Dynamics of retrograde $1/n$ mean motion resonances: the $1/{-2}$, $1/{-3}$ cases

Li, Miao; Huang, Yukun; Gong, Shengping

doi:10.1007/s10509-020-03867-6

Cited by 2 publications

(1 citation statement)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The semi-analytical method has been widely applied in analyzing mean motion resonances and secular dynamical effects [18,61]. In our previous papers by Huang et al [21], Li et al [23], and Li et al [81], we introduced the canonical action-angle variables used for investigating the retrograde dynamics. We have also presented the Hamiltonian transformation to study the Kozai-Lidov dynamics inside the retrograde resonance [64].…”

Section: Semi-analytical Modelmentioning

confidence: 99%

Dynamics of Polar Resonances and Their Effects on Kozai–Lidov Mechanism

Gong

2022

Applied Sciences

Self Cite

View full text Add to dashboard Cite

The research on highly inclined mean motion resonances (MMRs), even retrograde resonances, has drawn more attention in recent years. However, the dynamics of polar resonance with inclination i≈90∘ have received much less attention. This paper systematically studies the dynamics of polar resonance and their effects on the Kozai–Lidov mechanism in the circular restricted three-body problem (CRTBP). The maps of dynamics are obtained through the numerical method and semi-analytical method, by mutual authenticating. We investigate the secular dynamics inside polar resonance. The phase-space portraits on the e−ω plane are plotted under exact polar resonance and considering libration amplitude of critical angle σ. Simultaneously, we investigate the evolution of 5000 particles in polar resonance by numerical integrations. We confirm that the e−ω portraits can entirely explain the results of numerical experiments, which demonstrate that the phase-space portraits on the e−ω plane obtained through the semi-analytical method can represent the real Kozai–Lidov dynamics inside polar resonance. The resonant secular dynamical maps can provide meaningful guidance for predicting the long-term evolution of polar resonant particles. As a supplement, in the polar 2/1 case, we analyze the pure secular dynamics outside resonance, and confirm that the effect of polar resonance on secular dynamics is pronounced and cannot be ignored. Our work is a meaningful supplement to the general inclined cases and can help us understand the evolution of asteroids in polar resonance with the planet.

show abstract

Section: Semi-analytical Modelmentioning

confidence: 99%

Dynamics of Polar Resonances and Their Effects on Kozai–Lidov Mechanism

Gong

2022

Applied Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

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

Lei

Huang

et al. 2021

Monthly Notices of the Royal Astronomical Society

View full text Add to dashboard Cite

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 1Myr. 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.

show abstract

Dynamics of retrograde $1/n$ mean motion resonances: the $1/{-2}$, $1/{-3}$ cases

Cited by 2 publications

References 37 publications

Dynamics of Polar Resonances and Their Effects on Kozai–Lidov Mechanism

Dynamics of Polar Resonances and Their Effects on Kozai–Lidov Mechanism

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

Contact Info

Product

Resources

About