Article | Published:

Terrestrial magma ocean origin of the Moon


A conceptual framework for the origin of the Moon must explain both the chemical and the mechanical characteristics of the Earth–Moon system to be viable. The classic concept of an oblique giant impact explains the large angular momentum and the lack of a large iron-rich core to the Moon, but in this scenario it is difficult to explain the similarity in the isotopic compositions of the Earth and Moon without violating the angular momentum constraint. Here we propose that a giant, solid impactor hit the proto-Earth while it was covered with a magma ocean, under the conventional collision conditions. We perform density-independent smoothed particle hydrodynamic collision simulations with an equation of state appropriate for molten silicates. These calculations demonstrate that, because of the large difference in shock heating between silicate melts and solids (rocks), a substantial fraction of the ejected, Moon-forming material is derived from the magma ocean, even in a highly oblique collision. We show that this model reconciles the compositional similarities and differences between the Moon and Earth while satisfying the angular momentum constraint.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Data availability

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

Code availability

The codes used to generate these results are available from the corresponding author on request.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


  1. 1.

    Ringwood, A. E. Origin of the Earth and Moon (Springer, 1979).

  2. 2.

    Stevenson, D. J. Origin of the moon—the collision hypothesis. Annu. Rev. Earth Planet. Sci. 15, 271–315 (1987).

  3. 3.

    Canup, R. M. Dynamics of lunar formation. Annu. Rev. Astron. Astrophys. 42, 441–475 (2004).

  4. 4.

    Wetherill, G. W. Occurrence of giant impacts during the growth of the terrestrial planets. Science 228, 877–879 (1985).

  5. 5.

    Hayashi, C., Nakazawa, K. & Nakagawa, Y. in Protoplanets and Planets II (eds Black, D. C. & Matthews, M. S.) 1100–1153 (University of Arizona Press, 1985).

  6. 6.

    Hartmann, W. K. & Davis, D. R. Satellite-sized planetesimals and lunar origin. Icarus 24, 504–515 (1975).

  7. 7.

    Cameron, A. G. W. & Ward, W. R. The origin of the Moon. Lunar Planetary Sci. Conf. 7, 120–122 (1976).

  8. 8.

    Canup, R. M. Simulations of a late lunar-forming impact. Icarus 168, 433–456 (2004).

  9. 9.

    Benz, W., Slattery, W. L. & Cameron, A. G. W. The origin of the moon and the single-impact hypothesis I. Icarus 66, 515–535 (1986).

  10. 10.

    Zhang, J., Dauphas, N., Davis, A. M., Leya, I. & Fedkin, A. The proto-Earth as a significant source of lunar material. Nat. Geosci. 5, 251–255 (2012).

  11. 11.

    Dauphas, N., Burkhardt, C., Warren, P. H. & Teng, F.-Z. Geochemical arguments for an Earth-like Moon-forming impactor. Phil. Trans. R. Soc. Lond. A372, 20130244 (2014).

  12. 12.

    Young, E. D. et al. Oxygen isotopic evidence for vigorous mixing during the Moon-forming giant impact. Science 351, 493–496 (2016).

  13. 13.

    Herwartz, D., Pack, A., Friedrichs, B. & Bischoff, A. Identification of the giant impactor Theia in lunar rocks. Science 344, 1146–1150 (2014).

  14. 14.

    Melosh, H. J. New approaches to the Moon’s isotopic crisis. Phil. Trans. R. Soc. Lond. A372, 20130168 (2014).

  15. 15.

    Canup, R. M. Forming a Moon with an Earth-like composition via a giant impact. Science 388, 1052–1055 (2012).

  16. 16.

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

  17. 17.

    Reufer, A., Meier, M. M. M., Benz, W. & Wieler, R. A hit-and-run giant impact scenario. Icarus 221, 296–299 (2012).

  18. 18.

    Meier, M. M. M., Reufer, A. & Wieler, R. On the origin and composition of Theia: constraints from new models of the giant impact. Icarus 242, 316–328 (2014).

  19. 19.

    Rufu, R., Aharonson, O. & Perets, H. B. A multiple-impact origin for the Moon. Nat. Geosci. 10, 89–94 (2017).

  20. 20.

    Pahlevan, K. & Stevenson, D. J. Equilibration in the aftermath of the lunar-forming giant impact. Earth Planet. Sci. Lett. 262, 438–449 (2007).

  21. 21.

    Nakajima, M. & Stevenson, D. J. Investigation of the initial state of the Moon-forming disk: bridging SPH simulations and hydrostatic models. Icarus 233, 259–267 (2014).

  22. 22.

    Kaib, N. A. & Cowan, N. B. The feeding zones of terrestrial planets and insights into Moon formation. Icarus 252, 161–174 (2015).

  23. 23.

    Khan, A., Maclennan, J., Taylor, S. R. & Connoly, J. A. D. Are the Earth and the Moon compositionally alike? Inference on lunar composition and implications for lunar origin and evolution from geophysical modeling. J. Geophys. Res. (2006).

  24. 24.

    Sakai, R., Nagahara, H., Ozawa, K. & Tachibana, S. Composition of the lunar magma ocean constrained by the conditions for the crust formation. Icarus 229, 45–56 (2014).

  25. 25.

    Kuskov, O. L., Kronrod, V. A. & Kronrod, E. V. Thermo-chemical constraints on the interior structure and composition of the lunar mantle. Phys. Earth Planet. Inter. 235, 84–95 (2014).

  26. 26.

    Hosono, N., Saitoh, T., Makino, J., Genda, H. & Ida, S. The giant impact simulations with density independent smoothed particle hydrodynamics. Astrophys. J. 271, 131–157 (2016).

  27. 27.

    Tillotson, J. H. Metallic Equation of State for Hypervelocity Impact Report GA-3216 (General Dynamics, General Atomic Division, 1962).

  28. 28.

    Thompson, S. L. ANEOS Analytic Equations of State for Shock Physics Codes Input Manual 76 (Department of Energy, 1990);

  29. 29.

    Collins, G. S. & Melosh, H. J. Improvements to ANEOS for multiple phase transitions. Lunar Planetary Sci. Conf. 45, 2664 (2014).

  30. 30.

    Nakajima, M. & Stevenson, D. J. Melting and mixing states of the Earth’s mantle after the Moon-forming impact. Earth Planet. Sci. Lett. 427, 286–295 (2015).

  31. 31.

    Melosh, H. J. A hypercode equation of state for SiO2. Meteorit. Planet. Sci. 42, 2079–2098 (2007).

  32. 32.

    Benz, W., Cameron, A. G. W. & Melosh, H. J. The origin of the Moon and the single-impact hypothesis. III. Icarus 81, 113–131 (1989).

  33. 33.

    Canup, R. M. Lunar-forming impacts: processes and alternatives. Phil. Trans. R. Soc. Lond. A372, 20130175 (2014).

  34. 34.

    Karato, S. Asymmetric shock heating and the terrestrial magma ocean origin of the Moon. Proc. Jpn Acad. B90, 97–103 (2014).

  35. 35.

    Sasaki, S. & Nakazawa, K. Metal-silicate fractionation in the growing Earth: energy source for the terrestrial magma ocean. J. Geophys. Res. 91, 9231–9238 (1986).

  36. 36.

    Hayashi, C., Nakazawa, K. & Mizuno, H. Earth’s melting due to the blanketing effect of the primordial dense atmosphere. Earth Planet. Sci. Lett. 43, 22–28 (1979).

  37. 37.

    Elkins-Tanton, L. Magma oceans in the inner solar system. Annu. Rev. Earth Planet. Sci. 40, 113–139 (2012).

  38. 38.

    Solomatov, V. S. in Treatise on Geophysics Vol. 9 (ed. Schubert, G.) 82–103 (Elsevier, 2015).

  39. 39.

    Hosono, N., Saitoh, T. & Makino, J. Density-independent smoothed particle hydrodynamics for a non-ideal equation of state. Publ. Astron. Soc. Jpn 65, 108 (2013).

  40. 40.

    Ida, S., Canup, R. M. & Stewart, G. R. Lunar accretion from an impact-generated disk. Nature 389, 353–357 (1997).

  41. 41.

    Kokubo, E., Ida, S. & Makino, J. Evolution of a circumterrestrial disk and formation of a single Moon. Icarus 148, 419–436 (2000).

  42. 42.

    Canup, R. M., Ward, W. R. & Cameron, A. G. W. A scaling relationship for satellite-forming impacts. Icarus 150, 288–296 (2001).

  43. 43.

    Morishima, R. & Watanabe, S.-I. Two types of co-accretion scenarios for the origin of the Moon. Earth Planets Space 53, 213–231 (2001).

  44. 44.

    Melosh, H. J. & Sonett, C. P. in Origin of the Moon (eds Hartmann, W. K., Philips, R. J. & Taylor, G. J.) 621–642 (Lunar and Planetary Institute, 1986).

  45. 45.

    Mibe, K., Orihashi, Y., Nakai, S. & Fujii, T. Element partitioning between transition-zone minerals and ultramafic melt under hydrous conditions. Geophys. Res. Lett. (2006).

  46. 46.

    Badro, J., Brodhlot, J. P., Piet, H., Siebert, J. & Ryerson, F. J. Core formation and core composition from coupled geochemical and geophysical constraints. Proc. Natl Acad. Sci. USA 112, 12310–12314 (2015).

  47. 47.

    Clayton, R. N., Onuma, N. & Mayeda, T. K. A classification of meteorites based on oxygen isotopes. Earth Planet. Sci. Lett. 30, 10–18 (1976).

  48. 48.

    Lucy, L. B. A numerical approach to the testing of the fission hypothesis. Astrophys. J. 82, 1013–1024 (1977).

  49. 49.

    Gingold, R. A. & Monaghan, J. J. Smoothed particle hydrodynamics—theory and applications to non-spherical stars. Mont. Not. R. Astron. Soc. 181, 375–389 (1977).

  50. 50.

    Agertz, O. et al. Fundamental differences between SPH and grid methods. Mon. Not. R. Astron. Soc. 380, 963–978 (2007).

  51. 51.

    Saitoh, T. R. & Makino, J. A density-independent formulation of smoothed particle hydrodynamics. Astrophys. J. (2013).

  52. 52.

    Hopkins, P. F. A general class of Lagrangian smoothed particle hydrodynamics methods and implications for fluid mixing problems. Mon. Not. R. Astron. Soc. 428, 2840–2856 (2013).

  53. 53.

    Dehnen, W. & Aly, H. Improving convergence in smoothed particle hydrodynamics methods and implications for fluid mechanics simulations. Mon. Not. R. Astron. Soc. 425, 1068–1082 (2012).

  54. 54.

    Iwasawa, M. et al. Implementation and performance of FDPS: a framework for developing parallel particle simulation codes. Publ. Astron. Soc. Jpn 68, 54 (2016).

  55. 55.

    Hosono, N. et al. Unconvergence of very-large-scale giant impact simulations. Publ. Astron. Soc. Jpn 69, 26 (2017).

Download references


We thank K. Ozawa and H. Nagahara for a discussion of the lunar composition and of geochemistry, and J. Melosh for helpful comments. We used computational resources provided by the RIKEN Center for Computational Science through the HPCI System Research project (ID: ra000008).

Author information

N.H. performed numerical simulations and analysed the results. S.-I.K. developed a model of the terrestrial MO origin of the Moon and suggested the numerical simulations to test his model. N.H. and S.-I.K. interpretated the results and wrote the paper. J.M. and T.R.S. helped N.H. with the numerical schemes.

Competing interests

The authors declare no competing interests.

Correspondence to Natsuki Hosono.

Supplementary Information

  1. Supplementary Information

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark
Fig. 1: Snapshots of an impact simulation.
Fig. 2: Fraction of various materials in the disk and its mass for an MO depth of 1,500 km.
Fig. 3: PT conditions of materials outside the proto-Earth in the early stages of a GI.
Fig. 4: Disk mass versus target fraction in the Moon.