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.
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…
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…
Although the majority of Centaurs are thought to have originated in the scattered disk, with the high-inclination members coming from the Oort cloud, the origin of the high inclination component of trans-Neptunian objects (TNOs) remains uncertain. We report the discovery of a retrograde TNO, which we nickname "Niku", detected by the Pan-STARRS 1 Outer Solar System Survey. Our numerical integrations show that the orbital dynamics of Niku are very similar to that of 2008 KV$_{42}$ (Drac), with a half-life of $\sim 500$ Myr. Comparing similar high inclination TNOs and Centaurs ($q > 10$ AU, $a < …
Asymmetric debris discs have been found around stars other than the Sun; asymmetries are sometimes attributed to perturbations induced by unseen planets. The presence or absence of asymmetries in our own trans-Neptunian belt remains controversial. The study of sensitive tracers in a sample of objects relatively free from the perturbations exerted by the four known giant planets and most stellar flybys may put an end to this debate. The analysis of the distribution of the mutual nodal distances of the known extreme trans-Neptunian objects (ETNOs) that measure how close two orbits may get to eac…
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. …
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…
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 cauti…
We present several lines of evidence based on different kinds of observations to conclude that rotational fission has likely occurred for a fraction of the known Trans-Neptunian Objects (TNOs). It is also likely that a number of binary systems have formed from that process in the trans-neptunian belt. We show that Haumea is a potential example of an object that has suffered a rotational fission. Its current fast spin would be a slight evolution of a primordial fast spin, rather than the result of a catastrophic collision, because the percentage of objects rotating faster than 4 hours would not…
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…
Nearly all known extreme trans-Neptunian objects (ETNOs) have argument of perihelion close to 0 degrees. An existing observational bias strongly favours the detection of ETNOs with arguments of perihelion close to 0 degrees and 180 degrees yet no objects have been found at 180 degrees. No plausible explanation has been offered so far to account for this unusual pattern. Here, we study the dynamical evolution of comet 96P/Machholz 1, a bizarre near-Earth object (NEO) that may provide the key to explain the puzzling clustering of orbits around argument of perihelion close to 0 degrees recently f…
Aims. Numerous trans-Neptunian objects are known to be in mean-motion resonance with Neptune. We aim to describe their long-term orbital evolution (both past and future) by means of a one-degree-of-freedom secular model. In this paper, we focus only on objects with a semi-major axis larger than 50 astronomical units (au). Methods. For each resonant object considered, a 500 000-year numerical integration is performed. The output is digitally filtered to get the parameters of the resonant secular model. Their long-term (Giga-year) orbital evolution is then represented by the level curves of the …
The apparent clustering in longitude of perihelion $\varpi$ and ascending node $Ω$ of extreme trans-Neptunian objects (ETNOs) has been attributed to the gravitational effects of an unseen 5-10 Earth-mass planet in the outer solar system. To investigate how selection bias may contribute to this clustering, we consider 14 ETNOs discovered by the Dark Energy Survey, the Outer Solar System Origins Survey, and the survey of Sheppard and Trujillo. Using each survey's published pointing history, depth, and TNO tracking selections, we calculate the joint probability that these objects are consistent w…
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…
Asteroids that follow similar orbits may have a dynamical connection as their current paths could be the result of a past interaction with a massive perturber. The pair of extreme trans-Neptunian objects or ETNOs (474640) 2004 VN112-2013 RF98 exhibits peculiar relative orbital properties, including a difference in longitude of the ascending node of just 1.61 degrees and 3.99 degrees in inclination. In addition, their reflectance spectra are similar in the visible portion of the spectrum. The origin of these similarities remains unclear. Neglecting observational bias, viable scenarios that coul…
A few studies have reported a significant dearth of exoplanets with Neptune mass and radius with orbital periods below $2$--$4$ d. This cannot be explained by observational biases because many Neptunian planets with longer orbital periods have been detected. The existence of this desert is similar to the appearance of the so-called brown-dwarf desert that suggests different formation mechanisms of planets and stellar companions with short orbital periods. Similarly, the Neptunian desert might indicate different mechanisms of formation and evolution for hot Jupiters and short-period super-Earth…
We report the discovery and dynamical analysis of 2015 BP$_{519}$, an extreme Trans-Neptunian Object detected detected by the Dark Energy Survey at a heliocentric distance of 55 AU and absolute magnitude Hr= 4.3. The current orbit, determined from a 1110-day observational arc, has semi-major axis $a\approx$ 450 AU, eccentricity $e\approx$ 0.92 and inclination $i\approx$ 54 degrees. With these orbital elements, 2015 BP$_{519}$ is the most extreme TNO discovered to date, as quantified by the reduced Kozai action, which is is a conserved quantity at fixed semi-major axis $a$ for axisymmetric pert…
2007OR10 is currently the third largest known dwarf planet in the transneptunian region, with an effective radiometric diameter of ~1535 km. It has a slow rotation period of ~45 h that was suspected to be caused by tidal interactions with a satellite undetected at that time. Here we report on the discovery of a likely moon of 2007OR10, identified on archival Hubble Space Telescope WFC3/UVIS system images. Although the satellite is detected at two epochs, this does not allow an unambiguous determination of the orbit and the orbital period. A feasible 1.5-5.8x10^21 kg estimate for the system mas…
Trans-Neptunian Binary Mutual Events in the 2020s and 2030s
Florida Space Institute, University of Central Florida（佛罗里达太空研究所，中佛罗里达大学）；Lowell Observatory（洛厄尔天文台）；Northern Arizona University（北亚利桑那大学）；Brigham Young University Department of Physics & Astronomy（杨百翰大学物理与天文学系）
The existence of significant anisotropies in the distributions of the directions of perihelia and orbital poles of the known extreme trans-Neptunian objects (ETNOs) has been used to claim that trans-Plutonian planets may exist. Among the known ETNOs, the pair (474640) 2004 VN112-2013 RF98 stands out. Their orbital poles and the directions of their perihelia and their velocities at perihelion/aphelion are separated by a few degrees, but orbital similarity does not necessarily imply common physical origin. In an attempt to unravel their physical nature, visible spectroscopy of both targets was o…
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 …
Milgromian dynamics (MD or MOND) uniquely predicts motion in a galaxy from the distribution of its stars and gas in a remarkable agreement with observations so far. In the solar system, MD predicts the existence of some possibly non-negligible dynamical effects, which can be used to constrain the freedom in MD theories. Known extreme trans-Neptunian objects (ETNOs) have their argument of perihelion, longitude of ascending node, and inclination distributed in highly non-uniform fashion; ETNOs are bodies with perihelion distances greater than the orbit of Neptune and with semimajor axes greater …
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…
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…
Context. The paths followed by the known extreme trans-Neptunian objects (ETNOs) effectively avoid direct gravitational perturbations from the four giant planets, yet their orbital eccentricities are in the range between 0.69-0.97. Solar system dynamics studies show that such high values of the eccentricity can be produced via close encounters or secular perturbations. In both cases, the presence of yet-to-be-discovered trans-Plutonian planets is required. Aims. If the high eccentricities of the known ETNOs are the result of relatively recent close encounters with putative planets, the mutual …
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…
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 dynamically cold component of the Kuiper Belt is host to a population of very widely separated, near-equal mass binary systems. Such binaries, representing the tail of the separation distribution of the more common, more tightly-bound systems, are known to have on-sky separations up to ~4". Their wide separations make them highly valuable due to their delicacy and sensitivity to perturbation, and also makes them relatively easy targets to characterize from the ground. Parker et al. (2011) present a ground-based characterization of seven such systems with separations at discovery ranging fr…
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…
A second large programme (LP) for the physical studies of TNOs and Centaurs, started at ESO Cerro Paranal on October 2006 to obtain high-quality data, has recently been concluded. In this paper we present the spectra of these pristine bodies obtained in the visible range during the last two semesters of the LP. We investigate the spectral behaviour of the TNOs and Centaurs observed, and we analyse the spectral slopes distribution of the full data set coming from this LP and from the literature. We computed the spectral slope for each observed object, and searched for possible weak absorption f…
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…
Secular dynamics inside MMRs plays an essential role in governing the dynamical structure of the trans-Neptunian region and sculpting the orbital distribution of trans-Neptunian objects (TNOs). In this study, semi-analytical developments are made to explore the von Zeipel-Lidov-Kozai (ZLK) resonance inside mean motion resonances (MMRs). To this end, a semi-secular model is formulated by averaging theory and then a single-degree-of-freedom integrable model is achieved based on the adiabatic invariance approximation. In particular, we introduce a modified adiabatic invariant, which is continuous…
Numerical analysis of Lyapunov Times for Trans-Neptunian Objects and Main-Belt Asteroids: stability, accuracy, and methodological comparisons
Centrum Badań Kosmicznych Polskiej Akademii Nauk (CBK PAN)（波兰科学院太空研究中心）；Astronomical Observatory, University of Warsaw（华沙大学天文台）；Cilium Engineering Sp. z o.o.（Cilium工程公司）
Recently, Sheppard et al. (2016) presented the discovery of seven new trans-Neptunian objects with moderate eccentricities, perihelia beyond 40 AU, and semimajor axes beyond 50 AU. Like the few previously known objects on similar orbits, these objects' semimajor axes are just beyond the Kuiper belt edge and clustered around Neptunian mean motion resonances (MMRs). These objects likely obtained their observed orbits while trapped within MMRs, when the Kozai-Lidov mechanism raised their perihelia and weakened Neptune's dynamical influence. Using numerical simulations that model the production of…
Recent studies have revealed that all large (over 1000 km in diameter) trans-Neptunian objects (TNOs) form satellite systems. Although the largest Plutonian satellite, Charon, is thought to be an intact fragment of an impactor directly formed via a giant impact, whether giant impacts can explain the variations in secondary-to-primary mass ratios and spin/orbital periods among all large TNOs remains to be determined. Here we systematically perform hydrodynamic simulations to investigate satellite formation via giant impacts. We find that the simulated secondary-to-primary mass ratio varies over…
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…
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…
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 …
Stochastic impacts by large bodies are, at present, the usually accepted mechanisms able to account for the obliquity of the ice giants. We attempt to set constraints on giant impacts as the cause of Neptune's current obliquity in the framework of modern theories. We also use the present orbital properties of the Neptunian irregular satellites (with the exception of Triton) to set constraints on the scenario of giant impacts at the end of Neptune formation. We model the angular momentum transfer to proto-Neptune and the impulse transfer to its irregular satellites by the last stochastic collis…
It is a well-known fact that the presence of a massive perturber interacting with a population of minor bodies following very eccentric orbits can strongly affect the distribution of their nodal distances. The details of this process have been explored numerically and its outcome confirmed observationally in the case of Jupiter, where a bimodal distribution of nodal distances of comets has been found. Here, we show evidence for a possible bimodal distribution of the nodal distances of the extreme trans-Neptunian objects (ETNOs) in the form of a previously unnoticed correlation between nodal di…
Mean motion resonances play a fundamental role in the dynamics of the small bodies of the Solar System. The last decades of the 20th century gave us a detailed description of the dynamics as well as the process of capture of small bodies in coplanar or small inclination resonant orbits. More recently, semianalytical or numerical methods allowed us to explore the behavior of resonant motions for arbitrary inclination orbits. The emerging dynamics is very rich, including large orbital changes due to secular effects inside mean motion resonances. The process of capture in highly inclined or retro…
We carried out an extensive analysis of the stability of the outer solar system, making use of the frequency analysis technique over short-term integrations of nearly a hundred thousand test particles, as well as a statistical analysis of 200, 1 Gyr long numerical simulations, which consider the mutual perturbations of the giant planets and the 34 largest trans-Neptunian objects (we have called all 34 objects ``dwarf planets'', DPs, even if probably only the largest of them are true DPs). From the frequency analysis we produced statistical diffusion maps for a wide region of the $a$-$e$ phase-…
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…
Digital co-addition of astronomical images is a common technique for increasing signal-to-noise and image depth. A modification of this simple technique has been applied to the detection of minor bodies in the Solar System: first stationary objects are removed through the subtraction of a high-SN template image, then the sky motion of the Solar System bodies of interest is predicted and compensated for by shifting pixels in software prior to the co-addition step. This "shift-and-stack" approach has been applied with great success in directed surveys for minor Solar System bodies. In these surv…
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 trans-Neptunian objects (TNOs) are small Solar System bodies at large distances from the Sun. As such, their physical properties are difficult to measure. Accurate determination of their physical parameters is essential to model and theorize the actual composition and distribution of the population, and to improve our understanding of the formation and evolution of the Solar System. The objective of this work is to construct phase curves in two filters, $V$ and $R$, of a large TNO sample obtaining absolute magnitudes ($H$) and phase coefficients ($β$), and study possible relations between …
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…
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 (TNO) represent the leftovers of the formation of the Solar System. Their physical properties provide constraints to the models of formation and evolution of the various dynamical classes of objects in the outer Solar System. Based on a sample of 19 classical TNOs we determine radiometric sizes, geometric albedos and beaming parameters. Our sample is composed of both dynamically hot and cold classicals. We study the correlations of diameter and albedo of these two subsamples with each other and with orbital parameters, spectral slopes and colors. We have done three-band…
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…
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…
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…
