Hierarchical Three-Body Problem at High Eccentricities = Simple Pendulum
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913424466771968 |
|---|---|
| author | Klein, Ygal Y. Katz, Boaz |
| author_facet | Klein, Ygal Y. Katz, Boaz |
| contents | The gradual evolution of the restricted hierarchical three body problem is analyzed analytically, focusing on conditions of Kozai-Lidov Cycles that may lead to orbital flips from prograde to retrograde motion due to the octupole (third order) term which are associated with extremely high eccentricities. We revisit the approach described by Katz, Dong and Malhotra (\href{https://doi.org/10.1103/PhysRevLett.107.181101}{Phys. Rev. Lett. 107, 181101 (2011)}) and show that for most initial conditions, to an excellent approximation, the analytic derivation can be greatly simplified and reduces to a simple pendulum model allowing an explicit flip criterion. The resulting flip criterion is much simpler than the previous one but the latter is still needed in a small fraction of phase space. We identify a logical error in the earlier derivation but clarify why it does not affect the final results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07154 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hierarchical Three-Body Problem at High Eccentricities = Simple Pendulum Klein, Ygal Y. Katz, Boaz Earth and Planetary Astrophysics High Energy Astrophysical Phenomena The gradual evolution of the restricted hierarchical three body problem is analyzed analytically, focusing on conditions of Kozai-Lidov Cycles that may lead to orbital flips from prograde to retrograde motion due to the octupole (third order) term which are associated with extremely high eccentricities. We revisit the approach described by Katz, Dong and Malhotra (\href{https://doi.org/10.1103/PhysRevLett.107.181101}{Phys. Rev. Lett. 107, 181101 (2011)}) and show that for most initial conditions, to an excellent approximation, the analytic derivation can be greatly simplified and reduces to a simple pendulum model allowing an explicit flip criterion. The resulting flip criterion is much simpler than the previous one but the latter is still needed in a small fraction of phase space. We identify a logical error in the earlier derivation but clarify why it does not affect the final results. |
| title | Hierarchical Three-Body Problem at High Eccentricities = Simple Pendulum |
| topic | Earth and Planetary Astrophysics High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2407.07154 |