2021/10/12 by Barnabás Deme, Deme, Barnabás
Physics and Astronomy · #Astro and Planetary Science #Classical Physics (physics.class-ph) #FOS: Physical sciences #Gamma-ray bursts and supernovae #General Relativity and Quantum Cosmology (gr-qc) #Pulsars and Gravitational Waves Research
paper · pdf · doi:10.48550/arxiv.2110.09950
openalex publication_date 2021/10/12 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We investigate the hierarchical gravitational three-body problem, in which a binary is perturbed by a distant object that orbits on a Keplerian ellipse around the binary itself. This phenomenon, known as Kozai-Lidov mechanism in the literature, results in large-amplitude oscillations of the orbital elements, like eccentricity, which may significantly influence the evolution of many astrophysical systems: from minor bodies and planets to even supermassive black holes. The standard approach found in the literature describes this phenomenon in the framework of Hamiltonian mechanics. Here we derive the long term evolution of the triple with elementary tools, treating the binary as a dipole interacting with the gravitational field of the tertiary and describe the dynamics using forces and torques instead of the usual Hamiltonian formalism. This highlights another aspect of the problem and is likely an easier way to introduce the problem at the undergraduate level.