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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.17628 |
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| _version_ | 1866912845999898624 |
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| author | Arenas-Uribe, Felipe |
| author_facet | Arenas-Uribe, Felipe |
| contents | Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit deviations from spherical symmetry, including oblateness, localized mass concentrations, and higher-order shape irregularities. These features can significantly perturb spacecraft trajectories, especially in low-altitude or long-duration missions, leading to cumulative orbit prediction errors and increased control demands. This article presents a tutorial introduction to spherical harmonic gravity models, outlining their theoretical foundations and underlying assumptions. Higher-order gravitational fields are derived as solutions to the Laplace equation, providing a systematic framework to capture the effects of non-uniform mass distributions. The impact of these higher-order terms on orbital dynamics is illustrated through examples involving Low Earth Orbit satellites and spacecraft near irregularly shaped asteroids, highlighting the practical significance of moving beyond the point-mass approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17628 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Higher-Order Gravitational Models: A Tutorial on Spherical Harmonics and the Newtonian Model Arenas-Uribe, Felipe Earth and Planetary Astrophysics Instrumentation and Methods for Astrophysics Systems and Control 70F15 Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit deviations from spherical symmetry, including oblateness, localized mass concentrations, and higher-order shape irregularities. These features can significantly perturb spacecraft trajectories, especially in low-altitude or long-duration missions, leading to cumulative orbit prediction errors and increased control demands. This article presents a tutorial introduction to spherical harmonic gravity models, outlining their theoretical foundations and underlying assumptions. Higher-order gravitational fields are derived as solutions to the Laplace equation, providing a systematic framework to capture the effects of non-uniform mass distributions. The impact of these higher-order terms on orbital dynamics is illustrated through examples involving Low Earth Orbit satellites and spacecraft near irregularly shaped asteroids, highlighting the practical significance of moving beyond the point-mass approximation. |
| title | Higher-Order Gravitational Models: A Tutorial on Spherical Harmonics and the Newtonian Model |
| topic | Earth and Planetary Astrophysics Instrumentation and Methods for Astrophysics Systems and Control 70F15 |
| url | https://arxiv.org/abs/2601.17628 |