Retrograde periodic orbits in 1/2, 2/3 and 3/4 mean motion resonances with Neptune

Abstract

We study planar and three-dimensional retrograde periodic orbits, using the model of the restricted three-body problem (RTBP) with the Sun and Neptune as primaries and focusing on the dynamics of resonant trans-Neptunian objects (TNOs). The position and the stability character of the periodic orbits can provide important piece of information on the stability and long-term evolution of small TNOs in retrograde motion. Using the circular planar model as the basic model, families of retrograde symmetric periodic orbits are computed at the 1/2, 2/3 and 3/4 exterior mean motion resonances with Neptune. The bifurcations for planar families of the elliptic model and families of the circular spatial model are determined and the bifurcated families are computed. In our study of the planar elliptic model, we consider the eccentricity of the primaries in the whole interval $$0<e'<1$$ for dynamical completeness. In the spatial circular model, retrograde periodic orbits are obtained mainly from bifurcations of the retrograde planar orbits. Also, we obtain retrograde periodic motion from continuing direct orbits for inclination values larger than $$90^\circ $$ . The linear stability of orbits is of major importance. Generally, stable periodic orbits are associated with phase space domains of resonant motion where TNOs can be captured. TNOs of retrograde motion are not common, but new discoveries cannot be excluded.