Retrograde periodic orbits in 1/2, 2/3 and 3/4 mean motion resonances with Neptune
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(2020) 132:33
ORIGINAL ARTICLE
Retrograde periodic orbits in 1/2, 2/3 and 3/4 mean motion resonances with Neptune T. Kotoulas1 · G. Voyatzis1 Received: 23 December 2019 / Revised: 18 May 2020 / Accepted: 23 May 2020 © Springer Nature B.V. 2020
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◦ . 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. Keywords Periodic orbits · Restricted three-body problem · Kuiper belt · Trans-Neptunian objects
1 Introduction The dynamics of the prograde orbits exterior to Neptune have been extensively studied due to the existence of the trans-Neptunian objects (TNO) that form the Egdeworth–Kuiper belt
This article is part of the topical collection on Trans-Neptunian Objects Guest Editors: David Nesvorny and Alessandra Celletti
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T. Kotoulas [email protected] G. Voyatzis [email protected]
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Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece 0123456789().: V,-vol
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T. Kotoulas, G. Voyatzis
and beyond in a scattered disc (Jewitt 1999). Analytical and semi-analytical models can be constructed which describe efficiently the secular regular dynamics of TNOs [see Saillenfest et al. (2016) and references therein]. Resonant dynamics, particularly associated with mean motion resonances (MMR) between Neptune and TNOs play an important role in the orbital distribution and long-term stability (see Duncan et al. 1995; Morbidelli et al. 1995; Malhotra 1996; Nesvorny and Roig 2000, 2001; Kotoulas and Voyatzis 2004; Celletti et al. 2007; Lykawka and Mukai 2007; Brasil et al. 2014). Very recently, Malhotra et al. (2018) studied the dynamics of Neptune’s 2/5 resonance using Poincaré sections and then N −body simulations including the eff
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