1/1 resonant periodic orbits in three dimensional planetary systems

TL;DR

This paper investigates the existence and stability of three-dimensional resonant periodic orbits in two-planet systems with 1/1 mean motion resonance, revealing bifurcation conditions and stability regions.

Contribution

It identifies the specific mass ratio threshold for bifurcations from planar to spatial periodic orbits and characterizes the resulting families and their stability.

Findings

Bifurcations occur only for mass ratios less than 0.0205.

Spatial periodic orbit families connect to planar families, forming bridges.

Stable regions of regular orbits are mapped in phase space.

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.