Spheroidal forward modelling of the gravitational fields of 1-Ceres and the Moon
A novel, explicit, and efficient forward modelling of the spheroidal harmonic spectra of external planetary gravitational fields is developed in this article. We introduce the oblate spheroidal coordinate system and derive the mathematical apparatus for the analysis of the spheroidal harmonic spectr...
| Main Authors: | , , |
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| Format: | Journal Article |
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Elsevier
2019
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| Online Access: | http://purl.org/au-research/grants/arc/DP160104095 http://hdl.handle.net/20.500.11937/76064 |
| _version_ | 1848763616488062976 |
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| author | Sprlak, M. Han, S.-C. Featherstone, Will |
| author_facet | Sprlak, M. Han, S.-C. Featherstone, Will |
| author_sort | Sprlak, M. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | A novel, explicit, and efficient forward modelling of the spheroidal harmonic spectra of external planetary gravitational fields is developed in this article. We introduce the oblate spheroidal coordinate system and derive the mathematical apparatus for the analysis of the spheroidal harmonic spectrum from the volumetric bulk density and geometry of a gravitating body. We discretise the volume integral and formulate a new and efficient numerical algorithm for the spheroidal forward modelling. We provide complete sets of recursions for calculating the associated Legendre functions of the first kind and their integrals in the Supplementary material. We also develop a computer program that implements the numerical algorithm and we test its performance. For this purpose, we consider synthetic gravitational fields of 1 Ceres (a significantly flattened asteroid) and of the Moon (a nearly spherical body). These tests prove high numerical accuracy and applicability of the spheroidal forward modelling up to degree and order 2519. We finally apply our spheroidal forward modelling and its simpler spherical counterpart for computing global gravitational field models up to degree and order 2519 generated by realistic topographic mass distributions of 1 Ceres and of the Moon. These models are compared in the spatial and spectral domains to manifest an enhanced applicability of the spheroidal approach with respect to the spherical one. In particular, we show an extended convergence space when using the spheroidal forward modelling and the corresponding harmonic representation for the oblate 1 Ceres. |
| first_indexed | 2025-11-14T11:06:18Z |
| format | Journal Article |
| id | curtin-20.500.11937-76064 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T11:06:18Z |
| publishDate | 2019 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-760642021-08-20T05:10:54Z Spheroidal forward modelling of the gravitational fields of 1-Ceres and the Moon Sprlak, M. Han, S.-C. Featherstone, Will A novel, explicit, and efficient forward modelling of the spheroidal harmonic spectra of external planetary gravitational fields is developed in this article. We introduce the oblate spheroidal coordinate system and derive the mathematical apparatus for the analysis of the spheroidal harmonic spectrum from the volumetric bulk density and geometry of a gravitating body. We discretise the volume integral and formulate a new and efficient numerical algorithm for the spheroidal forward modelling. We provide complete sets of recursions for calculating the associated Legendre functions of the first kind and their integrals in the Supplementary material. We also develop a computer program that implements the numerical algorithm and we test its performance. For this purpose, we consider synthetic gravitational fields of 1 Ceres (a significantly flattened asteroid) and of the Moon (a nearly spherical body). These tests prove high numerical accuracy and applicability of the spheroidal forward modelling up to degree and order 2519. We finally apply our spheroidal forward modelling and its simpler spherical counterpart for computing global gravitational field models up to degree and order 2519 generated by realistic topographic mass distributions of 1 Ceres and of the Moon. These models are compared in the spatial and spectral domains to manifest an enhanced applicability of the spheroidal approach with respect to the spherical one. In particular, we show an extended convergence space when using the spheroidal forward modelling and the corresponding harmonic representation for the oblate 1 Ceres. 2019 Journal Article http://hdl.handle.net/20.500.11937/76064 10.1016/j.icarus.2019.113412 http://purl.org/au-research/grants/arc/DP160104095 http://creativecommons.org/licenses/by-nc-nd/4.0/ Elsevier fulltext |
| spellingShingle | Sprlak, M. Han, S.-C. Featherstone, Will Spheroidal forward modelling of the gravitational fields of 1-Ceres and the Moon |
| title | Spheroidal forward modelling of the gravitational fields of 1-Ceres and the Moon |
| title_full | Spheroidal forward modelling of the gravitational fields of 1-Ceres and the Moon |
| title_fullStr | Spheroidal forward modelling of the gravitational fields of 1-Ceres and the Moon |
| title_full_unstemmed | Spheroidal forward modelling of the gravitational fields of 1-Ceres and the Moon |
| title_short | Spheroidal forward modelling of the gravitational fields of 1-Ceres and the Moon |
| title_sort | spheroidal forward modelling of the gravitational fields of 1-ceres and the moon |
| url | http://purl.org/au-research/grants/arc/DP160104095 http://hdl.handle.net/20.500.11937/76064 |