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The orientations of orbital planes of minor planets are directional random variables. Their free inclination is the deviation of the orbit plane from the plane forced by the major planets. We construct a model of the distribution of free inclinations of classical Kuiper Belt objects (CKBOs) based on the von Mises–Fisher (vMF) distribution function, the analog of the normal distribution for directional statistics. The CKBOs are known to have a “cold” component of orbit planes concentrated near the forced plane and a more widely dispersed “hot” component. Adopting a model with a linear combination of two vMF functions, we find that the cold and hot components account for 57% and 43%, characterized by widths of 1.°7 and 12.°9, respectively. This model improves upon previous models based on smaller observational samples and empirical choices of functional forms for inclination distributions.

 

Mean plane measurements of the Kuiper Belt from observational data are of interest for their potential to test dynamical models of the solar system. Recent measurements have yielded inconsistent results. Here we report a measurement of the Kuiper Belt’s mean plane with a sample size more than twice as large as in previous measurements. The sample of interest is the nonresonant Kuiper Belt objects, which we identify by using machine learning on the observed Kuiper Belt population whose orbits are well determined. We estimate the measurement error with a Monte Carlo procedure. We find that the overall mean plane of the nonresonant Kuiper Belt (semimajor axis range of 35–150 au) and also that of the classical Kuiper Belt (semimajor axis range of 42–48 au) are both close to (within ∼0.°7) but distinguishable from the invariable plane of the solar system to greater than 99.7% confidence. When binning the sample into smaller semimajor axis bins, we find the measured mean plane is mostly consistent with both the invariable plane and the theoretically expected Laplace surface forced by the known planets. Statistically significant discrepancies are found only in the semimajor axis ranges 40.3–42 au and 45–50 au; these ranges are in proximity to theν₈secular resonance and Neptune’s 2:1 mean motion resonance where the theory for the Laplace surface is likely to be inaccurate. These results do not support a previously reported anomalous warp at semimajor axes above 50 au.

 

ABSTRACT Mean motion resonances are important in the analysis and understanding of the dynamics of planetary systems. While perturbative approaches have been dominant in many previous studies, recent non-perturbative approaches have revealed novel properties in the low-eccentricity regime for interior mean motion resonances of Jupiter in the fundamental model of the circular planar restricted three-body model. Here, we extend the non-perturbative investigation to exterior mean motion resonances in the low-eccentricity regime (up to about 0.1) and for perturber mass in the range of ∼5 × 10−5 to 1 × 10−3 (in units of the central mass). Our results demonstrate that first-order exterior resonances have two branches at low eccentricity as well as low-eccentricity bridges connecting neighbouring first-order resonances. With increasing perturber mass, higher order resonances dissolve into chaos, whereas low-order resonances persist with larger widths in their radial extent but smaller azimuthal widths. For low-order resonances, we also detect secondary resonances arising from small-integer commensurabilities between resonant librations and the synodic frequency. These secondary resonances contribute significantly to generating the chaotic sea that typically occurs near mean motion resonances of higher mass perturbers. 

Small Solar system bodies have widely dispersed orbital poles, posing challenges to dynamical models of Solar system origin and evolution. To characterize the orbit pole distribution of dynamical groups of small bodies it helps to have a functional form for a model of the distribution function. Previous studies have used the small-inclination approximation and adopted variations of the normal distribution to model orbital inclination dispersions. Because the orbital pole is a directional variable, its distribution can be more appropriately modelled with directional statistics. We describe the von Mises–Fisher (vMF) distribution on the surface of the unit sphere for application to small bodies’ orbital poles. We apply it to the orbit pole distribution of the observed Plutinos. We find a mean pole located at inclination i0 = 3.57° and longitude of ascending node Ω0 = 124.38° (in the J2000 reference frame), with a 99.7 per cent confidence cone of half-angle 1.68°. We also estimate a debiased mean pole located 4.6° away, at i0 = 2.26°, Ω0 = 292.69°, of similar-size confidence cone. The vMF concentration parameter of Plutino inclinations (relative to either mean pole estimate) is κ = 31.6. This resembles a Rayleigh distribution function, with width parameter σ = 10.2°. Unlike previous models, the vMF model naturally accommodates all physical inclinations (and no others), whereas Rayleigh or Gaussian models must be truncated to the physical inclination range 0–180°. Further work is needed to produce a theory for the mean pole of the Plutinos against which to compare the observational results.

 

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 space 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. 

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 and 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.

 

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 The Vera C. Rubin Observatory is expected to start the Legacy Survey of Space and Time (LSST) in early to mid-2025. This multiband wide-field synoptic survey will transform our view of the solar system, with the discovery and monitoring of over five million small bodies. The final survey strategy chosen for LSST has direct implications on the discoverability and characterization of solar system minor planets and passing interstellar objects. Creating an inventory of the solar system is one of the four main LSST science drivers. The LSST observing cadence is a complex optimization problem that must balance the priorities and needs of all the key LSST science areas. To design the best LSST survey strategy, a series of operation simulations using the Rubin Observatory scheduler have been generated to explore the various options for tuning observing parameters and prioritizations. We explore the impact of the various simulated LSST observing strategies on studying the solar system’s small body reservoirs. We examine what are the best observing scenarios and review what are the important considerations for maximizing LSST solar system science. In general, most of the LSST cadence simulations produce ±5% or less variations in our chosen key metrics, but a subset of the simulations significantly hinder science returns with much larger losses in the discovery and light-curve metrics. 

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.