Flip mechanism of Jupiter-crossing orbits in the non-hierarchical triple system

With the discovery of more and more retrograde minor bodies, retrograde orbits' production mechanism has attracted much attention. However, almost all of the current research on the flip mechanism is based on the hierarchical approximation. In this paper, we study the flip mechanism of Jupiter-crossing orbits in a non-hierarchical Sun-Jupiter triple system. Numerical experiments summarize the characteristics of flipping orbits, and this provides essential guidance for the semi-analytical method. The i - Omega portraits of flipping particles are obtained and verified by numerical integrations. Based on the previous numerical experiments, 200000 test particles in a particular range are generated and integrated over 1Myr. The flip region on the entire a - e parameter space is obtained. For each grid of the flip area, we plot the i - Omega portrait and measure the corresponding Jupiter's flip ability. The gaps around the mean motion resonances (MMRs) in the flip region are also investigated. The MMRs protect the particles in these gaps from flips. Different resonant widths cause the differences in the size of these gaps. The flip mechanism is systematically studied in a planet-crossing system. The complete map of Jupiter's flip ability in the entire flip region is depicted. Given the orbital parameters of the particle, we can assess whether the flip will occur in Jupiter's presence. Our work can also apply to build the flip maps of other massive planets. And it may help understand the evolution of retrograde minor bodies.

Automated summary

This study focuses on the flip mechanism of Jupiter-crossing orbits in a non-hierarchical Sun-Jupiter triple system, summarizing the characteristics of flipping orbits through numerical experiments and providing guidance for the semi-analytical method. The research systematically investigates the flip region and Jupiter's flip ability, as well as explores gaps around mean motion resonances to understand differences in resonant widths. Ultimately, the work aims to build flip maps for other massive planets and enhance understanding of the evolution of retrograde minor bodies.