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Perturbative analyses of planetary resonances commonly predict singularities and/or divergences of resonance widths at very low and very high eccentricities. We have recently re-examined the nature of these divergences using non-perturbative numerical analyses, making use of Poincaré sections but from a different perspective relative to previous implementations of this method. This perspective reveals fine structure of resonances which otherwise remains hidden in conventional approaches, including analytical, semi-analytical and numerical-averaging approaches based on the critical resonant angle. At low eccentricity, first order resonances do not have diverging widths but have two asymmetric branches leading away from the nominal resonance location. A sequence of structures called ``low-eccentricity resonant bridges" connecting neighboring resonances is revealed. At planet-grazing eccentricity, the true resonance width is non-divergent. At higher eccentricities, the new results reveal hitherto unknown resonant structures and show that these parameter regions have a loss of some -- though not necessarily entire -- resonance libration zones to chaos. The chaos at high eccentricities was previously attributed to the overlap of neighboring resonances. The new results reveal the additional role of bifurcations and co-existence of phase-shifted resonance zones at higher eccentricities. By employing a geometric point of view, we relate the high eccentricity phase spacemore »structures and their transitions to the shapes of resonant orbits in the rotating frame. We outline some directions for future research to advance understanding of the dynamics of mean motion resonances.« less

The most distant known trans-Neptunian objects (TNOs), those with perihelion distance above 38 au and semimajor axis above 150 au, are of interest for their potential to reveal past, external, or present but unseen perturbers. Realizing this potential requires understanding how the known planets influence their orbital dynamics. We use a recently developed Poincaré mapping approach for orbital phase space studies of the circular planar restricted three-body problem, which we have extended to the case of the 3D restricted problem withNplanetary perturbers. With this approach, we explore the dynamical landscape of the 23 most distant TNOs under the perturbations of the known giant planets. We find that, counter to common expectations, almost none of these TNOs are far removed from Neptune’s resonances. Nearly half (11) of these TNOs have orbits consistent with stable libration in Neptune’s resonances; in particular, the orbits of TNOs 148209 and 474640 overlap with Neptune’s 20:1 and 36:1 resonances, respectively. Five objects can be ruled currently nonresonant, despite their large orbital uncertainties, because our mapping approach determines the resonance boundaries in angular phase space in addition to semimajor axis. Only three objects are in orbital regions not appreciably affected by resonances: Sedna, 2012 VP113 andmore »2015 KG163. Our analysis also demonstrates that Neptune’s resonances impart a modest (few percent) nonuniformity in the longitude of perihelion distribution of the currently observable distant TNOs. While not large enough to explain the observed clustering, this small dynamical sculpting of the perihelion longitudes could become relevant for future, larger TNO data sets.

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Many of the unusual properties of Pluto’s orbit are widely accepted as evidence for the orbital migration of the giant planets in early solar system history. However, some properties remain an enigma. Pluto’s long-term orbital stability is supported by two special properties of its orbit that limit the location of its perihelion in azimuth and in latitude. We revisit Pluto’s orbital dynamics with a view to elucidating the individual and collective gravitational effects of the giant planets on constraining its perihelion location. While the resonant perturbations from Neptune account for the azimuthal constraint on Pluto’s perihelion location, we demonstrate that the long-term and steady persistence of the latitudinal constraint is possible only in a narrow range of additional secular forcing which arises fortuitously from the particular orbital architecture of the other giant planets. Our investigations also find that Jupiter has a largely stabilizing influence whereas Uranus has a largely destabilizing influence on Pluto’s orbit. Overall, Pluto’s orbit is rather surprisingly close to a zone of strong chaos.

Abstract Orbital resonance phenomena are notoriously difficult to communicate in words due to the complex dynamics arising from the interplay of gravity and orbital angular momentum. A well known example is Pluto’s 3:2 mean motion resonance with Neptune. We have developed a python software tool to visualize the full three-dimensional aspects of Pluto’s resonant orbital dynamics over time. The visualizations include still images and animated movies. By contrasting Pluto’s resonant dynamics with the dynamics of a nearby non-resonant orbit, this tool enables better understanding and exploration of complex planetary dynamics phenomena.

ABSTRACT Orbital resonances play an important role in the dynamics of planetary systems. Classical theoretical analyses found in textbooks report that libration widths of first-order mean motion resonances diverge for nearly circular orbits. Here, we examine the nature of this divergence with a non-perturbative analysis of a few first-order resonances interior to a Jupiter-mass planet. We show that a first-order resonance has two branches, the pericentric and the apocentric resonance zone. As the eccentricity approaches zero, the centres of these zones diverge away from the nominal resonance location but their widths shrink. We also report a novel finding of ‘bridges’ between adjacent first-order resonances: at low eccentricities, the apocentric libration zone of a first-order resonance smoothly connects with the pericentric libration zone of the neighbouring first-order resonance. These bridges may facilitate resonant migration across large radial distances in planetary systems, entirely in the low-eccentricity regime.