The most distant Kuiper belt objects exhibit the clustering in their orbits, and this anomalous architecture could be caused by Planet 9 with large eccentricity and high inclination. We then suppose that the orbital clustering of minor planets may be observed somewhere else in the solar system. In this paper, we consider the over 7000 Jupiter Trojans from the Minor Planet Center, and find that they are clustered in the longitude of perihelion ϖ, around the locations ϖJ + 60○ and ϖJ − 60○ (ϖJ is the longitude of perihelion of Jupiter) for the L4 and L5 swarms, respectively. Then we build a Hamiltonian system to describe the associated dynamical aspects for the co-orbital motion. The phase space displays the existence of the apsidally aligned islands of libration centered on Δϖ = ϖ − ϖJ ≈ ±60○, for the Trojan-like orbits with eccentricities e < 0.1. Through a detailed analysis, we have shown that the observed Jupiter Trojans with proper eccentricities ep < 0.1 spend most of their time in the range of |Δϖ| = 0 − 120○, while the more eccentric ones with ep > 0.1 are too few to affect the orbital clustering within this Δϖ range for the entire Trojan population. Our numerical results further prove that, even starting from a uniform Δϖ distribution, the apsidal alignment of simulated Trojans similar to the observation can appear on the order of the age of the solar system. We conclude that the apsidal asymmetric-alignment of Jupiter Trojans is robust, and this new finding can be helpful to design the survey strategy in the future.

Context. More than 10000 Jupiter Trojans have been detected so far. They are moving around the L4 and L5 triangular Lagrangian points of the Sun-Jupiter system and their distributions can provide important clues to the early evolution of the Solar System. Aims. The number asymmetry of the L4 and L5 Jupiter Trojans is a longstanding problem. We aim to test a new mechanism in order to explain this anomalous feature by invoking the jumping-Jupiter scenario. Methods. First, we introduce the orbital evolution of Jupiter caused by the giant planet instability in the early Solar System. In this scenario, Jupiter could undergo an outward migration at a very high speed. We then investigate how such a jump changes the numbers of the L4 (N 4 ) and L5 (N 5 ) Trojans. Results. The outward migration of Jupiter can distort the co-orbital orbits near the Lagrangian points, resulting in L4 Trojans being more stable than the L5 ones. We find that, this mechanism could potentially explain the unbiased number asymmetry of N 4 /N 5 ∼ 1.6 for the known Jupiter Trojans. The uncertainties of the system parameters, e.g. Jupiter's eccentricity and inclination, the inclination distribution of Jupiter Trojans, are also taken into account and our results about the L4/L5 asymmetry have been further validated. However, the resonant amplitudes of the simulated Trojans are excited to higher values compared to the current population. A possible solution is that collisions among the Trojans may reduce their resonant amplitudes.

Most recently, machine learning has been used to study the dynamics of integrable Hamiltonian systems and the chaotic 3-body problem. In this work, we consider an intermediate case of regular motion in a non-integrable system: the behaviour of objects in the 2:3 mean motion resonance with Neptune. We show that, given initial data from a short 6250 yr numerical integration, the best-trained artificial neural network (ANN) can predict the trajectories of the 2:3 resonators over the subsequent 18750 yr evolution, covering a full libration cycle over the combined time period. By comparing our ANN’s prediction of the resonant angle to the outcome of numerical integrations, the former can predict the resonant angle with an accuracy as small as of a few degrees only, while it has the advantage of considerably saving computational time. More specifically, the trained ANN can effectively measure the resonant amplitudes of the 2:3 resonators, and thus provides a fast approach that can identify the resonant candidates. This may be helpful in classifying a huge population of KBOs to be discovered in future surveys.

Aims. We aim to determine the relative angle between the total angular momentum of the minor planets and that of the Sun-planets system, and to improve the orientation of the invariable plane of the solar system. Methods. By utilizing physical parameters available in public domain archives, we assigned reasonable masses to 718041 minor planets throughout the solar system, including near-Earth objects, main belt asteroids, Jupiter trojans, trans-Neptunian objects, scattereddisk objects, and centaurs. Then we combined the orbital data to calibrate the angular momenta of these small bodies, and evaluated the specific contribution of the massive dwarf planets. The effects of uncertainties on the mass determination and the observational incompleteness were also estimated. Results. We determine the total angular momentum of the known minor planets to be 1.7817 × 10 46 g · cm 2 · s −1 . The relative angle α between this vector and the total angular momentum of the Sun-planets system is calculated to be about 14.74 • . By excluding the dwarf planets Eris, Pluto, and Haumea, which have peculiar angular momentum directions, the angle α drops sharply to 1.76 • ; a similar result applies to each individual minor planet group (e.g., trans-Neptunian objects). This suggests that, without these three most massive bodies, the plane perpendicular to the total angular momentum of the minor planets would be close to the invariable plane of the solar system. On the other hand, the inclusion of Eris, Haumea, and Makemake can produce a difference of 1254 mas in the inclination of the invariable plane, which is much larger than the difference of 9 mas induced by Ceres, Vesta, and Pallas as found previously. By taking into account the angular momentum contributions from all minor planets, including the unseen ones, the orientation improvement of the invariable plane is larger than 1000 mas in inclination with a 1σ error of ∼ 50 − 140 mas. Key words. methods: miscellaneous -celestial mechanics -reference systems -minor planets, asteroids: general -planets and satellites: dynamical evolution and stability 1 The Minor Planet Center separates the TNOs in stable orbits from the SDOs in scattered (unstable) orbits. Nevertheless, the distinction between these two populations may no be clear cut.

Context. This paper extends our previous study of the early evolution of Jupiter and its two Trojan swarms by introducing the possible perturbations of a free-floating planet (FFP) invading the Solar System. Aims. In the framework of the invasion of a FFP, we aim to provide some new scenarios to explain the number asymmetry of the L4 and L5 Jupiter Trojans, as well as some other observed features (e.g. the resonant amplitude distribution). Methods. We investigate two different cases: (i) the indirect case, where Jupiter experiences a scattering encounter with the FFP and jumps outwards at a speed that is sufficiently high to make the L4 point temporarily disappear, resulting in a change in the numbers of the L4 (N4) and L5 (N5) Trojan swarms; (ii) the direct case, in which the FFP traverses the L5 region and affects the stability of the local Trojans. Results. In the indirect case, the outward migration of Jupiter can be fast enough to make the L4 islands disappear temporarily, inducing an increase in the resonant amplitude of local Trojans. After the migration is over, the L4 Trojans come back to the reappeared and enlarged islands. As for the L5 islands, they always exist but expand even more considerably. Since the L4 swarm suffers less excitation in the resonant amplitude than the L5 swarm, more L4 Trojans are stable and could survive to the end. In the direct case, the FFP could deplete a considerable fraction of the L5 Trojans, while the L4 Trojans at large distances are not affected and all of them could survive. Conclusions. Both the indirect and direct cases could result in a number ratio of R45 = N4/N5 ~ 1.6 that can potentially explain the current observations. The latter has the advantage of producing the observed resonant amplitude distribution. To achieve these results, we propose that the FFP should have a mass of at least of a few tens of Earth masses and its orbital inclination should be allowed to be as high as 40°.