33.

    Elkins-Tanton, L. Linked magma ocean solidification and atmospheric growth for Earth and Mars. Earth Planet. Sci. Lett. 271, 181–191 (2008).

  34. 34.

    Day, J. M. D., Pearson, D. G. & Taylor, L. A. Highly siderophile element constraints on accretion and differentiation of the Earth-Moon system. Science 315, 217–219 (2007).

  35. 35.

    Day, J. M. D., Brandon, A. D. & Walker, R. J. Highly siderophile elements in Earth, Mars, the Moon, and Asteroids. Rev. Mineral. Geochem. 81, 161–238 (2016).

  36. 36.

    Day, J. M. D. Geochemical constraints on residual metal and sulfide in the sources of lunar mare basalts. Am. Mineral. 103, 1734–1740 (2018).

  37. 37.

    Walker, R. J., Horan, M. F., Shearer, C. K. & Papike, J. J. Low abundances of highly siderophile elements in the lunar mantle: evidence for prolonged late accretion. Earth Planet. Sci. Lett. 224, 399–413 (2004).

  38. 38.

    Taylor, G. J. & Wieczorek, M. A. Lunar bulk chemical composition: a post-Gravity recovery and Interior Laboratory reassessment. Phil. Trans. A 372, 20130242 (2014).

  39. 39.

    Morgan, J. W., Gros, J., Takahashi, H. & Hertogen, H. Lunar breccia 73215: siderophile and volatile elements. Proc. Lunar Sci. Conf. 7, 2189–2199 (1976).

  40. 40.

    Gros, J., Tahahashi, H., Hertogen, J. Morgan, J. W. & Anders, E. Composition of the projectiles that bombarded the lunar highlands. Proc. Lunar Sci. Conf. 7, 2403–2425 (1976).

  41. 41.

    Norman, M. D., Bennett, V. C. & Ryder, G. Targeting the impactors: siderophile element signatures of lunar impact melts from Serenatatis. Earth Planet. Sci. Lett. 202, 217–228 (2002).

  42. 42.

    Puchtel, I. S. et al. Osmium isotope and highly siderophile element systematics of lunar impact melt breccias: implications for the late accretion history of the Moon and Earth. Geochim. Cosmochim. Acta 72, 3022–3042 (2008).

  43. 43.

    Gleißner, P. & Becker, H. Formation of Apollo 16 impactites and the composition of late accreted material: constraints from Os isotopes, highly siderophile elements and sulfur abundances. Geochim. Cosmochim. Acta 200, 1–24 (2017).

  44. 44.

    Schultz, P. H. & Gault, D. E. Prolonged global catastrophes from oblique impacts. Spec. Pap. Geol. Soc. Am. 247, 239–262 (1990).

  45. 45.

    Daly, R. T. & Shultz, P. H. Predictions for impactor contamination on Ceres based on hypervelocity impact experiments. Geophys. Res. Lett. 42, 7890–7898 (2015).

  46. 46.

    Daly, R. T. & Shultz, P. H. Delivering a projectile component to the vestan regolith. Icarus 264, 9–19 (2016).

  47. 47.

    Daly, R. T. & Schultz, P. H. Projectile preservation during oblique hypervelocity impacts. Meteorit. Planet. Sci. 54, 1364–1390 (2018).

  48. 48.

    Thompson, S. L. & Lauson, H. S. Improvements in the CHART D Radiation- Hydrodynamic Code III: Revised Analytic Equations of State. Report SC-RR-71 0714 (Sandia National Laboratory, 1972).

  49. 49.

    Benz, W. et al. The origin of the Moon and the single-impact hypothesis III. Icarus 81, 113–131 (1989).

  50. 50.

    Lee, D.-C. & Halliday, A. N. Core formation on Mars and differentiated asteroids. Nature 388, 854–857 (1997).

  51. 51.

    Davison, T. M. et al. Numerical modeling of oblique hypervelocity impacts on strong ductile targets. Meteorit. Planet. Sci. 46, 1510–1524 (2011).

  52. 52.

    Potter, R. W. et al. in Large Meteorite Impacts and Planetary Evolution V (eds Osinski, G. R. & Kring, D. A.) 99–113 (Lunar and Planetary Institute, 2015).

  53. 53.

    Marchi, S. et al. A new chronology for the Moon and Mercury. Astron. J. 137, 4936–4948 (2009).

  54. 54.

    Collins, G. S., Melosh, H. J. & Ivanov, B. A. Modeling damage and deformation in impact simulations. Meteorit. Planet. Sci. 39, 217–231 (2004).

  55. 55.

    Ahrens, T. J. & O’Keefe, J. D. Shock melting and vaporization of lunar rocks and minerals. Moon 4, 214–249 (1972).

  56. 56.

    Pierazzo, E., Vickery, A. M. & Melosh, H. J. A reevaluation of impact melt product. Icarus 127, 408–423 (1997).

  57. 57.

    Pierazzo, E. & Melosh, H. J. Hydrocode modeling of oblique impacts: the fate of the projectile. Meteorit. Planet. Sci. 35, 117–130 (2000).

  58. 58.

    Marchi, S. et al. Widespread mixing and burial of Earth’s hadean crust by asteroid impacts. Nature 511, 578–582 (2014).

  59. 59.

    Schultz, P. H. & Sugita, S. Fate of the Chicxulub impactor. In 28th Annu. Lunar Planet. Sci. Conf. 1261–1262 (1997).

  60. 60.

    Collins, G. S., Miljkovic, K. & Davison, T. M. The effect of planetary curvature on impact crater ellipticity. EPSC Abstr. 8, EPSC2013-989 (2013).

  61. 61.

    Bottke, W. F. et al. Dating the Moon-forming impact event with asteroidal meteorites. Science 348, 321–323 (2015).

  62. 62.

    Laneuville, M., Wieczorek, M., and Breuer, D. Asymmetric thermal evolution of the Moon. J. Geophys. Res. Planets 118, 1435–1452 (2013).

  63. 63.

    Ivanov, B. A. & Artemieva, N. A. in Catastrophic Events and Mass Extinctions: Impacts and Beyond Vol. 356 (eds Koeberl, C. & MacLeod, K. G.) 619–630 (Geological Society of America, 2002).

  64. 64.

    Miljkovic, K. et al. Asymmetric distribution of lunar impact basins caused by variations in target properties. Science 342, 724–726 (2013).

  65. 65.

    Freed, A. M. et al. The formation of lunar mascon basins from impact to contemporary form. J. Geophys. Res. 119, 2378–2397 (2014).

  66. 66.

    Potter, R. W. K. et al. Constraining the size of the South Pole-Aitken basin impact. Icarus 220, 730–743 (2012).

  67. 67.

    Zhu, M. -H. et al. Numerical modeling of the ejecta distribution and formation of the Orientale basin. J. Geophys. Res. 120, 2118–2134 (2015).

  68. 68.

    Melosh, H. J. Impact Cratering: A Geological Process (Oxford Univ. Press, 1989).

  69. 69.

    Joy, K. H. et al. Direct detection of projectile relics from the end of the lunar basin-forming epoch. Science 336, 1426–1429 (2012).

  70. 70.

    Liu, J. G. et al. Diverse impactors in Apollo 15 and 16 impact melt rocks: evidence from osmium isotopes and highly siderophile elements. Geochim. Cosmochim. Acta 155, 122–153 (2015).

  71. 71.

    Croft, S. K. The scaling of complex craters. Proc. Lunar Planet. Sci. Conf. 16, 828–842 (1985).

  72. 72.

    McKinnon, W. B. & Schenk, P. M. Ejecta blanket scaling on the Moon and Mercury and interferences for projectile populations. Lunar Planet. Sci. XVI, 544–545 (1985).

  73. 73.

    Wilhelms, D. E. The Geologic History of the Moon. USGS Professional Paper 1348 (US Geological Survey, 1987).

  74. 74.

    Miljkovic, K. et al. Elusive formation of impact basins on the young Moon. In Proc. 48th Lunar Planetary Science Conference 1361 (2017).

  75. 75.

    Gault, D. E. & Wedekind, J. A. Experimental studies of oblique impact. In Proc. 9th  Lunar Planetary Science Conference 3843–3875 (1978).

  76. 76.

    Pierazzo, E. & Melosh, H. J. Melt production in oblique impacts. Icarus 145, 252–261 (2000).

  77. 77.

    Pierazzo, E. & Melosh, H. J. Understanding oblique impacts from experiments, observations and modeling. Annu. Rev. Earth Planet. Sci. 28, 141–167 (2000).

  78. 78.

    Jones, A. P. et al. Impact induced melting and the development of large igneous provinces. Earth Planet. Sci. Lett. 202, 551–561 (2002).

  79. 79.

    Kendall, J. D. & Melosh, H. J. Differentiated planetesimals impacts into a terrestrial magma ocean: fate of the iron core. Earth Planet. Sci. Lett. 448, 24–33 (2016).

  80. 80.

    Shuvalov, V. V. et al. Crater ejecta: markers of impact catastrophes. Phys. Solid Earth 48, 241–255 (2012).

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We thank J. M. D. Day and R. J. Walker for useful discussions. We acknowledge the developers of iSALE (www.isale-code.de), in particular D. Elbeshausen, who developed iSALE-3D. M.-H.Z. is supported by the Science and Technology Development Fund of Macau (079/2018/A2). K.W., H.B., N.A. and M.-H.Z. are funded by Deutsche Forschungsgeimenschaft (DFG) grant SFB-TRR 170 (A4, C2), TRR-170 Pub. No. 55. Q.-Z.Y. is funded by the NASA Emerging Worlds Program (NNX16AD34G).

Peer review information

Nature thanks James Day and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information

M.-H.Z. conceived the idea and performed the impact simulations. N.A. performed the Monte Carlo modelling. M.-H.Z., A.M., Q.-Z.Y, H.B. and K.W. interpreted the results. All authors contributed to the discussion of the results and wrote the manuscript.

Competing interests

The authors declare no competing interests.

Correspondence to Meng-Hua Zhu.

Extended data figures and tables

Extended Data Fig. 1 Thermal profiles of the Moon.

Two possible thermal profiles (TP1 and TP2) for the Moon, which we use in this study to test the effects of temperature on the impactor-retention ratio.

Extended Data Fig. 2 Effects of lunar thermal profiles on the impactor-retention ratio.

We calculated impactor-retention ratios for oblique impacts of impactors with diameters (d) of 210 km and velocities (v) of 15 km s−1. The impact angles were varied from 15° to 90°. TP1 and TP2 represent the temperature profiles used here (Extended Data Fig. 1).

Extended Data Fig. 3 Fraction of retained impactor material deposited within the transient crater in all simulations.

In our simulations, this fraction is between 0.9 and 1.0 for impact angles greater than 20° (relative to the lunar surface). For large impactors (d > 100 km) with impact angles smaller than 20°, the fraction of retained material within the transient cavity is less than 0.9. The dashed line represents the fraction of 0.96 that we use in our calculations (see Fig. 3) for simplicity. The dotted line represents the fraction of 0.90 used in Extended Data Fig. 6. The numbers in the key represent the impactor diameter (D) and impact velocity (V).

Extended Data Fig. 4 Lunar impact fluxes.

The differential number of lunar craters larger than 20 km as a function of time for the production functions discussed in the text4,9.

Extended Data Fig. 5 Two scenarios involving a differentiated impactor hitting the Moon.

The arrows represent the impact direction and the lines show the extent of interaction of the impactor core with the Moon. When the core of a differentiated impactor is accreted to the Moon (a), we record the total mass of impactors accreted to the Moon. However, when the impactor’s core is not accreted to the Moon (b), we do not record any accreted mass.  This simplification is justified because in reality the HSEs of a differentiated impactor should almost entirely be dominated by its core.

Extended Data Fig. 6 Cumulative impactor masses that hit and are accreted into the Moon.

a, b, The total impactor masses hitting the Moon (blue) and being accreted to the Moon (purple) from different starting times (between 4.5 Gyr to 3.5 Gyr ago) to the present day, for assumed crustal thicknesses of 34 km (a) and 43 km (b). The cumulative masses accreted to the lunar crust (orange) and mantle (green) are estimated separately. This figure is similar to Fig. 3, except that we assume that around 10% of the retained impactor material is deposited beyond the transient crater and mixed with the crust.

Extended Data Table 1 Parameters of exponent functions for impactor-retention ratio
Extended Data Table 2 Model parameters used in iSALE-3D simulations

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Fig. 1: Impactor-retention ratios for different velocities, impact angles, and ratios of impactor-to-target sizes.
Fig. 2: Average impactor-retention ratios as a function of time.
Fig. 3: Cumulative impactor-mass distribution as a function of time.
Extended Data Fig. 1: Thermal profiles of the Moon.
Extended Data Fig. 2: Effects of lunar thermal profiles on the impactor-retention ratio.
Extended Data Fig. 3: Fraction of retained impactor material deposited within the transient crater in all simulations.
Extended Data Fig. 4: Lunar impact fluxes.
Extended Data Fig. 5: Two scenarios involving a differentiated impactor hitting the Moon.
Extended Data Fig. 6: Cumulative impactor masses that hit and are accreted into the Moon.


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