Abstract
Spherical harmonic expansions are routinely used to represent the gravitational potential and its higher-order spatial derivatives in global geodetic, geophysical, and planetary science applications. The convergence domain of external spherical harmonic expansions is the space outside the minimum Brillouin sphere (the smallest sphere containing all masses of the planetary body). Nevertheless, these expansions are commonly employed inside this bounding surface without any corrections. Justification of this procedure has been debated for several decades, but conclusions among scholars are indefinite and even contradictory.In this contribution, we examine the use of external spherical harmonic expansions for the gravitational field modelling inside the minimum Brillouin sphere. We employ the most recent lunar topographic LOLA (Lunar Orbiter Laser Altimeter) products and the measurements of the lunar gravitational field by the GRAIL (Gravity Recovery and Interior Laboratory) satellite mission. We analyse selected quantities calculated from the most recent GRAIL-derived gravitational field models and forward-modelled (topography-inferred) quantities synthesised by internal/external spherical harmonic expansions. The comparison is performed in the spectral domain (in terms of degree variances depending on the spherical harmonic degree) and in the spatial domain (in terms of spatial maps). To our knowledge, GRAIL is the first gravitational sensor ever, which helped to resolve the long-lasting convergence/divergence problem for the analytical downward continuation of the external spherical harmonic expansions, see (Šprlák and Han, 2021). ReferencesŠprlák M, Han S-C (2021) On the Use of Spherical Harmonic Series Inside the Minimum Brillouin Sphere: Theoretical Review and Evaluation by GRAIL and LOLA Satellite Data. Earth-Science Reviews, 222, 103739, https://doi.org/10.1016/j.earscirev.2021.103739.
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