Hill's level surfaces in the circular restricted three-body problem solved
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913131702255616 |
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| author | Huré, Jean-Marc |
| author_facet | Huré, Jean-Marc |
| contents | We report the closed-form expression for Hill's surfaces in the circular restricted three-body problem. The solution $ϕ(r,θ)$, derived in the primary-centric spherical coordinate system, is deduced from a cubic equation delivering at most two roots on each side of a separatrix. The famous patterns (tadpole, horseshoe and peanut shapes, Roche lobes and Hill's quasi-spheres) are exactly produced. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21426 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hill's level surfaces in the circular restricted three-body problem solved Huré, Jean-Marc Instrumentation and Methods for Astrophysics We report the closed-form expression for Hill's surfaces in the circular restricted three-body problem. The solution $ϕ(r,θ)$, derived in the primary-centric spherical coordinate system, is deduced from a cubic equation delivering at most two roots on each side of a separatrix. The famous patterns (tadpole, horseshoe and peanut shapes, Roche lobes and Hill's quasi-spheres) are exactly produced. |
| title | Hill's level surfaces in the circular restricted three-body problem solved |
| topic | Instrumentation and Methods for Astrophysics |
| url | https://arxiv.org/abs/2604.21426 |