Search Results (87)

Orbit determination from optical observations remains a challenging problem due to the absence of direct range measurements and the presence of sparse, noisy, and irregularly sampled data. This work presents TRACER (Tracking, Recognition, and Analysis for Celestial Ephemerides Retrieval), a robust and fully automated framework for angles-only orbit determination. The proposed approach integrates probabilistic and deterministic strategies within a unified, decision-driven architecture. In particular, statistical ranging is employed for short-arc regimes to explore admissible solutions, while deterministic methods, including modified Gauss and Väisälä techniques, are used for longer arcs and refinement. Candidate solutions are evaluated through a unified scoring function that combines observational consistency with physically motivated penalties. A key contribution of TRACER is the introduction of a randomized subset-selection outer loop, which repeatedly solves the orbit determination problem on different observation subsets and validates solutions against the full dataset, enhancing robustness in challenging scenarios. Additional mechanisms for adaptive subarc selection, recovery from failure, and progressive data assimilation further improve reliability. The resulting framework enables fully autonomous orbit determination without manual intervention, bridging the gap between individual algorithms and operational pipelines for real-world astrometric data processing. Full article

This article offers a broad-brush account of the Newtonian three-body problem, from its origins with Newton to its vibrant present, emphasizing its enduring influence on theoretical physics. It unfolds through a series of self-contained episodes that illuminate the scientific fields and the paradigm shift that have grown out of this problem. Full article

Central configurations are fundamental equilibrium solutions of the Newtonian n-body problem and play a key role in understanding the structure and dynamics of gravitational systems. However, the classification and enumeration of such configurations remain incomplete in the four-body case, particularly for symmetric configurations. In this work, we develop a framework for determining and classifying symmetric four-body Dziobek configurations. The method allows the explicit determination of the number of admissible configurations directly from the mass parameters, without requiring prior knowledge of their geometric structure. Combined with previously established semi-analytical relations, this approach provides a systematic characterization of symmetric configurations in terms of mass ratios. As a physically relevant application, we apply the framework to the Earth–Moon system and determine the possible symmetric four-body central configurations involving Earth- and Moon-mass bodies and an additional object of arbitrary mass. We identify both isolated configurations and continuous families of equilibrium solutions, extending the concept of libration points to the four-body problem. The presented semi-analytical approach contributes to the understanding of equilibrium structures in multi-body gravitational systems and provides a foundation for further studies in celestial mechanics, planetary dynamics, and spacecraft motion in complex gravitational environments. Full article

Calculation of heat transfer in granular materials is an important task for many applications, from thermal management in electronics to exploring celestial soils. Usually, an effective thermal-conductivity model is employed to predict heat flux in unstructured granular media, such as a packed bed. However, a more advanced approach, the discrete element method (DEM), can capture the complex effects of mechanical loading and material mixtures on thermal transport coefficients, which traditional models struggle with. Pivotal for this approach is knowing the heat transfer coefficient between two adjacent particles. Currently, in most DEM-capable software, only particles in direct surface contact are considered to have non-zero heat conduction. We propose considering particles that are close to each other but don’t have a contact area with a non-zero surface area. We perform numerical modeling of the conductive heat transfer coefficient between equal spherical particles separated by media, assuming the fluid’s thermal conductivity is at least an order of magnitude lower. We use numerical solutions of differential equations to account for both thermal resistance within particles and through the gap between them. We found a simple generalized correlation for the heat transfer coefficient between particles and a general formula for the angular distribution of heat flux density across the particle surface. By employing a non-dimensional approach, the obtained formulas are constructed using non-dimensional parameters: the ratio of the particle’s thermal conductivity to that of the medium, and the ratio of the gap width between particles to their radius. The resulting formula is simple and convenient for DEM heat transfer calculations in packed and fluidized beds. Full article

Automated recognition of celestial bodies from observational imagery is a cornerstone of autonomous space exploration. However, deploying deep learning models in space environments entails rigorous requirements not only for accuracy but also for reliability (calibration) and safety (anomaly rejection). Traditional Convolutional Neural Networks (CNNs) trained on small-scale astronomical datasets often suffer from overfitting and overconfidence on Out-of-Distribution (OOD) artifacts. In this work, we present a robust classification framework based on DINOv2, a Vision Transformer pre-trained via discriminative self-supervised learning. We curate a high-fidelity dataset of seven planetary classes sourced from NASA archives and propose a two-stage domain adaptation strategy to transfer large-scale foundation model features to this fine-grained task. Extensive experiments show that our method reaches 100% Top-1 accuracy on the canonical split, and remains highly stable under split variation, achieving 99.43% ± 0.85% Top-1 accuracy across R = 5 repeated stratified splits. More importantly, we address the critical issue of model trustworthiness. Through post hoc temperature scaling, our model achieves a state-of-the-art Expected Calibration Error (ECE) of 0.08%, representing a 36-fold improvement over ResNet50 (2.90%) and a 4.5-fold improvement over the EfficientNet-B3 baseline (0.36%). Furthermore, by integrating Energy-based OOD detection, the system effectively rejects non-planetary artifacts with an AUROC of 93.7%. Qualitative analysis using Grad-CAM reveals that self-supervised attention mechanisms naturally focus on intrinsic planetary features (e.g., surface textures and rings) while ignoring background noise, confirming the superior robustness of vision foundation models in astronomical vision tasks. Full article

The Planet Nine hypothesis encompasses a body of about 5–8 Earth’s masses whose orbital plane would be inclined to the ecliptic by one or two tens of degrees and whose perihelion distance would be as large as about 240–385 astronomical units. Recently, a couple of his epigones have appeared: Planet X and Planet Y. The former is similar to a minor version of Planet Nine in that all its physical and orbital parameters would be smaller. Instead, the latter would have a mass ranging from that of Mercury to Earth’s and a semimajor axis within 100–200 astronomical units. By using realistic upper bounds for the orbital precessions of Saturn, one can obtain insights on their position which, for Planet Nine, appears approximately confined around its aphelion. Planet Y can only be a Mercury-sized object at no less than about 125 astronomical units, while Planet X appears to be ruled out. Dedicated data reductions by modeling such perturber(s) are required to check the present conclusions, to be intended as hints of what might be detectable should planetary ephemerides include them. A probe on the same route of Voyager 1 would be perturbed by Planet Nine by about 20–40 km after some decades. Full article

Forty-two Jupiter Mass Binary Objects (JuMBOs) have been discovered in the Trapezium Cluster: either brown dwarf stars or planets mutually orbiting in pairs. Here it is shown that, just as in galaxies and wide binaries, the mutual orbits of the objects in each of these twin systems deviate from the Newtonian and level off around a mutual acceleration of $2c^2/\Theta =2\times {10}^{-10}$ m/s² supporting the minimum acceleration predicted by Quantised Inertia (QI), a theory that attributes inertial mass to an interaction between information horizons and quantum fields and predicts galaxy rotation without the need for dark matter. QI further predicts that the JuMBOs with separations of 400 AU should show orbital anomalies of 70 m/s. This could be tested using spectral Doppler data. Full article

We present the ContEvol (continuous evolution) formalism, a family of implicit numerical methods which only need to solve linear equations and are almost symplectic. Combining values and derivatives of functions, ContEvol outputs allow users to recover full history and render full distributions. Using the classic harmonic oscillator as a prototype case, we show that ContEvol methods lead to lower-order errors than two commonly used Runge–Kutta methods. Applying first-order ContEvol to simple celestial mechanics problems, we demonstrate that deviation from equation(s) of motion of ContEvol tracks is still 𝒪(h⁵) (h is the step length) by our definition. Numerical experiments with an eccentric elliptical orbit indicate that first-order ContEvol is a viable alternative to classic Runge–Kutta or the symplectic leapfrog integrator. Solving the stationary Schrödinger equation in quantum mechanics, we manifest ability of ContEvol to handle boundary value or eigenvalue problems. Important directions for future work, including mathematical foundations, higher dimensions, and technical improvements, are discussed at the end of this article. Full article

Stochastic differential equations (SDEs) with multiple conserved quantities are ubiquitous in scientific fields, modeling systems from molecular dynamics to celestial mechanics. While geometric numerical integrators that preserve single invariants are well-established, constructing efficient and high-order numerical schemes for SDEs with multiple conserved quantities remains a challenge. Existing approaches often suffer from high computational costs or lack desirable numerical properties like symmetry. This paper introduces two novel classes of projection-based numerical methods tailored for SDEs with multiple conserved quantities. The first method projects the increments of an underlying numerical scheme onto a discrete tangent space, ensuring all invariants are preserved by construction. The second method leverages a local coordinates approach, transforming the SDE onto the manifold defined by the invariants, solving it numerically, and then projecting back, guaranteeing the solution evolves on the correct manifold. We prove that both methods inherit the mean-square convergence order of their underlying schemes. Furthermore, we propose a simplified strategy that reduces computational expense by redefining the multiple invariants into a single one, offering a practical trade-off between exact preservation and efficiency. Numerical experiments confirm the theoretical findings and demonstrate the superior efficiency and structure-preserving capabilities of our methods. Full article

The Planet Optimization Algorithm (POA) is a meta-heuristic inspired by celestial mechanics, drawing on Newtonian gravitational principles to simulate planetary dynamics in optimization search spaces. While the POA demonstrates a strong performance in continuous domains, we propose an Improved Binary Planet Optimization Algorithm (IBPOA) tailored to the classical 0-1 knapsack problem (0-1 KP). Building upon the POA, the IBPOA introduces a novel improved transfer function (ITF) and a greedy repair operator (GRO). Unlike general binarization methods, the ITF integrates theoretical foundations from branch-and-bound (B&B) and reduction algorithms, reducing the search space while guaranteeing optimal solutions. This improvement is strengthened further through the incorporation of the GRO, which significantly improves the searching capability. Extensive computational experiments on large-scale instances demonstrate the IBPOA’s effectiveness for the 0-1 KP, showing a superior performance in its convergence rate, population diversity, and exploration–exploitation balance. The results from 30 independent runs confirm that the IBPOA consistently obtains the optimal solutions across all 15 benchmark instances, spanning three categories. Wilcoxon’s rank-sum tests against seven state-of-the-art algorithms reveal that the IBPOA significantly outperforms all competitors $(p<0.05)$, though it is occasionally matched in its solution quality by the binary reptile search algorithm (BinRSA). Crucially, the IBPOA achieves solutions 4.16 times faster than the BinRSA on average, establishing an optimal balance between solution quality and computational efficiency. Full article

While Kepler is regarded as a major figure in standard historical accounts of the scientific revolution of early modern Europe, he is typically seen as having one foot in the new scientific culture and one in the old. In some of his work, Kepler appears, along with Galileo, to be on a trajectory towards Newton’s celestial mechanics. In addition to his advocacy of Copernicus’s heliocentrism, he appealed to physical causes in his explanations of the movements of celestial bodies. But other work appears to express a neo-Platonic “metaphysics” or “mysticism”, as most obvious in his embrace of the ancient tradition of the “music of the spheres”. Here I problematize this distinction. The musical features of Kepler’s purported neo-Platonic “metaphysics”, I argue, was also tied to Platonic and neo-Platonic features of the methodology of a tradition of mathematical astronomy that would remain largely untouched by his shift to heliocentrism and that would be essential to his actual scientific practice. Importantly, certain features of the geometric practices he inherited—ones later formalized as “projective geometry”—would also carry those “harmonic” structures expressed in the thesis of the music of the spheres. Full article

This paper offers new insights into gravitational interactions within a general non-inertial reference frame. By utilizing symbolic tensor calculus, the study establishes a unified framework that connects time derivatives in non-inertial frames to those in inertial frames. The research introduces new first integrals of motion for a system of many particles in arbitrary non-inertial and barycentric rotating reference frames. These first integrals provide a kinematic and geometric visualization of motion in non-inertial frames. Additionally, a generalized potential energy function is presented for broader applicability. For the gravitational two-body problem, the paper delivers a closed-form, coordinate-free solution for the motion of each body relative to the original frame. Consequently, sufficient conditions for stability against collisions are established within the context of the two-body problem in a non-inertial reference frame. Furthermore, the paper examines the relative orbital motion of spacecraft, presenting a closed-form and coordinate-free solution in the local vertical local horizontal (LVLH) non-inertial frame, which is centered on the center of mass of the main spacecraft. Full article

Armillary spheres were developed in the East and the West for a long time. They independently developed various functions for astronomy. In this article, we discuss the differences in mechanical structures, appearance, and functions between the armillary spheres in ancient China and Europe. The earliest armillary sphere in ancient China was invented by Luo Xia Hong (落下閎) between 156 BC and 87 BC. Then, the armillary sphere in ancient China improved with the historical development of astronomy. The famous armillary sphere was built in an astronomical clock tower (水運儀象台) by Su Song (蘇頌) in the Song (宋) dynasty. This armillary sphere was an astronomical apparatus for the observation of celestial phenomena and the correction of time standards. However, the armillary sphere in Europe had different applications, even though the structures were similar. The armillary spheres in Europe simulated the sun’s trajectory in one day to predict the sunrise and sunset positions. They adjusted the tilting angle of the celestial sphere with the altitude of observation to observe the path of the stars around the ecliptic. Through this review, the armillary spheres in ancient China and Europe are defined clearly. Full article

Goldfish (Carassius auratus), subjected to millennia of artificial selection and breeding, have diversified into numerous ornamental varieties, such as the celestial-eye (CE) goldfish, noted for its unique dorsal eye rotation. Previous studies have primarily focused on anatomical modifications in CE goldfish eyes, yet the molecular underpinnings of their distinctive eye orientation remain poorly understood. This study employed high-throughput transcriptome and proteome sequencing on 110-day-old full-sibling CE goldfish, which displayed either anterior or upward eye rotations. Verification of these findings was conducted using quantitative PCR (qPCR) for transcriptomic data and parallel reaction monitoring (PRM) for proteomic analysis. Our research identified 73,685 genes and 7717 proteins, pinpointing 8 common differentially expressed genes (DEGs) and proteins (DEPs) implicated in cytoskeleton remodeling, cell adhesion, apoptosis, and optic nerve regeneration. Enrichment analyses further delineated pathways associated with apoptosis, necroptosis, and cell adhesion molecules. The results indicated a significant role for genes involved in cytoskeletal dynamics, nervous system function, and apoptotic processes in the dorsal eye rotation of CE goldfish. Analyses of abnormalities in ocular membrane structures, along with disturbances in lipid and protein synthesis metabolism and energy metabolism during developmental stages, provided compelling evidence for the potential use of CE goldfish as a model organism in studying human eye-related disorders. This investigation provided the first comprehensive transcriptomic and proteomic overview of eye rotation in CE goldfish, offering insights crucial for the genetic breeding of new ornamental fish varieties. Full article

Traditional celestial navigation mainly utilized the sextant to measure the attitude and the position contour method to calculate and resolve the vessel’s positioning problem, but these methods are not rigorous, having major deficiencies in the positioning accuracy. Currently, the small field-of-view star sensor is becoming the main attitude measurement equipment on vessels, and its measurement accuracy directly affects the vessel positioning results. Aiming at this problem, this research provides a model of small field-of-view star sensor positioning accuracy based on the two-star combination method, and numerical solutions are given. In addition, it focuses on the influence of the measurement error of the star sensor, especially the elevation angle error, on the positioning accuracy of the vessel and gives the star selection strategy for practical application. In particular, the star selection strategy is also applicable to other two-star positioning methods. The results show that the analytical solution is computationally simple and real-time, and the effect of measurement errors on positioning can be minimized by the star selection strategy. This study reveals the error influence mechanism based on the dual-star combination approach, which has significant implications for practical vessel navigation using small-field-of-view star sensors. Full article