Translated spherical harmonics for semi-global gravitational field modeling: examples for Martian moon Phobos and asteroid 433 Eros: Translated spherical harmonics for semi-global...: X. Hu.
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| Title: | Translated spherical harmonics for semi-global gravitational field modeling: examples for Martian moon Phobos and asteroid 433 Eros: Translated spherical harmonics for semi-global...: X. Hu. |
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| Authors: | Hu, Xuanyu1 (AUTHOR) xuanyuhu@gmail.com |
| Source: | Journal of Geodesy. Mar2025, Vol. 99 Issue 3, p1-17. 17p. |
| Abstract: | The gravitational field of a planetary body is most often modeled by an exterior spherical harmonic series, which is uniformly convergent outside the smallest mass-enclosing sphere centered at the origin of the coordinate system, known as the Brillouin sphere. The model can become unstable inside the spherical boundary. Rarely deliberated or emphasized is an obvious fact that the radius of the Brillouin sphere, which is the maximum radius coordinate of the body, changes with the origin. The sphere can thus be adjusted to fit a certain convex portion of irregular body shape via an appropriate coordinate translation, thereby maximizing the region of model stability above the body. We demonstrate that it is, while perhaps counterintuitive, rational to displace the coordinate origin from the center of figure, or even off the body entirely. We review concisely the theory and a method of spherical harmonic translation. We consider some textbook examples that illuminate the physical meaning and the practical advantage of the transformation, the discussion of which, as it turns out, is not so easily encountered. We provide seminormalized as well as fully normalized version of the algorithms, which are compact and easy to work with for low-degree applications. At little cost, the proposed approach enables the spherical harmonics to be comparable with the far more complicated ellipsoidal harmonics in performance in the case of two small objects, Phobos and 433 Eros. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Geodesy is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
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| Header | DbId: egs DbLabel: Engineering Source An: 183999813 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Translated spherical harmonics for semi-global gravitational field modeling: examples for Martian moon Phobos and asteroid 433 Eros: Translated spherical harmonics for semi-global...: X. Hu. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hu%2C+Xuanyu%22">Hu, Xuanyu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> xuanyuhu@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Geodesy%22">Journal of Geodesy</searchLink>. Mar2025, Vol. 99 Issue 3, p1-17. 17p. – Name: Abstract Label: Abstract Group: Ab Data: The gravitational field of a planetary body is most often modeled by an exterior spherical harmonic series, which is uniformly convergent outside the smallest mass-enclosing sphere centered at the origin of the coordinate system, known as the Brillouin sphere. The model can become unstable inside the spherical boundary. Rarely deliberated or emphasized is an obvious fact that the radius of the Brillouin sphere, which is the maximum radius coordinate of the body, changes with the origin. The sphere can thus be adjusted to fit a certain convex portion of irregular body shape via an appropriate coordinate translation, thereby maximizing the region of model stability above the body. We demonstrate that it is, while perhaps counterintuitive, rational to displace the coordinate origin from the center of figure, or even off the body entirely. We review concisely the theory and a method of spherical harmonic translation. We consider some textbook examples that illuminate the physical meaning and the practical advantage of the transformation, the discussion of which, as it turns out, is not so easily encountered. We provide seminormalized as well as fully normalized version of the algorithms, which are compact and easy to work with for low-degree applications. At little cost, the proposed approach enables the spherical harmonics to be comparable with the far more complicated ellipsoidal harmonics in performance in the case of two small objects, Phobos and 433 Eros. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Geodesy is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s00190-025-01944-8 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 1 Titles: – TitleFull: Translated spherical harmonics for semi-global gravitational field modeling: examples for Martian moon Phobos and asteroid 433 Eros: Translated spherical harmonics for semi-global...: X. Hu. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hu, Xuanyu IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 09497714 Numbering: – Type: volume Value: 99 – Type: issue Value: 3 Titles: – TitleFull: Journal of Geodesy Type: main |
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