The phase space structure of retrograde mean motion resonances with Neptune: the 4/5, 7/9, 5/8 and 8/13 cases

Abstract We compute planar and three-dimensional retrograde periodic orbits in the vicinity of restricted three-body problem (RTBP) with Sun Neptune as primaries we concentrate on dynamics higher-order exterior mean motion resonances Neptune. By using circular model basic model, families symmetric are computed at 4/5, 7/9, 5/8 8/13 resonances. determine bifurcation points from to elliptic find all corresponding families. In order obtain a global view orbits, eccentricity takes values whole interval $$0<e'<1$$ 0 < e ′ 1 . Then, possible vertical critical (v.c.o) proceed 3-body problem. this generated mainly v.c.o. Also, if continue direct for $$i>90^\circ $$ i > 90 ∘ , then can 3D orbits. The linear stability is examined too. Stable associated phase space domains resonant where TNOs be captured. study structure above resonances, construct dynamical maps inclination ( $$0<i<180^\circ 180 ) by well-known “MEGNO Chaos Indicator”. Finally, discuss about which currently located these