1/1 resonant periodic orbits in three dimensional planetary systems

Abstract

We study the dynamics of a two-planet system, which evolves being in a $1/1$ mean motion resonance (co-orbital motion) with non-zero mutual inclination. In particular, we examine the existence of bifurcations of periodic orbits from the planar to the spatial case. We find that such bifurcations exist only for planetary mass ratios $\rho =\frac{m_2}{m_1}<0.0205$. For $\rho$ in the interval $0<\rho <0.0205$, we compute the generated families of spatial periodic orbits and their linear stability. These spatial families form bridges, which start and end at the same planar family. Along them the mutual planetary inclination varies. We construct maps of dynamical stability and show the existence of regions of regular orbits in phase space.

Accepted for publication in the proceedings of IAU Symposium 310: Complex Planetary Systems

References in corpus (1)

• On the co-orbital motion of two planets in quasi-circular orbits

Cited by in corpus (5)

• Linking long-term planetary $N$-body simulations with periodic orbits: application to white dwarf pollution
• Dynamical mass and multiplicity constraints on co-orbital bodies around stars
• On quasi-satellite periodic motion in asteroid and planetary dynamics
• Regular and chaotic orbits in the dynamics of exoplanets
• Disruption of exo-asteroids around white dwarfs and the release of dust particles in debris rings in co-orbital motion