A study of the 1/2 retrograde resonance: Periodic orbits and resonant capture
arXiv:2104.05795 · doi:10.1007/s10569-021-10020-0
Abstract
We describe the families of periodic orbits in the 2-dimensional 1/2 retrograde resonance at mass ratio 0.001, analyzing their stability and bifurcations into 3-dimensional periodic orbits. We explain the role played by periodic orbits in adiabatic resonance capture, in particular how the proximity between a stable family and an unstable family with a nearly critical segment, associated with Kozai separatrices, determines the transition between distinct resonant modes observed in numerical simulations. Combining the identification of stable, critical and unstable periodic orbits with analytical modeling, resonance capture simulations and computation of stability maps helps to unveil the complex 3-dimensional structure of resonances.
arXiv commentPreprint version of article. The final version with small corrections will be published in Celestial Mechanics and Dynamical Astronomy
References in corpus (18)
- Retrograde resonance in the planar three-body problem
- Stability of prograde and retrograde planets in circular binary systems
- Asteroids in retrograde resonance with Jupiter and Saturn
- Resonant periodic orbits in the exoplanetary systems
- Resonance capture at arbitrary inclination
- An interstellar origin for Jupiter's retrograde co-orbital asteroid
- Fly-by encounters between two planetary systems I: solar system analogues
- A numerical investigation of coorbital stability and libration in three dimensions
- On fitting planetary systems in counter-revolving configurations
- Are retrograde resonances possible in multi-planet systems?
- Periodic orbits of the retrograde coorbital problem
- An interstellar origin for high-inclination Centaurs
- Resonance capture at arbitrary inclination: II. Effect of the radial drift rate
- Inclined asymmetric librations in exterior resonances
- Resonance libration and width at arbitrary inclination
- Spatial resonant periodic orbits in the restricted three-body problem
- The disturbing function for asteroids with arbitrary inclinations
- On retrograde orbits, resonances and stability