Science

The von Zeipel–Lidov–Kozai (ZLK) mechanism plays an important role in the long-term dynamical evolution of trans-Neptunian objects (TNOs) subjected to planetary gravitational perturbations. Despite its theoretical significance, a systematic observational census of TNOs exhibiting clear ZLK dynamics has been lacking. We performed a comprehensive search for ZLK resonances among all 1,037 numbered objects from the AstDyS catalog with semimajor axes a > 30 au. Using numerical integrations spanning up to 300 Myr, we identify 81 objects (≈7.8% of the sample) that are trapped in ZLK resonance, with an additional 23 transient objects exhibiting alternating libration and circulation. A key finding is that all TNOs in ZLK resonance are simultaneously trapped in two-body mean motion resonances (MMRs) with Neptune, providing direct empirical confirmation of theoretical predictions. The most populated MMRs are 2N-3 (58 objects), 4N-7 (15 objects), 1N-2 (9 objects), and 3N-5 (7 objects). For non-1N-2 MMRs, libration centers cluster near 90° and 270°, while the 1N-2 resonance shows shifted centers at approximately 120°, 150°, 300°, and 330°. We identify several dynamically interesting objects in ZLKR, including the retrograde TNO (585899) 2020 HM98 in 2N+9 and the distant object (652920) 2014 GR53 in the high-order 1N-18 MMR, confirming that resonances of type 1:N and high-order MMRs can maintain ZLK dynamics at large heliocentric distances.

We present a systematic evaluation of modern multimodal large language models (LLMs) for the classification of mean-motion and secular resonances from images of resonant arguments. Four benchmark datasets (RB-TEST, RB-PILOT, RB-SMALL, RB-FULL) were constructed to cover clear, ambiguous, and transient cases, with both binary and three-class outputs. Using standardized prompts (a full prompt for large models and a simplified variant for small models that cannot process complex instructions), we tested flagship commercial models, large open-source models, and small locally runnable models. Commercial LLMs reach F1=100% on simple cases and up to 94% on the three-class RB-SMALL dataset, while the best open-source models also reach 100% on unambiguous cases and 76% on the complex ones. On the full binary benchmark, open-source models approach commercial performance (F1≈90–96%). Most errors occur in transient and resonance-sticking regimes. The results show that LLMs can perform resonance classification at levels comparable to those of classical or machine-learning methods without training or fine-tuning, and that even small open-source models achieve practically useful accuracy. The released benchmarks establish a reproducible standard for evaluating LLMs on dynamical astronomy tasks.

This paper presents a major enhancement to the resonances Python package that now implements full support for identifying and analyzing secular resonances. Building upon the established mean-motion resonance framework, the implementation introduces: (1) a flexible mathematical expression parser supporting arbitrary combinations of fundamental frequencies (g, s, gi, si), enabling analysis of both linear resonances (v5, v6, v16) and more than 70 nonlinear resonances from the literature; (2) specialized libration detection algorithms optimized for secular timescales, with automated parameter adaptation for extended integration times; (3) integration with existing mean-motion resonance workflows through consistent interfaces, allowing unified dynamical studies. The package has been tested through automated unit and integration tests and manual validation against examples from the literature, with all test cases---including v6, v16, z1, z2, 2v6 - v5, and 3v6 - 2v5 resonances passed successfully (with minor exceptions). The new version maintains the simplicity of the original interface, requiring only 3--4 lines of code for standard analyses, while providing researchers with powerful tools for systematic dynamical analysis and asteroid family studies. The package is available on GitHub under the MIT license.

Methods. We took orbital elements from the Minor Planet Center database and NASA JPL. For this research we used the open-source package resonances for (1) numerical integrations of orbits for asteroids over 100 000 years with planetary perturbations and (2) resonance identification. We identified all objects captured in two-body and three-body MMRs, as well as those captured in more than one resonance. Results. The study reveals that 53.76% of asteroids in the studied sample are resonant. The subset of two-body resonances contains 40.07% resonant asteroids, while the three-body subset contains 23.72% resonant asteroids. The number of asteroids trapped in two-body MMRs is significantly higher (40.07% vs. 2.0--5.0%) than previously known because of the inclusion of high-order mean motion resonances. The highest amount of two-body resonant asteroids is found at order ~36. Additionally, our results indicate that 25.57% of asteroids are involved in multiple MMRs, either through simultaneous trapping or through the phenomenon of resonance sticking, migrating from one resonance to another. Conclusions. We conclude that resonances whose order is close to the mean of all those analyzed here trap the largest number of asteroids, and that about half of the analyzed main belt asteroids are resonant. Moreover, roughly one quarter of resonant asteroids undergo migration from one MMR to another. Taken together, these results highlight the significant role of MMRs in shaping asteroid dynamics.

Near-Earth asteroid 2024 YR₄ is a dynamically interesting object due to its predicted close approach to Earth in 2032 and its potential previous residence in mean-motion resonances (MMRs). We investigated the previous resonant status of 2024 YR₄ through numerical integrations backward for 100,000 years using a statistical approach with 1,000 virtual asteroids within the initial uncertainties and employing the ias15 (modified Everhart) integrator. The statistical analysis revealed a probability for 2024 YR₄ of 72% to have been trapped in the 3J-1 resonance in its previous dynamical history, including the nominal orbit. The resonance sticking phenomenon is evident; the asteroid experienced multiple temporary captures in various resonances. Beyond the dominant 3J-1 MMR, 16% of the simulated cases show capture in the 1M-2 resonance and 12% in the 2M+3J-5 resonance, but these secondary captures typically persist for only 2,000–10,000 years. These findings agree with existing models of near-Earth asteroid production, where chaotic diffusion arising from overlapping mean-motion and secular resonances transports objects from the main belt into near-Earth orbits.

In this study, a large-scale numerical investigation of resonant objects in the Neptune region is presented, focusing on both two-body and three-body mean-motion resonances (MMRs). Two separate simulations were conducted to identify resonant populations and quantify their prevalence. In Simulation 1, two-body MMRs with Uranus and Neptune up to the resonant order q≤10, as well as three-body MMRs involving both planets up to the order q≤6, were examined. Using automated resonance classification techniques, it was found that 42.1% of objects are resonant, increasing to 58.2% when including controversial cases. This is significantly higher than the resonant fraction observed in the main asteroid belt. The results confirm that two-body MMRs with Neptune dominate, with a smaller but significant fraction of three-body resonances and two-body resonances with Uranus. In Simulation 2, the analysis was extended to higher-order (q≤20) and high-integer-coefficient (mi≤50) two-body resonances with Neptune, testing whether previously classified non-resonant objects might belong to higher-order MMRs. This second simulation revealed an additional 108 resonances and 104 new confirmed resonant objects, bringing the total fraction of resonant asteroids in the region to 49.3% confirmed cases and 65.1% with controversial cases included. Many new two-body MMRs with Neptune are found. Notably, some objects were found to be trapped in multiple resonances simultaneously. These results demonstrate that MMRs play an important role in shaping the trans-Neptunian region, with an overall resonance fraction more than three times higher than in the main asteroid belt. All objects in this region may be in fact resonant.

This paper studies the connection between existential concerns and the belief in a just world. We hypothesized that people who cannot cope with the threat to their belief in a just world will face existential concerns. To justify this hypothesis, we used a mixed-methods approach starting with a qualitative part and followed by a quantitative one. The qualitative part involved in-depth interviews with individuals (N=31, ~3.5h per interview) who have experienced situations perceived as unjust. The analysis of the interviews revealed that the experiences of unjust events actualize existential anxiety causing participants to confront existential problems arose. For the quantitative part we used the scales measuring existential concerns and the belief in a just world for several groups (500 participants in total) that had different strategies to cope with a critical event. The results demonstrated that participants facing threats to their belief in a just world had higher levels of existential anxiety. The effect size between the groups is large or medium depending on the scale.

This study explores how well various machine learning classifiers can identify mean-motion resonances in the main belt using supervised learning. The most popular classifiers are assessed: k-Nearest Neighbours, Decision Tree, Gradient Boosting, AdaBoost, Random Forest, and Naïve Bayes. In contrast to previous studies that often relied on default ML configurations, this research conducts a detailed investigation, fine-tuning, and testing of each classifier across various parameters. The results show that simpler models, especially k-Nearest Neighbours and Decision Tree, perform better than more complex ones, particularly in terms of F1 scores. The paper provides guides on selecting features, parameters, and training set sizes for optimal classifier performance and outlines a method for developing effective machine-learning models for asteroid classification.

This study explores how well various machine learning classifiers can identify mean-motion resonances in the main belt using supervised learning. The most popular classifiers are assessed: k-Nearest Neighbours, Decision Tree, Gradient Boosting, AdaBoost, Random Forest, and Naïve Bayes. In contrast to previous studies that often relied on default ML configurations, this research conducts a detailed investigation, fine-tuning, and testing of each classifier across various parameters. The results show that simpler models, especially k-Nearest Neighbours and Decision Tree, perform better than more complex ones, particularly in terms of F1 scores. The paper provides guides on selecting features, parameters, and training set sizes for optimal classifier performance and outlines a method for developing effective machine-learning models for asteroid classification.

Classical machine learning has been actively utilized in astronomy to address various challenges, including predicting orbital stability, classifying asteroids, galaxies, and other objects, and analyzing images. However, the emerging trend in artificial intelligence involves the use of large language models such as GPT-4 and ChatGPT. These models are trained on a large corpus of text and can perform a wide range of natural language processing tasks, including text generation, translation, summarization, and classification. Surprisingly, these capabilities present significant potential for application in astronomy. This paper demonstrates how the new model gpt-4-vision-preview can analyze visual patterns and accurately classify asteroids as resonant or nonresonant with high accuracy. This process requires no training, fine-tuning, or coding beyond writing the appropriate prompt in natural language. Moreover, this approach can be extended to other common problems within astronomy.

The paper examines the psychological facet of innocent suffering. One can find a description of this phenomenon in social psychology as a factor that affects the belief in a just world, but there is a lack of qualitative scientific data about related psychological features, processes, copings, and consequences on the personality level.

In this paper, a new open-source package ‘resonances’ written in python is introduced. It allows to find, analyse, and plot two-body and three-body mean-motion eccentricity-type resonances in the Solar and other planetary systems. The package has a better accuracy of the automatic identification procedure for resonant objects compared to previous studies. Furthermore, it has built-in integrations with AstDyS and NASA JPL catalogues. The code is extensively documented and tested with automatic tests. The package is available on GitHub under MIT Licence.

A catalog of asteroids in two-body orbital resonances with the planets of the Solar System has been created. The AstDyS database was a source of the input data, and all the numbered objects (467303 objects at the time of the analysis) were considered. The orbits were integrated in the framework of a pure gravitational problem considering all the planets of the Solar System and Pluto. From the analysis of the behavior of the resonant argument and the semimajor axis on the 100-kyr interval, the resonance membership and the libration type (pure or transient) were verified for each of the asteroids. A more accurate method to identify the resonant argument librations was developed on the basis of the analysis of mutual periodograms. We found 23251 resonant asteroids, ~36% of which (8397 objects) are in pure resonances.

In this paper, we apply the following machine-learning methods that do not require numerical integration — namely, k-Nearest Neighbours, Decision tree, Gradient boosting and Logistic regression — to the identification of three-body resonant asteroids in the main belt. It is shown that the results of the identification by machine-learning methods are accurate and take significantly less time than numerical integration (seconds versus days). We have identified 404 new asteroids subjected to the three-body resonance 4J-2S-1 using a machine-learning methodology.

We identify the asteroids in three-body mean-motion resonances with Jupiter and Mars on the set of all known on April 2016 numbered asteroids (467308 objects). The resonant objects are identified by the direct analysis of the behavior (libration/circulation) of the resonant arguments on 100000 yrs. All essential perturbations during the integration of the equations of the motion are taken into account. The number of the asteroids in different resonances has been calculated for all possible resonances with the order less or equal 6.

Using the 99942 Apophis asteroid (currently known as one of the most dangerous asteroids that is approaching the Earth) as an example, we estimate the error of predicting its motion with the use of several integrators over the time interval from 2012 to 2029. The minimum distance (and its error) between the Earth's center and Apophis was estimated for the rendezvous moment on April 13, 2029. It is shown that this error for various integrators is comparable in the order of magnitude with the influence of certain components of the dynamic model of motion, such as, for example, the influence of harmonics of the Earth's gravitational filed, solar-light pressure, the Jarkowski effect, etc.

An essential role in the asteroidal dynamics is played by the mean motion resonances. Two-body planet-asteroid resonances are widely known, due to the Kirkwood gaps. Besides, so-called three-body mean motion resonances exist, in which an asteroid and two planets participate. Identification of asteroids in three-body (namely, Jupiter-Saturn-asteroid) resonances was initially accomplished by D.Nesvorny and A.Morbidelli (1998), who, by means of visual analysis of the time behaviour of resonant arguments, found 255 asteroids to reside in such resonances. We develop specialized algorithms and software for massive automatic identification of asteroids in the three-body, as well as two-body, resonances of arbitrary order, by means of automatic analysis of the time behaviour of resonant arguments. In the computation of orbits, all essential perturbations are taken into account. We integrate the asteroidal orbits on the time interval of 100000 yr and identify main-belt asteroids in the three-body Jupiter-Saturn-asteroid resonances up to the 6th order inclusive, and in the two-body Jupiter-asteroid resonances up to the 9th order inclusive, in the set of ~250000 objects from the "Asteroids - Dynamic Site" (AstDyS) database. The percentages of resonant objects, including extrapolations for higher-order resonances, are determined. In particular, the observed fraction of pure-resonant asteroids (those exhibiting resonant libration on the whole interval of integration) in the three-body resonances up to the 6th order inclusive is approximately 0.9% of the whole set; and, using a higher-order extrapolation, the actual total fraction of pure-resonant asteroids in the three-body resonances of all orders is estimated as approximately 1.1% of the whole set.