A long-term orbit analysis of inclined triple systems: A hierarchy change process including the ZKL mechanism

Abstract We have carried out orbital inspections of hierarchical triple systems with masses $m_0=m_2=1$ and $m_1=0.1$, initially set under the influence of the $6:1$ mean motion resonance (MMR) and the von Zeipel–Kozai–Lidov (ZKL) mechanism, aiming at investigating the role of the ZKL mechanism on the instability of the system. The systems were found to be hierarchically unstable within $2\times 10^5$ UoT, while an analysis of nearby orbits indicates that the systems could have a shorter life-time, $6.5\times 10^4$ UoT. The bodies $m_1$ and $m_2$ repeatedly have a chance of coming closer than usual when the phases of three distinct quantities, accounting for the degree or possibility of an $(m_1,m_2)$-approach, match well. On the other hand, we did not find any coplanar and hierarchically stable orbits that could become unstable simply by replacing their initial inclination with a larger value.