Looking at the orbits of small bodies with large semimajor axes, we are compelled to see patterns. Some of these patterns are noted as strong indicators of new or hidden processes in the outer Solar System, others are substantially generated by observational biases, and still others may be completely overlooked. We can gain insight into the current and past structure of the outer Solar System through a careful examination of these orbit patterns. In this chapter, we discuss the implications of the observed orbital distribution of distant trans-Neptunian objects (TNOs). We start with some cautions on how observational biases must affect the known set of TNO orbits. Some of these biases are intrinsic to the process of discovering TNOs, while others can be reduced or eliminated through careful observational survey design. We discuss some orbital element correlations that have received considerable attention in the recent literature. We examine the known TNOs in the context of the gravitational processes that the known Solar System induces in orbital distributions. We discuss proposed new elements of the outer Solar System, posited ancient processes, and the types of TNO orbital element distributions that they predict to exist. We conclude with speculation.
Context: The discovery of distant trans-Neptunian objects has led to heated discussions about the structure of the outer Solar System. Aims: We study the dynamical evolution of small bodies from the Hill regions of migrating giant gaseous clumps that form in the outer solar nebula via gravitational fragmentation. We attempt to determine whether the observed features of the orbital distribution of distant trans-Neptunian objects could be caused by this process. Methods: We consider a simple model that includes the Sun, two point-like giant clumps with masses of ~ 10 Jupiter masses, and a set of…
Two populations of minor bodies in the outer Solar System remain particularly elusive: Scattered Disk objects and Sedna-like objects. These populations are important dynamical tracers, and understanding the details of their spatial- and size-distributions will enhance our understanding of the formation and on-going evolution of the Solar System. By using newly-derived limits on the maximum heliocentric distances that recent pencil-beam surveys for Trans-Neptunian Objects were sensitive to, we determine new upper limits on the total numbers of distant SDOs and Sedna-like objects. While generall…
Aims. We study the dynamical evolution of a system consisting of the giant planets and a massive planetesimal disk over the age of the Solar System. The main question addressed in this study is whether distant trans-Neptunian objects could have come about as a result of the combined action of planetary perturbations and the self-gravity of the disk. Methods. We carried out a series of full N-body numerical simulations of gravitational interactions between the giant planets and a massive outer disk of planetesimals. Results. Our simulations show that the collective gravity of the giant planets …
We explore the distant giant planet hypothesis by integrating the large semi-major axis, large pericenter Trans-Neptunian Objects (TNOs) in the presence of the giant planets and an external perturber whose orbit is consistent with the proposed distant, eccentric, and inclined giant planet, so called planet 9. We find that TNOs with semi-major axes greater than 250 au experience some longitude of perihelion shepherding, but that a generic outcome of such evolutions is that the TNOs evolve to larger pericenter orbits, and commonly get raised to retrograde inclinations. This pericenter and inclin…
We use a secular model to describe the non-resonant dynamics of trans-Neptunian objects in the presence of an external ten-earth-mass perturber. The secular dynamics is analogous to an "eccentric Kozai mechanism" but with both an inner component (the four giant planets) and an outer one (the eccentric distant perturber). By the means of Poincaré sections, the cases of a non-inclined or inclined outer planet are successively studied, making the connection with previous works. In the inclined case, the problem is reduced to two degrees of freedom by assuming a non-precessing argument of periheli…
The most distant known trans-Neptunian objects (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 Poincare mapping approach for orbital phase space studies of the circular planar restricted three body problem, which we have extended to the case of the three-dimensional restricted problem with $N$ planetary perturbers. With this approach, we explore the dy…
The trans-Neptunian region of the solar system exhibits an intricate dynamical structure, much of which can be explained by an instability-driven orbital history of the giant planets. However, the origins of a highly inclined, and in certain cases retrograde, population of trans-Neptunian objects remain elusive within the framework of this evolutionary picture. In this work, we show that the existence of a distant, Neptune-like planet that resides on an eccentric and mildly inclined orbit fully accounts for the anomalous component the trans-Neptunian orbital distribution. Adopting the same par…
Observations of clustering among the orbits of the most distant trans-Neptunian objects (TNOs) has inspired interest in the possibility of an undiscovered ninth planet lurking in the outskirts of the solar system. Numerical simulations by a number of authors have demonstrated that, with appropriate choices of planet mass and orbit, such a planet can maintain clustering in the orbital elements of the population of distant TNOs, similar to the observed sample. However, many aspects of the rich underlying dynamical processes induced by such a distant eccentric perturber have not been fully explor…
Dynamical features of a massive disk of distant trans-Neptunian objects are considered in the model of the formation of small bodies in the Hill region of a giant gas-dust clump that arose as a result of gravitational instability and fragmentation of the protoplanetary disk. The dynamical evolution of orbits of small bodies under the action of gravitational perturbations from the outer planets and self-gravity of the disk has been studied for a time interval of the order of a billion years. It is shown that the secular effects of the gravitational action of a massive disk of small bodies lead …
Space-based observatories at the second Sun-Earth Lagrange Point (L2) offer a unique opportunity to efficiently determine the orbits of distant solar system objects by taking advantage of the parallax effect that arises from nearly simultaneous ground- and space-based observations. Given the typical orbit of an observatory about L2, the observational baseline of $\sim1.5\times10^6$ km between L2 and Earth results in an instantaneous parallax of $\sim$10''-100'', even for the most distant of detectable trans-Neptunian objects (TNOs) in our solar system. Current ground-based strategies for measu…
We present photometric observations and numerical simulations of 2016 SD$_{106}$, a low inclination ($i=4.8^{\circ}$) extreme trans-Neptunian Object with a large semi-major axis ($a=350$ au) and perihelion ($q= 42.6$ au). This object possesses a peculiar neutral color of $g-r = 0.45\pm0.05$ and $g-i=0.72\pm0.06$, in comparison with other distant trans-Neptunian objects, all of which have moderate-red to ultra-red colors. A numerical integration based on orbital fitting on astrometric data covering eight years of arc confirms that 2016 SD$_{106}$ is a metastable object without significant scatt…
We use astrometry of Pluto and other TNOs to constrain the sky location, distance, and mass of the possible additional planet (Planet Nine) hypothesized by Batygin and Brown (2016). We find that over broad regions of the sky, the inclusion of a massive, distant planet degrades the fits to the observations. However, in other regions, the fits are significantly improved by the addition of such a planet. Our best fits suggest a planet that is either more massive or closer than argued for by Batygin and Brown (2016) based on the orbital distribution of distant trans-neptunian objects (or by Fienga…
We present results from a new pipeline custom-designed to search for faint, undiscovered solar system bodies using full-frame image data from the NASA Transiting Exoplanet Survey Satellite (TESS) mission. This pipeline removes the baseline flux of each pixel before aligning and co-adding frames along plausible orbital paths of interest. We first demonstrate the performance of the pipeline by recovering the signals of three trans-Neptunian objects -- 90377 Sedna ($V=20.64$), 2015 BP519 ($V=21.81$), and 2007 TG422 ($V=22.32$) -- both through shift-stacking along their known sky-projected paths a…
The dynamical structure of the Kuiper belt beyond 50 au is not well understood. Here we report results of a numerical model with long-range, slow and grainy migration of Neptune. The model implies that bodies scattered outward by Neptune to semimajor axes a>50 au often evolve into resonances which subsequently act to raise the perihelion distances of orbits to q>40 au. The implication of the model is that the orbits with 50<a<100 au and q>40 au should cluster near (but not in) the resonances with Neptune (3:1 at a=62.6 au, 4:1 at a=75.9 au, 5:1 at a=88.0 au, etc.). The recent detection of seve…
This paper reports the discovery and orbital characterization of two extreme trans-Neptunian objects (ETNOs), 2016 QV$_{89}$ and 2016 QU$_{89}$, which have orbits that appear similar to that of a previously known object, 2013 UH$_{15}$. All three ETNOs have semi-major axes $a\approx 172$ AU and eccentricities $e\approx0.77$. The angular elements $(i,ω,Ω)$ vary by 6, 15, and 49 deg, respectively between the three objects. The two new objects add to the small number of TNOs currently known to have semi-major axes between 150 and 250 AU, and serve as an interesting dynamical laboratory to study t…
The existence of an outer planet beyond Pluto has been a matter of debate for decades and the recent discovery of 2012 VP113 has just revived the interest for this controversial topic. This Sedna-like object has the most distant perihelion of any known minor planet and the value of its argument of perihelion is close to 0 degrees. This property appears to be shared by almost all known asteroids with semimajor axis greater than 150 au and perihelion greater than 30 au (the extreme trans-Neptunian objects or ETNOs), and this fact has been interpreted as evidence for the existence of a super-Eart…
We have been conducting a survey for distant solar system objects beyond the Kuiper Belt edge (~50 AU) with new wide-field cameras on the Subaru 8 meter and CTIO 4 meter telescopes. We are interested in the orbits of objects that are decoupled from the giant planet region in order to understand the structure of the outer solar system, including whether a massive planet exists beyond a few hundred AU as first reported by Trujillo and Sheppard (2014). In addition to discovering extreme trans-Neptunian objects detailed elsewhere, we have found several objects with high perihelia (q>40 AU) that di…
The outer solar system exhibits an anomalous pattern of orbital clustering, characterized by an approximate alignment of the apsidal lines and angular momentum vectors of distant, long-term stable Kuiper belt objects. One explanation for this dynamical confinement is the existence of a yet-undetected planetary-mass object, "Planet Nine (P9)". Previous work has shown that trans-Neptunian objects, which originate within the scattered disk population of the Kuiper belt, can be corralled into orbital alignment by Planet Nine's gravity over ~Gyr timescales, and characteristic P9 parameters have bee…
New data on the distribution of distant trans-Neptunian objects and on the properties of comets indicate the importance of dynamical processes in the outer part of the protoplanetary disk in the formation of the observed structure of the Solar system. In this paper, we examined the possible action of giant gaseous clumps, resulting from gravitational instability and fragmentation of circumstellar disks, on the orbital distribution of the population of small bodies in the outer Solar system. Basically, we studied those features of migration and gravitational interaction of giant clumps that wer…
NASA's Transiting Exoplanet Survey Satellite (TESS) is performing a homogeneous survey of the sky from space in search of transiting exoplanets. The collected data are also being used for detecting passing Solar system objects, including 17 new outer Solar system body candidates located at geocentric distances in the range 80-200 au, that need follow-up observations with ground-based telescope resources for confirmation. Here, we present results of a proof-of-concept mini-survey aimed at recovering two of these candidates that was carried out with the 4.2 m William Herschel Telescope and a QHY…
We present the first comprehensive thermal and rotational analysis of the second most distant trans-Neptunian object (225088) 2007 OR10. We combined optical light curves provided by the Kepler space telescope -- K2 extended mission and thermal infrared data provided by the Herschel Space Observatory. We found that (225088) 2007 OR10 is likely to be larger and darker than derived by earlier studies: we obtained a diameter of d=1535^{+75}_{-225} km which places (225088) 2007 OR10 in the biggest top three trans-Neptunian objects. The corresponding visual geometric albedo is p_V=0.089^{+0.031}_{-0…
To date, studies of $\textit{Laplace Surface}$ dynamics have concerned themselves with test particle orbits of fixed shape and orientation in the combined field of an oblate central body (to which the particle is bound) and a distant, inclined, companion which is captured to quadrupolar order. While amply sufficient for satellites around planets on near-circular orbits, the quadrupolar approximation fails to capture essential dynamical features induced by a wide binary companion (be it a star, a planet or a black hole) on a fairly eccentric orbit. With similar such astronomical settings in min…
The study of the surface properties of Centaurs and Trans-Neptunian Objects (TNOs) provides essential information about the early conditions and evolution of the outer Solar System. Due to the faintness of most of these distant and icy bodies, photometry currently constitutes the best technique to survey a statistically significant number of them. Our aim is to investigate color properties of a large sample of minor bodies of the outer Solar System, and set their taxonomic classification. We carried out visible and near-infrared photometry of Centaurs and TNOs, making use, respectively, of the…
Probing close-in satellites of Trans-Neptunian Objects through thermal and direct size measurements
Instituto de Astrofísica de Andalucía, IAA-CSIC（安达卢西亚天体物理研究所）；Deutsches Zentrum für Astrophysik (DZA)（德国天体物理学中心）；Max-Planck-Institut für extraterrestrische Physik（马克斯·普朗克地外物理学研究所）
The scattered disk is a vast population of trans-Neptunian minor bodies that orbit the sun on highly elongated, long-period orbits. The stability of scattered disk objects is primarily controlled by a single parameter - their perihelion distance. While the existence of a perihelion boundary that separates chaotic and regular motion of long-period orbits is well established through numerical experiments, its theoretical basis as well as its semi-major axis dependence remain poorly understood. In this work, we outline an analytical model for the dynamics of distant trans-Neptunian objects and sh…
The accumulating, but small, set of large semi-major axis trans-Neptunian objects (TNOs) shows an apparent clustering in the orientations of their orbits. This clustering must either be representative of the intrinsic distribution of these TNOs, or else arise as a result of observation biases and/or statistically expected variations for such a small set of detected objects. The clustered TNOs were detected across different and independent surveys, which has led to claims that the detections are therefore free of observational bias. This apparent clustering has led to the so-called "Planet 9" h…
We present a method to identify distant solar system objects in long-term wide-field asteroid survey data, and conduct a search for them in the Pan-STARRS1 (PS1) image data acquired from 2010 to mid-2015. We demonstrate that our method is able to find multi-opposition orbital links, and we present the resulting orbital distributions which consist of 154 Centaurs, 255 classical Trans-Neptunian Objects (TNOs), 121 resonant TNOs, 89 Scattered Disc Objects (SDOs) and 10 comets. Our results show more than half of these are new discoveries, including a newly discovered 19th magnitude TNO. Our identi…
A distant, massive planet in the outer solar system has recently been proposed to explain some observed features of extreme trans-Neptunian objects (TNOs). Here we use N-body simulations of the formation of the Kuiper belt and Oort cloud as well as a survey simulator to compare models of the solar system with and without a 9th planet to one another as well as to observations. The main mechanism for TNOs to be deposited into the distant ($a$ > au), detached ($q$ > au) region of the Kuiper Belt in the 8-planet model is Kozai-Lidov oscillation of objects in mean motion resonances (MMR) with Neptu…
This article reviews the different mechanisms affecting the orbits of trans-Neptunian objects, ranging from internal perturbations (planetary scattering, mean-motion resonances, secular effects) to external perturbations (galactic tides, passing stars). We outline the theoretical tools that can be used to model and study them, focussing on analytical approaches. We eventually compare these mechanisms to the observed distinct populations of trans-Neptunian objects and conclude on how they participate to the sculpting of the whole distribution.
The Trans-Neptunian Objects (TNOs) may preserve evidence of planet building in their orbital and size-distributions. While all populations show steep size-distributions for large objects, recently relative deficit of Neptunian Trojans and scattering objects with diameters $D<100\,\mathrm{km}$ were detected. We have investigated this deficit with a 32 square degree survey, detecting 77 TNOs to a limiting $r$-band magnitude of 24.6. Our Plutinos sample (18 objects in 3:2 mean motion resonance with Neptune) also shows a deficit of $D<100\,\mathrm{km}$ objects. We reject a single power-law size-di…
The Pluto system is an archetype for the multitude of icy dwarf planets and accompanying satellite systems that populate the vast volume of the solar system beyond Neptune. New Horizons' exploration of Pluto and its five moons gave us a glimpse into the range of properties that their kin may host. Furthermore, the surfaces of Pluto and Charon record eons of bombardment by small trans-Neptunian objects, and by treating them as witness plates we can infer a few key properties of the trans-Neptunian population at sizes far below current direct-detection limits. This chapter summarizes what we hav…
The outer Solar System contains a large number of small bodies (known as trans-Neptunian objects or TNOs) that exhibit diverse types of dynamical behavior. The classification of bodies in this distant region into dynamical classes -- sub-populations that experience similar orbital evolution -- aids in our understanding of the structure and formation of the Solar System. In this work, we propose an updated dynamical classification scheme for the outer Solar System. This approach includes the construction of a new (automated) method for identifying mean-motion resonances. We apply this algorithm…
Recent observational surveys of trans-neptunian binary (TNB) systems have dramatically increased the number of known mutual orbits. Our Kozai Cycle Tidal Friction (KCTF) simulations of synthetic trans-neptunian binaries show that tidal dissipation in these systems can completely reshape their original orbits. Specifically, solar torques should have dramatically accelerated the semimajor axis decay and circularization timescales of primordial (or recently excited) TNBs. As a result, our initially random distribution of TNBs in our simulations evolved to have a large population of tight circular…
The Outer Solar System Origins Survey (OSSOS), a wide-field imaging program in 2013-2017 with the Canada-France-Hawaii Telescope, surveyed 155 deg$^{2}$ of sky to depths of $m_r = 24.1$-25.2. We present 838 outer Solar System discoveries that are entirely free of ephemeris bias. This increases the inventory of trans-Neptunian objects (TNOs) with accurately known orbits by nearly 50%. Each minor planet has 20-60 Gaia/Pan-STARRS-calibrated astrometric measurements made over 2-5 oppositions, which allows accurate classification of their orbits within the trans-Neptunian dynamical populations. The…
Trans-Neptunian objects and Centaurs are small solar system bodies that reside in the outer parts of the solar system. These objects present photometric behaviours that are influenced due to a change in their aspect angle. Using absolute photometric measurements and rotational light-curves at different location on their orbits allow to model their photometric behaviour and obtain physical properties such as pole orientation, shape, density, and even detecting different peculiarities as departure from hydrostatic equilibrium or rings. In this work, I present how these models are performed in or…
Trans-Neptunian objects (TNOs) are icy/rocky bodies that move beyond the orbit of Neptune in a region known as the trans-Neptunian belt (or Edgeworth-Kuiper belt). In contrast to the predictions of accretion models that feature protoplanetary disk planetesimals evolving on dynamically cold orbits (with both very small eccentricities, e, and inclinations, i), in reality TNOs exhibit surprisingly wide ranges of orbital eccentricities and inclinations. Several theoretical models have addressed the origin and orbital evolution of the main dynamical classes of TNOs, but none have successfully repro…
The dependences of inclinations of orbits of secondaries in the discovered trans-Neptunian binaries on the distance between the primary and the secondary, on the eccentricity of orbits of the secondary around the primary, on the ratio of diameters of the secondary and the primary, and on the elements of heliocentric orbits of these binaries are studied. These dependences are interpreted using the model of formation of a satellite system in a collision of two rarefied condensations composed of dust and/or objects less than 1 m in diameter. It is assumed in this model that a satellite system for…
We test whether the population of "extreme" trans-Neptunian objects (eTNOs) detected in the Y4 Dark Energy Survey (DES) data exhibit azimuthal asymmetries which might be evidence of gravitational perturbations from an unseen super-Earth in a distant orbit. By rotating the orbits of the detected eTNOs, we construct a synthetic population which, when subject to the DES selection function, reproduces the detected distribution of eTNOs in the orbital elements $a,e,$ and $i$ as well as absolute magnitude $H$, but has uniform distributions in mean anomaly $M$, longitude of ascending node $Ω,$ and ar…
The discovery of the largest trans-neptunian object 2003 UB313 (dwarf planet Eris) was made more than 5 years ago, but the question on the true relation of the sizes of Pluto and Eris (and according to of their densities) remains debatable in view of a sizable scatter of their size's estimates obtained by the various methods. Here, we first used a semi-empirical approach to deduce the expression linking the orbital parameter eccentricity to the physical properties of the trans-neptunian dwarf planets and have applied it to determining the mean size of these planets. In doing so is proved that …
The formation of trans-Neptunian satellite systems at the stage of rarefied preplanetesimals (i.e., condensations of dust and/or objects less than 1 m in diameter) is discussed. It is assumed that trans-Neptunian objects (including those with satellites) could form as a result of compression of parental rarefied preplanetesimals. The formulas for calculating the angular momentum of two colliding condensations with respect to their center of mass, which were applied earlier in (Ipatov, 2010) in the comparison of such momenta with the angular momenta of observed satellite systems, are used to es…
Because of the objectively existing causes, such as an irregular shape of a celestial body, the lack of the satellites, the low values of albedo at moderate sizes, and a large remoteness from the Sun, creating a more exact the physical properties database of trans-Neptunian dwarf planets in comparison with existing that continues to remain a problem. We offer a new calculation procedure of the physical properties of these objects involving earlier unknown the relationships harmonizing these properties. It allows us to conjecture of they are a group of uniform celestial bodies by their origin b…
This work explores the orbital distribution of minor bodies in the outer Solar System emplaced as a result of a Nice model migration from the simulations of Brasser & Morbidelli (2013). This planetary migration scatters a planetesimal disk from between 29-34 AU and emplaces a population of objects into the Kuiper belt region. From the 2:1 Neptune resonance and outward, the test particles analyzed populate the outer resonances with orbital distributions consistent with trans-Neptunian object (TNO) detections in semi-major axis, inclination, and eccentricity, while capture into the closest reson…
Neptunian Trojans (NTs), trans-Neptunian objects in 1:1 mean-motion resonance with Neptune, are generally thought to have been captured from the original trans-Neptunian protoplanetary disk into co-orbital resonance with the ice giant during its outward migration. It is possible, therefore, that the colour distribution of NTs is a constraint on the location of any colour transition zones that may have been present in the disk. In support of this possible test, we obtained $g$, $r$, and $i$-band observations of 18 NTs, more than doubling the sample of NTs with known visible colours to 31 object…
The hypothesis of an additional planet in the outer Solar System has gained new support as a result of the confinement noted in the angular orbital elements of distant trans-Neptunian objects. Orbital parameters proposed for the external perturber suggest semimajor axes between 500 and 1000 au, perihelion distances between 200 and 400 au for masses between 10 and 20 $M_{\oplus}$. In this paper we study the possibility that lower perihelion distances for the additional planet can lead to angular confinements as observed in the population of objects with semimajor axes greater than 250 au and pe…
A relatively massive and moderately eccentric disk of trans-Neptunian objects (TNOs) can effectively counteract apse precession induced by the outer planets, and in the process shepherd highly eccentric members of its population into nearly-stationary configurations which are anti-aligned with the disk itself. We were sufficiently intrigued by this remarkable feature to embark on an extensive exploration of the full spatial dynamics sustained by the combined action of giant planets and a massive trans-Neptunian debris disk. In the process, we identified ranges of disk mass, eccentricity and pr…
We report photometric observations of the trans-Neptunian object 2004~TT$_{357}$ obtained in 2015 and 2017 using the 4.3~m Lowell's Discovery Channel Telescope. We derive a rotational period of 7.79$\pm$0.01~h and a peak-to-peak lightcurve amplitude of 0.76$\pm$0.03~mag. 2004 TT$_{357}$ displays a large variability that can be explained by a very elongated single object or can be due to a contact/close binary. The most likely scenario is that 2004 TT$_{357}$ is a contact binary. If it is in hydrostatic equilibrium, we find that the lightcurve can be explained by a system with a mass ratio q$_{…
The sensitivity of ALMA makes it possible to detect thermal mm/submm emission from small/distant Solar System bodies at the sub-mJy level. Measured fluxes are primarily sensitive to the objects' diameters, but deriving precise sizes is somewhat hampered by the uncertain effective emissivity at these wavelengths. Following Brown and Butler (2017) who presented ALMA data for four binary TNOs, we report ALMA 1.29 mm measurements of four Centaurs (2002 GZ$_{32}$, Bienor, Chiron, Chariklo) and two TNOs (Huya and Makemake), sampling a range of size, albedo and composition. These thermal fluxes are c…
In this work, we focused on observations of six trans-Neptunian objects (TNOs) whose apparent magnitudes are brighter than 20 mag. We present the results of astrometric and photometric observations of (134340) Pluto, (136108) Haumea, (136472) Makemake, (136199) Eris, (90482) Orcus and (20000) Varuna obtained at the Kyiv comet station (Code MPC 585) in 2017-2019. For observations, we used the 0.7-m reflector AZT-8 with the FLI PL4710 CCD camera and filters of the Johnson-Cousins photometric system. From our images, we measured the objects astrometric positions, calculated apparent magnitudes in…
A number of intriguing patterns have been identified in the distributions of the orbital elements of the known extreme trans-Neptunian objects or ETNOs --those with semimajor axis greater than 150 au and perihelion distance greater than 30 au. The announcement of the discovery of 2015 BP519, also known as Caju, has been hailed by some as a consistent piece of robust evidence for the existence of a yet-to-be-discovered massive planet far beyond the trans-Neptunian belt. In this Note, we use the latest data available to provide evidence against 2015 BP519 having followed the same dynamical pathw…
Recently, the first collisional family was identified in the trans-Neptunian belt. The family consists of Haumea and at least ten other ~100km-sized trans-Neptunian objects (TNOs) located in the region a = 42 - 44.5 AU. In this work, we model the long-term orbital evolution of an ensemble of fragments representing hypothetical post-collision distributions at the time of the family's birth. We consider three distinct scenarios, in which the kinetic energy of dispersed particles were varied such that their mean ejection velocities (veje) were of order 200 m/s, 300 m/s and 400 m/s, respectively. …
