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The tidal–rotational shape of the Moon and evidence for polar wander

Abstract

The origin of the Moon’s large-scale topography is important for understanding lunar geology1, lunar orbital evolution2 and the Moon’s orientation in the sky3. Previous hypotheses for its origin have included late accretion events4, large impacts5, tidal effects6 and convection processes7. However, testing these hypotheses and quantifying the Moon’s topography is complicated by the large basins that have formed since the crust crystallized. Here we estimate the large-scale lunar topography and gravity spherical harmonics outside these basins and show that the bulk of the spherical harmonic degree-2 topography is consistent with a crust-building process controlled by early tidal heating throughout the Moon. The remainder of the degree-2 topography is consistent with a frozen tidal–rotational bulge that formed later, at a semi-major axis of about 32 Earth radii. The probability of the degree-2 shape having both tidal-heating and frozen shape characteristics by chance is less than 1%. We also infer that internal density contrasts eventually reoriented the Moon’s polar axis by 36 ± 4°, to the configuration we observe today. Together, these results link the geology of the near and far sides, and resolve long-standing questions about the Moon’s large-scale shape, gravity and history of polar wander.

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Figure 1: Lunar topography and gravity power spectra, with best-fit power laws for degrees n = 3 to 50.
Figure 2: The topography, gravity and appearance of the Moon, with black lines illustrating basins removed in the analysis.
Figure 3: The ratio C2,0/C2,2 for crustal thickness (or compensated topography), as a function of global mean tidal heat flux, for 114 model cases.

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References

  1. Zuber, M. T., Smith, D. E., Lemoine, F. G. & Neumann, G. A. The shape and internal structure of the Moon from the Clementine Mission. Science 266, 1839–1843 (1994)

    Article  CAS  ADS  Google Scholar 

  2. Jeffreys, H. On the figures of the Earth and Moon. Geophys. J. Int. 4, 1–13 (1937)

    Article  ADS  Google Scholar 

  3. Melosh, H. J. Large impact craters and the moon’s orientation. Earth Planet. Sci. Lett. 26, 353–360 (1975)

    Article  ADS  Google Scholar 

  4. Jutzi, M. & Asphaug, E. Forming the lunar farside highlands by accretion of a companion moon. Nature 476, 69–72 (2011)

    Article  CAS  ADS  Google Scholar 

  5. Wilhelms, D. E. The geologic history of the Moon. USGS Prof. Paper 1348 (US Government Printing Office, 1987)

    Google Scholar 

  6. Sedgwick, W. F. On the figure of the Moon. Messenger Math. 27, 171–173 (1898)

    Google Scholar 

  7. Loper, D. E. & Werner, C. L. On lunar asymmetries 1. Tilted convection and crustal asymmetry. J. Geophys. Res. 107 http://dx.doi.org/10.1029/2000JE001441 (2002)

  8. Urey, H. C., Elsasser, W. M. & Rochester, M. G. Note on the internal structure of the Moon. Astrophys. J. 129, 842–848 (1959)

    Article  ADS  Google Scholar 

  9. Lambeck, K. & Pullan, S. The lunar fossil bulge hypothesis revisited. Phys. Earth Planet. Inter. 22, 29–35 (1980)

    Article  ADS  Google Scholar 

  10. Stevenson, D. J. Origin and implications of the degree two lunar gravity field. Proc. Lunar Sci. Conf. 32, 1175 (2001)

    Google Scholar 

  11. Smith, D. E., Zuber, M. T., Neumann, G. A. & Lemoine, F. G. Topography of the Moon from the Clementine LIDAR. J. Geophys. Res. 102, 1591–1611 (1997)

    Article  ADS  Google Scholar 

  12. Williams, J. G., Boggs, D. H., Yoder, C. F., Ratcliff, J. T. & Dickey, J. O. Lunar rotational dissipation in solid body and molten core. J. Geophys. Res. 106, 27933–27968 (2001)

    Article  ADS  Google Scholar 

  13. Zuber, M. T. et al. Gravity field of the Moon from the gravity recovery and interior laboratory (GRAIL) mission. Science 339, 668–671 (2013)

    Article  CAS  ADS  Google Scholar 

  14. Smith, D. E. et al. Initial observations from the Lunar Orbiter Laser Altimeter (LOLA). Geophys. Res. Lett. 37, L18204 (2010)

    ADS  Google Scholar 

  15. Ojakangas, G. W. & Stevenson, D. J. Thermal state of an ice shell on Europa. Icarus 81, 220–241 (1989)

    Article  CAS  ADS  Google Scholar 

  16. Garrick-Bethell, I., Nimmo, F. & Wieczorek, M. A. Structure and formation of the lunar farside highlands. Science 330, 949–951 (2010)

    Article  CAS  ADS  Google Scholar 

  17. Garrick-Bethell, I. & Zuber, M. T. Elliptical structure of the lunar South Pole-Aitken basin. Icarus 204, 399–408 (2009)

    Article  CAS  ADS  Google Scholar 

  18. Namiki, N. et al. Farside gravity field of the Moon from four-way Doppler measurements of SELENE (Kaguya). Science 323, 900–905 (2009)

    Article  CAS  ADS  Google Scholar 

  19. Garrick-Bethell, I., Wisdom, J. & Zuber, M. T. Evidence for a past high eccentricity lunar orbit. Science 313, 652–655 (2006)

    Article  CAS  ADS  MathSciNet  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  21. Zhong, S., Parmentier, E. M. & Zuber, M. T. A dynamic origin for the global asymmetry of lunar mare basalts. Earth Planet. Sci. Lett. 177, 131–140 (2000)

    Article  CAS  ADS  Google Scholar 

  22. Laneuville, M., Wieczorek, M. A., Breuer, D. & Tosi, N. Asymmetric thermal evolution of the Moon. J. Geophys. Res. 118, 1435–1452 (2013)

    Article  Google Scholar 

  23. Melosh, H. J. Mascons and the moon's orientation. Earth Planet. Sci. Lett. 25, 322–326 (1975)

    Article  ADS  Google Scholar 

  24. Zhong, S. & Zuber, M. T. Long-wavelength topographic relaxation for self-gravitating planets and implications for the time-dependent compensation of surface topography. J. Geophys. Res. 105, 4153–4164 (2000)

    Article  ADS  Google Scholar 

  25. Siegler, M. A., Bills, B. G. & Paige, D. A. Effects of orbital evolution on lunar ice stability. J. Geophys. Res. 116, E03010 (2011)

    Article  ADS  Google Scholar 

  26. Dwyer, C. A., Stevenson, D. J. & Nimmo, F. A long-lived lunar dynamo driven by continuous mechanical stirring. Nature 479, 212–214 (2011)

    Article  CAS  ADS  Google Scholar 

  27. Solomon, S. C. & Longhi, J. Magma oceanography: 1. Thermal evolution. Proc. Lunar Sci. Conf. 8, 583–599 (1977)

    ADS  Google Scholar 

  28. Borg, L. E., Connelly, J. N., Boyet, M. & Carlson, R. W. Chronological evidence that the Moon is either young or did not have a global magma ocean. Nature 477, 70–72 (2011)

    Article  CAS  ADS  Google Scholar 

  29. Meyer, J., Elkins, L. T. & Wisdom, J. Coupled thermal–orbital evolution of the early Moon. Icarus 208, 1–10 (2010)

    Article  ADS  Google Scholar 

  30. Runcorn, S. K. Lunar magnetism, polar displacements and primeval satellites in the Earth–Moon system. Nature 304, 589–596 (1983)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the BK21-plus programme through the National Research Foundation (NRF), funded by the Ministry of Education of Korea. Conversations with E. Mazarico are appreciated. We acknowledge the GRAIL and LRO teams for the gravity and topography data used in the analysis.

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Authors and Affiliations

Authors

Contributions

I.G.-B. and M.T.Z. planned the research. V.P. performed the power-law calculations and helped develop the spherical harmonic fitting procedures. F.N. performed the tidal heating calculations. I.G.-B. performed the remainder of the research and wrote the paper, with contributions from all authors.

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Correspondence to Ian Garrick-Bethell.

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The authors declare no competing financial interests.

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This file contains Supplementary Text, Supplementary References, Supplementary Tables 1-13 and Supplementary Figures 1-14. (PDF 9259 kb)

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Garrick-Bethell, I., Perera, V., Nimmo, F. et al. The tidal–rotational shape of the Moon and evidence for polar wander. Nature 512, 181–184 (2014). https://doi.org/10.1038/nature13639

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