Planar periodic orbits in exterior resonances with Neptune

Abstract

In the framework of the planar restricted three body problem we study a considerable number of resonances associated to the Kuiper Belt dynamics and located between 30 and 48 a.u. Our study is based on the computation of resonant periodic orbits and their stability. Stable periodic orbits are surrounded by regular librations in phase space and in such domains the capture of trans-Neptunian object is possible. All the periodic orbits found are symmetric and there is evidence for the existence of asymmetric ones only in few cases. In the present work first, second and third order resonances are under consideration. In the planar circular case we found that most of the periodic orbits are stable. The families of periodic orbits are temporarily interrupted by collisions but they continue up to relatively large values of the Jacobi constant and highly eccentric regular motion exists for all cases. In the elliptic problem and for a particular eccentricity value of the primary bodies the periodic orbits are isolated. The corresponding families, where they belong to, bifurcate from specific periodic orbits of the circular problem and seem to continue up to the rectilinear problem. Both stable and unstable orbits are obtained for each case. In the elliptic problem the unstable orbits found are associated with narrow chaotic domains in phase space. The evolution of the orbits, which are located in such chaotic domains, seems to be practically regular and bounded for long time intervals.

On the 2/1 resonant planetary dynamics - periodic orbits and dynamical stability

“…From this point, we have a bifurcation of the family A A 1 p of asymmetric periodic orbits. Voyatzis and Kotoulas (2005) showed that many families of the external resonances have such critical points and conjectured the bifurcation of asymmetric orbits.…”

The dynamical stability of a Kuiper Belt-like region

“…As a particular example, the 2/5 resonance is presented in Fig. 1 (a large number of resonances in the Kuiper Belt is studied in Voyatzis & Kotoulas 2005). Fig.…”

“…3. There are two bifurcation points belonging to the family II and to the family C of circular orbits (for a minor body eccentricity e ≈ 0), each one giving rise to two families of periodic orbits, where the planet is initially at perihelion (family E p ) or at aphelion (family E a ) (see also Voyatzis & Kotoulas 2005). For a particular value of e N (say e N = 0.009), the associated periodic orbits are isolated and they correspond to specific eccentricity values of the small body.…”

Three dimensional periodic orbits in exterior mean motion resonances with Neptune

“…For the EKB resonances, the planar circular problem has been extensively studied (Malhotra 1996;Kotoulas & Hadjidemetriou 2002;Voyatzis & Kotoulas 2005b). For all resonances (particularly of first, second and third order), the circular planar RTBP admits two families of symmetric periodic orbits called f amily I and f amily II which bifurcate from the family of circular orbits.…”

“…For all resonances (particularly of first, second and third order), the circular planar RTBP admits two families of symmetric periodic orbits called f amily I and f amily II which bifurcate from the family of circular orbits. In family I the small body is at perihelion at t = 0, while in family II the small body is at aphelion at t = 0 (for more details, see Voyatzis & Kotoulas 2005b). In Kotoulas & Voyatzis (2005a) The family of circular orbits C in the planar case is not continued near the first order resonances for µ > 0.…”