Stability of Hilda asteroids at 3:2 resonance point in restricted three-body problem
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929491624853504 |
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| author | Asano, Kosuke Noba, Kenichi Petrosky, Tomio |
| author_facet | Asano, Kosuke Noba, Kenichi Petrosky, Tomio |
| contents | Stability of Hilda Asteroids in the solar system around the 3:2 resonance point is analyzed in terms of the Sun-Jupiter-asteroid elliptic restricted three-body problem. We show that the Hamiltonian of the system is well-approximated by a single-resonance Hamiltonian around the 3:2 resonance. This implies that orbits of the Hilda asteroids are approximately integrable, thus their motion is stable. This is in contrast to other resonances such as the 3:1 and the 2:1 resonances at which Kirkwood gaps occur. Indeed, around the 3:1 and the 2:1 resonances, the Hamiltonians are approximated by double-resonance Hamiltonians that are nonintegrable and thus indicate chaotic motions. By a suitable canonical transformation, we reduce the number of degrees of freedom for the system and derive a Hamiltonian which has two degrees of freedom. As a result, we can analyze the stability of the motion by constructing Poincare surface of section. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05102 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of Hilda asteroids at 3:2 resonance point in restricted three-body problem Asano, Kosuke Noba, Kenichi Petrosky, Tomio Earth and Planetary Astrophysics 86-08 G.1.0; J.2 Stability of Hilda Asteroids in the solar system around the 3:2 resonance point is analyzed in terms of the Sun-Jupiter-asteroid elliptic restricted three-body problem. We show that the Hamiltonian of the system is well-approximated by a single-resonance Hamiltonian around the 3:2 resonance. This implies that orbits of the Hilda asteroids are approximately integrable, thus their motion is stable. This is in contrast to other resonances such as the 3:1 and the 2:1 resonances at which Kirkwood gaps occur. Indeed, around the 3:1 and the 2:1 resonances, the Hamiltonians are approximated by double-resonance Hamiltonians that are nonintegrable and thus indicate chaotic motions. By a suitable canonical transformation, we reduce the number of degrees of freedom for the system and derive a Hamiltonian which has two degrees of freedom. As a result, we can analyze the stability of the motion by constructing Poincare surface of section. |
| title | Stability of Hilda asteroids at 3:2 resonance point in restricted three-body problem |
| topic | Earth and Planetary Astrophysics 86-08 G.1.0; J.2 |
| url | https://arxiv.org/abs/2409.05102 |