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Mass and moment of inertia constraints on the lunar crustal thickness: Relations between crustal density, mantle density, and the reference radius of the crust-mantle boundary


The gravity inversion for the lunar crustal thickness needs three parameters: the crustal density, mantle density, and the reference radius of the crust-mantle boundary. The assumption of crust and mantle densities is found to significantly affect on the resultant crustal thickness variations. Moreover, the recent seismic analyses suggest the possibility of thinner crustal thickness around the Apollo 12 site than that proposed in the Apollo-era, on which the previous gravity inversions relied upon. Therefore the validity of the assumption used in previous gravity-inversion studies must be re-examined in detail. By using a simple three-layered mass model of the Moon including a uniform crust, mantle, and core, we determine possible combinations of the three parameters, satisfying the mass and moment of inertia constraints. The results show that the set of the parameters used in Neumann et al. (1996) can be consistent with mass and moment of inertia constraints, while those in Wieczorek and Phillips (1998) does not satisfy the constraints.


  • Anderson, D. L., Theory of the Earth, 366 pp., Blackwell, Boston, MA, 1989.

    Google Scholar 

  • Binder, A. B., Lunar Prospector: Overview, Science, 281, 1475–1476, 1998.

    Article  Google Scholar 

  • Cohen, E. R. and B. N. Taylor, The 1986 adjustment of the fundamental physical constants, Rev. Mod. Phys., 59, 1121–1148, 1987.

    Article  Google Scholar 

  • Goins, N. R., A. M. Dainty, and M. N. Toksöz, Lunar seismology, the internal structure of the Moon, J. Geophys. Res., 86, 5061–5074, 1981.

    Article  Google Scholar 

  • Khan, A. and K. Mosegaard, An inquiry into the lunar interior: A nonlinear inversion of the Apollo lunar seismic data, J. Geophys. Res., 107(E6), 3–1–3–23, 2002.

    Google Scholar 

  • Konopliv, A. S., A. B. Binder, L. L. Hood, A. B. Kucinskas, W. L. Sjogren, and J. G. Williams, Improved gravity field of the Moon from Lunar Prospector, Science, 281, 1476–1480, 1998.

    Article  Google Scholar 

  • Konopliv, A. S., S. W. Asmar, E. Carranza, W. L. Sjogren, and D. N. Yuan, Recent gravity models as a result of the Lunar Prospector mission, Icarus, 150, 1–18, 2001.

    Article  Google Scholar 

  • Kuskov, O. L., Composition and structure of the upper mantle of the Moon, Geokhimiya, 12, 1683–1698, 1995.

    Google Scholar 

  • Kuskov, O. L., V. A. Kronrod, and L. L. Hood, Geochemical constraints on the seismic properties of the lunar mantle, Phys. Earth Planet. Inter., 134, 175–189, 2002.

    Article  Google Scholar 

  • Lawrence, D. J., W. C. Feldman, R. C. Elphic, R. C. Little, T. H. Prettyman, S. Maurice, P. G. Lucey, and A. B. Binder, Iron abundances on the lunar surface as measured by the Lunar Prospector gamma-ray and nutron spectrometers, J. Geophys. Res., 107, 13–1–13–26, 2002.

    Google Scholar 

  • Lognonné, P., J. Gagnepain-Beyneix, and H. Chenet, A new seismic model of the Moon: implication for structure, thermal evolution and formation of the Moon, Earth Planet. Sci. Lett., 211, 27–44, 2003.

    Article  Google Scholar 

  • Nakamura, Y., Seismic velocity structure of the lunar mantle, J. Geophys. Res., 88, 677–686, 1983.

    Article  Google Scholar 

  • Nakamura, Y., G. V. Latham, H. J. Dorman, A.-B. K. Ibrahim, J. Koyama, and P. Horvath, Shallow moonquakes—Depth, distribution and implications as to the present state of the lunar interior, Proc. Lunar Planet. Sci. Conf., 10th, 2299–2309, 1979.

    Google Scholar 

  • Neumann, G. A., M. T. Zuber, D. E. Smith, and F. G. Lemoine, The lunar crust: global structure and signature of major basins, J. Geophys. Res., 101, 16841–16843, 1996.

    Article  Google Scholar 

  • Nozette et al., The Clementine mission to the Moon: Scientific overview, Science, 266, 1835–1839, 1994.

    Article  Google Scholar 

  • Papike, J. J., Planetary Materials. Reviews in Mineralogy Vol. 36, 1014 pp., Mineralogical Society of America, Washington, 1998.

  • Smith, D. E., M. T. Zuber, G. A. Neumann, and F. G. Lemoine, Topography of the Moon from the Clementine lidar, J. Geophys. Res., 102, 1519–1611, 1997.

    Google Scholar 

  • Toksöz, M. N., A. M. Dainty, S. C. Solomon, and K. Anderson, Structure of the Moon, Rev. Geophys. Space Phys., 12, 539–567, 1974.

    Article  Google Scholar 

  • Wieczorek, M. A., The thickness of the lunar crust: How low can we go?, Pros. Lunar. Planet. Sci., XXXIV, 1330, 2003.

    Google Scholar 

  • Wieczorek, M. A. and R. J. Phillips, Potential anomalies on a sphere: Applications to the thickness of the lunar crust, J. Geophys. Res., 103, 1715–1724, 1998.

    Article  Google Scholar 

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

    Article  Google Scholar 

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Correspondence to Hajime Hikida.

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Hikida, H., Mizutani, H. Mass and moment of inertia constraints on the lunar crustal thickness: Relations between crustal density, mantle density, and the reference radius of the crust-mantle boundary. Earth Planet Sp 57, 1121–1126 (2005).

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Key words

  • Gravity inversion
  • crustal thickness
  • mass and moment of inertia