Hierarchical three-body problem at high eccentricities = simple pendulum I: octupole
Year: 2024
Type: article
Abstract: ABSTRACT The gradual evolution of the restricted hierarchical three body problem is analysed 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 (2011) and show that for most initial conditions, to an excellent approximation, the analytical 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.
Authors: Ygal Y Klein, Boaz Katz
Institution: Weizmann Institute of Science
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $1,434
OpenAlex ID: W4402853967