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 − Ω portraits of flipping particles are obtained and verified by numerical integrations. Based on the previous numerical experiments, 200 000 test particles in a particular range are generated and integrated over 1 Myr. The flip region on the entire a − e parameter space is obtained. For each grid of the flip area, we plot the i − Ω 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.