Hierarchical Three-Body Problem at High Eccentricities = Simple Pendulum II: Octupole including Brown's Hamiltonian
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910560255213568 |
|---|---|
| author | Klein, Ygal Y. Katz, Boaz |
| author_facet | Klein, Ygal Y. Katz, Boaz |
| contents | The very long-term evolution of the hierarchical restricted three-body problem with a massive perturber is analyzed analytically in the high eccentricity regime. Perturbations on the time scale of the outer orbit can accumulate over long timescales and be comparable to the effect of the octupole term. These perturbations are described by Brown's Hamiltonian - having different forms in the literature. We show that at the high eccentricity regime - the effect of Brown's Hamiltonian is an azimuthal precesssion of the eccentricity vector and can be solved analytically. In fact, the dynamics are equivalent to a simple pendulum model allowing an explicit flip criterion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04003 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hierarchical Three-Body Problem at High Eccentricities = Simple Pendulum II: Octupole including Brown's Hamiltonian Klein, Ygal Y. Katz, Boaz Earth and Planetary Astrophysics High Energy Astrophysical Phenomena The very long-term evolution of the hierarchical restricted three-body problem with a massive perturber is analyzed analytically in the high eccentricity regime. Perturbations on the time scale of the outer orbit can accumulate over long timescales and be comparable to the effect of the octupole term. These perturbations are described by Brown's Hamiltonian - having different forms in the literature. We show that at the high eccentricity regime - the effect of Brown's Hamiltonian is an azimuthal precesssion of the eccentricity vector and can be solved analytically. In fact, the dynamics are equivalent to a simple pendulum model allowing an explicit flip criterion. |
| title | Hierarchical Three-Body Problem at High Eccentricities = Simple Pendulum II: Octupole including Brown's Hamiltonian |
| topic | Earth and Planetary Astrophysics High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2408.04003 |