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GRAIL and LOLA Satellite Data Resolve the Long-Lasting Convergence/Divergence Problem for the Analytical Downward Continuation of the External Spherical Harmonic Expansions
Šprlák, Michal ; Han, Shin-Chan ; Pitoňák, Martin ; Novák, Pavel
Spherical harmonic expansions are routinely used to represent the gravitational potential and its higherorder 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 39 http://dx.doi.org/10.13164/seminargnss.2023.38 quantities calculated from the most recent GRAIL-derived gravitational field models and forwardmodelled (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 [1].
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Crustal Density and Global Gravitational Field Estimation of the Moon from GRAIL and LOLA Satellite Data
Šprlák, Michal ; Han, Shin-Chan ; Featherstone, Will ; Novák, Pavel ; Pitoňák, Martin
We employ Newton’s integral in the spectral domain to solve two geodetic/geophysical tasks for the Moon, see [1]. Firstly, we determine density distribution within the lunar crust (inverse problem). For this purpose, we exploit GL1500E GRAIL gravitational field model and LOLA topography to estimate: 1) constant, 2) laterally variable, and 3) 3D spatially variable crustal density. Secondly, we calculate lunar gravitational field models inferred by these three crustal compositions (forward problem) up to spherical harmonic degree 2519 (corresponding to a spatial resolution of 2.2 km at the lunar equator). We test the performance of our new models, and of recent and independent forward models, against the official Level 1B and Level 2 GRAIL products. Our high resolution global gravitational field models will be an asset to future lunar lander navigation and geophysical exploration of the Moon.
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