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There is a complex inclination structure present in the trans-Neptunian object (TNO) orbital distribution in the main classical-belt region (between orbital semimajor axes of 39 and 48 au). The long-term gravitational effects of the giant planets make TNO orbits precess, but nonresonant objects maintain a nearly constant “free” inclination (I_free) with respect to a local forced precession pole. Because of the likely cosmogonic importance of the distribution of this quantity, we tabulate free inclinations for all main-belt TNOs, each individually computed using barycentric orbital elements with respect to each object’s local forcing pole. We show that the simplest method, based on the Laplace–Lagrange secular theory, is unable to give correct forcing poles for objects near theν₁₈secular resonance, resulting in poorly conservedI_freevalues in much of the main belt. We thus instead implemented an averaged Hamiltonian to obtain the expected nodal precession for each TNO, yielding significantly more accurate free inclinations for nonresonant objects. For the vast majority (96%) of classical-belt TNOs, theseI_freevalues are conserved to < 1° over 4 Gyr numerical simulations, demonstrating the advantage of using this well-conserved quantity in studies of the TNO population and its primordial inclination profile; our computed distributions only reinforce the idea of amore »very coplanar surviving “cold” primordial population, overlain by a largeI-width implanted “hot” population.

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Dynamically excited objects within the Kuiper Belt show a bimodal distribution in their surface colors, and these differing surface colors may be a tracer of where these objects formed. In this work, we explore radial color distributions in the primordial planetesimal disk and implications for the positions of ice line/color transitions within the Kuiper Belt’s progenitor populations. We combine a full dynamical model of the Kuiper Belt’s evolution due to Neptune’s migration with precise surface colors measured by the Colours of the Outer Solar System Origins Survey in order to examine the true color ratios within the Kuiper Belt and the ice lines within the primordial disk. We investigate the position of a dominant, surface color–changing ice line, with two possible surface color layouts within the initial disk: (1) inner neutral surfaces and outer red and (2) inner red surfaces and outer neutral. We performed simulations with a primordial disk that truncates at 30 au. By radially stepping the color transition out through 0.5 au intervals, we show that both disk configurations are consistent with the observed color fraction. For an inner neutral, outer red primordial disk, we find that the color transition can be at${28}_{-3}^{+2}$aumore »at a 95% confidence level. For an inner red, outer neutral primordial disk, the color transition can be at${27}_{-3}^{+3}$au at a 95% confidence level.

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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

Abstract There have been 77 TNOs discovered to be librating in the distant trans-Neptunian resonances (beyond the 2:1 resonance, at semimajor axes greater than 47.7 au) in four well-characterized surveys: the Outer Solar System Origins Survey (OSSOS) and three similar prior surveys. Here, we use the OSSOS Survey Simulator to measure their intrinsic orbital distributions using an empirical parameterized model. Because many of the resonances had only one or very few detections, j : k resonant objects were grouped by k in order to have a better basis for comparison between models and reality. We also use the Survey Simulator to constrain their absolute populations, finding that they are much larger than predicted by any published Neptune migration model to date; we also find population ratios that are inconsistent with published models, presenting a challenge for future Kuiper Belt emplacement models. The estimated population ratios between these resonances are largely consistent with scattering–sticking predictions, though further discoveries of resonant TNOs with high-precision orbits will be needed to determine whether scattering–sticking can explain the entire distant resonant population or not.

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.