Published August 3, 2018 | Version v1.0
Dataset Open

Spherical harmonic models of the gravitational field implied by the Moon's topographic masses

  • 1. Department of Theoretical Geodesy and Geoinformatics, Slovak University of Technology in Bratislava
  • 2. Institute for Astronomical and Physical Geodesy and Institute for Advanced Study, Technical University of Munich
  • 3. School of Earth and Planetary Sciences and Western Australian Geodesy Group, Curtin University


Provided are 12 spherical harmonic models of the gravitational field implied by the Moon's topographic masses.  The models mitigate the divergence effect of spherical harmonics on the Moon's topography when compared with spectral gravity forward modelling methods.  The topographic masses are expanded up to degrees 90, 180, 360 and 720, and the maximum degree of the gravitational models varies from 360 up to 2160.  All models are available in the gfc format as defined by ICGEM.  One of the models, STU_Moon_topography_to720_gravity_to2160, can also be accessed from ICGEM, where it can be find under a shortened name STU_MoonTopo720.

The models rely on the Runge-Krarup theorem and enable generally a more accurate evaluation of the gravitational field in the proximity to the lunar topography as compared to the models from spectral gravity forward modelling.  This is because the latter ones may suffer from the divergence effect when evaluating the spherical harmonic series on or below the limit sphere encompassing all the gravitating masses (that is, also on the topography).

The datasets have been published in Bucha, B., Hirt, C., Kuhn, M., 2019. Divergence-free spherical harmonic gravity field modelling based on the Runge—Krarup theorem: a case study for the Moon. Journal of Geodesy 93, 489-513,


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