Approximating Periodic Orbits with Algebraic Curves and Related Minimal Problems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914515357007872 |
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| author | Huang, Ruiqi Leykin, Anton |
| author_facet | Huang, Ruiqi Leykin, Anton |
| contents | The Circular Restricted Three-Body Problem (CR3BP) models the motion of a massless body under the gravitational influence of two primaries. We present a method for approximating a given family of periodic orbits by low-degree implicit algebraic curves, producing one-parameter families of algebraic orbit models.
These models enable the construction of minimal problems motivated by liaison navigation, where spacecraft states are inferred from inter-spacecraft measurements. Relevant applications include initial orbit determination and spacecraft positioning.
Each minimal problem defines a parameterized family of instances; for generic parameters, the number of solutions equals the degree of the associated branched covering map. We compute these degrees using both symbolic and numerical methods, and we outline a homotopy-continuation-based solver construction that can be practical for low-degree cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26332 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Approximating Periodic Orbits with Algebraic Curves and Related Minimal Problems Huang, Ruiqi Leykin, Anton Algebraic Geometry Earth and Planetary Astrophysics The Circular Restricted Three-Body Problem (CR3BP) models the motion of a massless body under the gravitational influence of two primaries. We present a method for approximating a given family of periodic orbits by low-degree implicit algebraic curves, producing one-parameter families of algebraic orbit models. These models enable the construction of minimal problems motivated by liaison navigation, where spacecraft states are inferred from inter-spacecraft measurements. Relevant applications include initial orbit determination and spacecraft positioning. Each minimal problem defines a parameterized family of instances; for generic parameters, the number of solutions equals the degree of the associated branched covering map. We compute these degrees using both symbolic and numerical methods, and we outline a homotopy-continuation-based solver construction that can be practical for low-degree cases. |
| title | Approximating Periodic Orbits with Algebraic Curves and Related Minimal Problems |
| topic | Algebraic Geometry Earth and Planetary Astrophysics |
| url | https://arxiv.org/abs/2604.26332 |