With the deployment of mega-constellations, the proliferation of on-orbit Resident Space Objects (RSOs) poses a severe challenge to Space Situational Awareness (SSA). RSOs produce elongated and stripe-like signatures in long-exposure imagery as a result of their relative orbital motion. The accurate detection of these signatures is essential for critical applications like satellite navigation and space debris monitoring. However, on-orbit detection faces two challenges: the obscuration of dim RSOs by complex stray light interference, and their dense overlapping trajectories. To address these challenges, we propose the Shape-Aware Attention Network (SAANet), establishing a unified Shape-Aware Paradigm. The network features a streamlined Shape-Aware Feature Pyramid Network (SA-FPN) with structurally integrated Two-way Orthogonal Attention (TTOA) to explicitly model linear topologies, preserving dim signals under intense stray light conditions. Concurrently, we propose an Adaptive Linear Oriented Bounding Box (AL-OBB) detection head that leverages a Joint Geometric Constraint Mechanism to resolve the ambiguity of regressing targets amid dense, overlapping trajectories. Experiments on the AstroStripeSet and StarTrails datasets demonstrate that SAANet achieves state-of-the-art (SOTA) performance, achieving Recalls of 0.930 and 0.850, and Average Precisions (APs) of 0.864 and 0.815, respectively.

Unified modeling of relative motion in eccentric orbits under J2 perturbation for non-cooperative targets

An analytical solution to the nonlinear differential equation describing the equation of motion of a particle moving in an unforced physical system with linear damping, governed by a cubic potential well, is presented in terms of the Jacobi elliptic functions. In the attractive region of the potential the system becomes an anharmonic damped oscillator, however with asymmetric displacement. An expression for the period of oscillation is derived, which for a nonlinear damped system is time dependent, and in particular it contains a quartic root of an exponentially decaying term in the denominator. Initially the period is longer as compared to that of a linear oscillator, however gradually it decreases to that of a linear damped oscillator. Transforming the undamped nonlinear differential equation into the differential equation describing orbital motion of planets, the perihelion advance of Mercury can be estimated to 42.98 arcseconds/century, close to present day observations of 43.1±0.5 arcseconds/century. Some familiarity with the Jacobi elliptic functions is required, in particular with respect to the differential behavior of these functions, however, they are standard functions of advanced mathematical computer algebra tools. The expression derived for the solution to the nonlinear physical system, and in particular the expression for the period of oscillation, is useful for an accurate evaluation of experiments in introductory and advanced physics labs, but also of interest for specialists working with nonlinear phenomena governed by the cubic potential well.

Understanding planetary orbits is a fundamental concept in astronomy. Many secondary school students encounter difficulties comprehending the shape and characteristics of orbits, which are not perfect circles but ellipses with varying degrees of eccentricity. These challenges are particularly evident when students are tasked with sketching or calculating the eccentricity of a planet's orbit, a measure of how elongated the orbit is. This study aims to explore and compare the efficacy of two pedagogical approaches manual simulation and digital simulation—in enhancing students' understanding of planetary orbit shapes and the concept of eccentricity. A descriptive-comparative research design is employed to depict and contrast the effectiveness of these two teaching methods. The experiment, crafted based on expert design, involves four qualified astronomy educators to apply both approaches. The manual simulation requires students to draw orbits and compute eccentricity manually, whereas the digital simulation leverages software to visualize the motion of planetary orbits. Evaluation is conducted through Focus Group Discussions (FGD) with four subject matter experts to provide feedback on the effectiveness of the two methods, the challenges faced by students, and the level of comprehension achieved. The results from the manual experiment indicate that the orbital eccentricity ranges between 0.2 and 0.4, suggesting that the planets' orbits are elliptical. These findings align with Kepler’s laws, which state that planetary orbits are elliptical, with the Sun at one of the foci. Results from the NASA Eyes application further corroborate this, showing that the orbits of planets in the solar system are indeed elliptical, both at perihelion (the point closest to the Sun) and aphelion (the end farthest from the Sun). In conclusion, this research substantiates that the orbits of planets in the solar system are elliptical, consistent with Kepler's laws.

The purpose of the work is to build an updated model of the illumination of artificial satellites in circular Earth orbits and to study the duration and nature of solar illumination in orbits with different inclinations and altitudes throughout the year. The mathematical model uses the equation of the circular cone of the shadow, built taking into account the movement of the Sun relative to the Earth. The center of the cross section of the base of the cone coincides with the center of the Earth. The motion of the satellite is simulated by Kepler’s orbit. The computer model makes it possible to determine with a given accuracy the duration of the satellite’s stay in the Earth’s shadow. Simulation of the duration of illumination of satellites at two altitudes has been performed: 5,000 km and 35,786 km (geosynchronous orbit altitude) throughout the year. Curves of the duration of the satellites’ stay in the shadow are given. The shape of the curves varies from a nearly straight line for inclined orbits 25°, then they become periodic, and then divide into two parts, resembling the shape of a parabola. Among all the possible inclinations of the orbits of satellites, extreme ones have been detected. These are orbits with an angle of inclination 23°26', which defines a straight orbit. On them, an artificial satellite falls into the Earth’s shadow throughout the year at each orbit. The second group of extreme orbits are orbits with inclinations, in which the satellite falls into the shadow only near the time of the equinoxes. Shortest duration of stay of satellites in the shadow moving in orbits with an angle of inclination 113°26'. Falling into the shadow lasts from 15.02 to 23.04 and from 19.08 to 27.10 for an altitude of 5,000 km, and from 12.03 to 28.03 and from 14.09 to 01.10 for an altitude of 35,786 km. The results of the simulations will allow us to clarify the effect of sunlight and solar wind pressure on the motion of satellites over time. This will allow the use of additional satellite accelerations resulting from radiative impact to change the orbits of space debris and clean up near-Earth space.

Abstract In this paper, we present a detailed analysis of the light variation of KIC 5623923 using high-precision time-series data from the Kepler mission. The analysis reveals this target is an eclipsing binary system with δ Scuti-type pulsations from the primary component, rather than from the secondary as previously reported. The frequency analysis of three short-cadence data reveals 41 significant frequencies, including the orbital frequency ( f orb = 0.827198 day −1 ) due to orbital motion from the binary system and the pulsational frequencies. Most of the pulsational signal lies in the frequency range of 20–32 day −1 , with amplitude between 0.3 and 8.8 mmag, in which seven peaks are identified as “independent” modes. The strongest one ( f 3 = 28.499399 day −1 ) likely corresponds to a high-order radial mode. In other peaks ( f 7 , f 10 , and f 18 ), several pairs of multiplet structures centered on them are found. The fitting of spectral energy distribution using the collected photometry measurement of multiple bands reveals the effective temperatures of the primary and secondary components as 834 8 − 225 + 230 K and 475 3 − 229 + 237 K, respectively, which place the primary star in the classical pulsating instability zone. The characteristic light-curve morphology and short orbital period are consistent with a tidally locked system. Based on the characteristics of amplitude spectra of pulsating stars in close binaries, the analysis of the multiplet structures reveals that three independent frequencies (i.e., f 7 , f 10 , and f 18 ) correspond to nonradial modes with l = 2, while the associated sidelobes are produced by the orbital motion. We highlight the potential of this method in future studies of pulsating binary stars.

The observed magnetic moment of an electron implies that it cannot be a point particle and, therefore, should have a substructure. This paper proposes that the electron consists of three hypothetical constituent particles: Two negatively charged ones orbiting around a positively charged particle. Our analysis encompasses the electron’s zitterbewegung and magnetic moment, leveraging the fundamental constants of Planck and Coulomb. We show that: (1) Coulombic interactions between constituents, multiplied by the inverse of the fine structure constant, link the zero-point energy to the electron’s zitterbewegung frequency, and (2) the electron’s magnetic moment results from the orbital motion of the constituents, leading to a unique derivation of the Bohr magneton. These insights into the quantum characteristics of electrons present new research opportunities in nuclear interactions and the physics of composite particles.

Abstract We present a new three-parameter family of self-consistent equilibrium models for quasi-relaxed stellar systems that are subject to the combined action of external tides and rigid internal rotation. These models provide an idealised description of globular clusters that rotate asynchronously with respect to their orbital motion around a host galaxy. Model construction proceeds by extension of the truncated King models, using a newly defined asynchronicity parameter to couple the tidal and rotational perturbations. The method of matched asymptotic expansion is used to derive a global solution to the free boundary problem posed by the corresponding set of Poisson-Laplace equations. We explore the relevant parameter space and outline the intrinsic properties of the resulting models, both structural and kinematic. Their triaxial configuration, characterised by extension in the direction of the galactic centre and flattening toward the orbital plane, is found to depart further from spherical symmetry for larger values of the asynchronicity parameter. We hope that these simplified analytical models serve as useful tools for investigating the interplay of tidal and rotational effects, providing an equilibrium description that complements, and may serve as a basis for, more realistic numerical simulations.

The paper addresses the problem of on-off spacecraft relative control in sliding mode for autonomous on-orbit servicing operations under actuator amplitude limits, action discreteness, and parametric uncertainties. The goal is to develop and assess an approach that combines sliding-mode control with modern reinforcement-learning methods tailored for resource-constrained onboard implementation. Relative motion dynamics is formulated in an orbital coordinate frame with normalized states and discretized in time. Binary actions with pulse-width modulation, subject to constraints on the thrust level, pulse duration, and duty cycle, represent the impulsive nature of actuation. We propose a combined synthesis in which the sliding-surface parameters and switching rules are tuned via proximal policy optimization within an actor-critic architecture. The actor and critic are implemented as neural networks that approximate the policy and the value function, respectively. The actor neural network takes the state vector as input information and outputs the mean and standard deviation of the parameters of the sliding mode control law. The value function penalizes both the state error and control effort, thus enabling a trade-off among the response speed, accuracy, and propellant consumption. Two uncoupled agents are designed to control spacecraft relative orbital motion in in-plane and out-of-plane directions independently. The proximal policy optimization hyperparameters are selected to ensure a trade-off among the learning time, stability, and control performance. The reinforcement-learning agents are trained and analyzed considering four cases that differ in the thrust levels and weighting matrices. The quality functional combines state deviation and thrust use penalties, thus enabling a trade-off among the response speed, accuracy, and propellant consumption. The results confirm the potential of this approach for autonomous spacecraft control under constraints and uncertainty. Compared with reported baselines, the trained agent shows superior robustness to plant-parameter uncertainty, which we attribute to the inherent robust properties of sliding-mode control. These findings have the potential to improve the efficiency and autonomy of on-orbit servicing operations.

The geostationary orbit (GEO), a finite one-dimensional longitudinal resource, has emerged as a critical research focus driven by the rapid development of global communication systems. This scarcity motivates current research efforts toward multi-satellite collocation within single longitudinal slots. This article investigates the optimization design problem of configurations at fixed longitudes in GEO. First, a kinematic model describing the relative fixed-point motion of geostationary satellites was established. Subsequently, the long-term stability conditions of these fixed-point configurations under J2 perturbations were analyzed, with collocation flight stability and passive flight safety formulated as design constraints. The particle swarm optimization (PSO) algorithm was employed to design circular and straight-line spatial configurations, and their corresponding Kepler orbital elements were numerically simulated. Comparative analysis confirmed that circular configurations demonstrate superior stability compared to straight-line configurations.

We introduce a novel high-resolution cluster simulation designed to serve as the massive halo counterpart of the modern cosmological galaxy evolution framework. The zoom-in simulation targets a volume of 4.1σ overdensity region, which is expected to evolve into a galaxy cluster with a virial mass of 5 M_⊙, comparable to that of the Virgo Cluster. The zoom-in volume extends out to 3.5 virial radii from the central halo. The novelties of M_⊙ is effective for tracing the early assembly of massive galaxies as well as the formation of dwarf galaxies. The spatial resolution of 68,parsecs in the best-resolved regions in the adaptive-mesh-refinement approach is a powerful tool for studying the detailed kinematic structure of galaxies. The time interval between snapshots is also exceptionally short (i.e., 15 Myr). This is ideal for monitoring changes in the physical properties of galaxies, particularly during their orbital motion within a larger halo. The simulation includes up-to-date feedback schemes for supernovae (SNe) and active galactic nuclei (AGNs). The chemical evolution is calculated for ten elements, along with dust calculation that includes the formation, size change, and destruction. To overcome the limitations of the Eulerian approach used for gas dynamics in this study, we employed Monte Carlo-based tracer particles in 10^ 14 are exemplified by its resolution. Its stellar mass resolution of 2 10^ 4 enabling a wide range of scientific investigations. The simulation has passed z=0.8, covering well over half of its cosmic history. We released the early data with the expectation they will facilitate studies of the early evolution of galaxies and overdensities.

Abstract We present the continuation of a systematic search for new southern Galactic symbiotic stars, selecting candidates from the SuperCOSMOS Hα Survey and 2MASS. Follow-up spectroscopy with the Southern African Large Telescope (SALT) was used to confirm their symbiotic nature and to characterize the cool and hot components of the full sample, including systems from earlier work. We report 14 newly confirmed bona fide symbiotic stars and identify 6 additional strong candidates. Photometric variability was examined using our data and archival light curves from multiple all-sky surveys. Most systems are variable, with the majority showing periodic modulation consistent with orbital motion or pulsations. Possible photometric orbital periods are reported for 19 confirmed and 3 candidate systems, pending spectroscopic confirmation. Eight objects exhibit signs of outburst activity. In one of the systems, multiple brightenings occur at similar orbital phases, closely resembling the evolution of FN Sgr, a symbiotic binary with a magnetic white dwarf. The peculiar variability of another symbiotic star is best explained by dust-obscuration events. These results expand the census of Galactic symbiotic stars.

Optical trapping is a non-invasive technique for manipulating nano- and microscopic objects and is widely used to investigate biological processes, such as membrane viscosity, membrane-cytoskeleton interactions, and the regulation of cellular functions. Optical vortex beams can maintain orbital angular momentum (OAM) and have recently been used for optical manipulation. When nanoparticles in aqueous solutions are rotated at the laser focus owing to the optical forces derived from the optical vortex beam, their subsequent motion is governed by the OAM. The dynamics of nanoparticles attached to the biological membrane may be further affected by the viscoelasticity of the membrane and hydrodynamic coupling; however, it is unclear whether such rotational motion on lipid bilayers can be controlled. In this study, we applied an optical vortex beam to the two-dimensional rotational manipulation of fluorescent nanoparticles attached to a supporting lipid bilayer (SLB) and investigated their rotational behavior. We revealed that the single nanoparticles attached to the SLB rotated more slowly than those in an aqueous solution, but their orbital motion was still clearly driven by the OAM of the beam. The orbital radius of rotation was tuned according to the magnitude of the topological charge, and an angle velocity that changed linearly in proportion to both the laser power and nanoparticle diffusion coefficient was identified, which was consistent with theoretical calculations. These results suggest that optical vortex beams can manipulate nanoparticles attached to SLB with controllable rotational dynamics. Such rotational manipulation of nanoparticles on lipid bilayers can provide a platform for studying the effects of nanoparticle rotation on the local organization of membrane components and can be useful for developing methods to regulate their dynamic properties.

Cislunar satellite motion prediction via hybrid parametric and deep learning models

In naval and ocean engineering, accurate simulation of incident waves is essential for predicting the motion response of offshore structures. Traditional wave generation methods, such as piston- and flap-type wave makers, often face challenges in accurately replicating the orbital motion of water particles beneath the free surface, which can limit their applicability in high-fidelity simulations. In this study, a numerical investigation is conducted to compare the performance of piston-type, flap-type, and double-flap-type wave makers using STAR-CCM+2310(18.06.006-R8). The influence of water depth on wave height accuracy is evaluated across different measurement locations within a numerical wave tank. Theoretical analysis of wave generation mechanisms is incorporated to clarify the applicability limits of linear theory and to better interpret the numerical results. Results indicate that, under the tested two-dimensional CFD conditions, the double-flap-type wave maker tended to provide closer agreement with theoretical predictions, particularly at greater depths, compared with conventional methods. These findings suggest potential advantages of the double-flap configuration and provide insights for refining wave generation techniques in numerical and experimental wave tanks, thereby supporting more reliable hydrodynamic analyses of floating structures.

ABSTRACT In three previous papers, we analysed the origin of the properties of halo substructure found in simulations. This was achieved by deriving them analytically in the peak model of structure formation, using the statistics of nested peaks (with no free parameter) plus a realistic model of subhalo stripping and shock-heating (with only one parameter). However, to simplify the treatment we neglected dynamical friction (DF). Here, we revisit that work by accounting for DF. That is also done in a fully analytic manner that avoids the numerical integration of the subhalo orbital motion. We obtain very simple expressions for the abundance and radial distribution of subhaloes of different masses that disentangle the effects of DF from those of tidal stripping and shock-heating. These analytic expressions reproduce and explain the results of simulations and allow one to extend them to haloes of any mass, redshift, and formation times in any desired cosmology.

We propose a framework for topological soliton dynamics in trapped spinor superfluids, decomposing the force acting on the soliton by the surrounding fluid into the buoyancy force and spin corrections arising from the density depletion at soliton core and the coupling between the orbital motion and the spin mixing, respectively. Our formulation applies to large-amplitude soliton motion in general superfluids with spin degrees of freedom under arbitrary external potentials. For ferrodark solitons (FDSs) in spin-1 Bose-Einstein condensates, the spin correction could diverge, change the direction of the total force, and enable mapping the FDS motion in a harmonic trap to the atomic-mass particle dynamics in an emergent quartic potential. Initially placing a type-I FDS near the trap center, a single-sided oscillation happens, which maps to the particle moving around a local minimum of the emergent double-well potential. As the initial distance of a type-II FDS from the trap center increases, the motion exhibits three regimes: trap-centered harmonic and anharmonic oscillations followed by single-sided oscillations. Correspondingly the emergent quartic potential undergoes a transition from a single minimum to a double-well shape, where the particle motion shifts from oscillating around the single minimum to crossing between two minima via the local maximum, then the symmetry-breaking motion around one of the two minima. In a hard-wall trap with linear potential, the FDS motion maps to a harmonic oscillator.

We theoretically consider orbital rotation of a spheroidal submicron particle in the field of two counter-propagating circularly polarized Gaussian beams. We derived equations connecting the parameters of the circular orbits centered on the beams axis to the optical force and torque. The equations show that, besides orbital rotation, the spheroidal particle simultaneously rotates around its equatorial axis. We found that two distinct dynamic regimes are possible. The orbital motion can be accompanied by a rapid proper rotation with angular velocity an order of magnitude larger than the angular velocity of the orbital rotation. Alternatively, the orbital and proper rotations can be synchronized. The direction of orbital rotation can either coincide with or be opposite to the direction of rotation of the electric vector. The findings are confirmed by direct numerical simulations. The results can be of use in development of nano-scale gyroscopes as well in shape-selective sorting of submicron particles.

Abstract Understanding the long-term evolution of lunar orbit is an essential task in astronomy and astrophysics because lunar and planetary ephemerides are indispensable in many important applications, such as spacecraft navigation and reference frame transformations. Recently, it has been suggested that climate dynamics, particularly sea level change due to melting of polar ice sheets, can subtly modulate ocean tides, thus altering the tidal dissipation and lunar recession rate by ∼2.6% in the 21st century. In our study, we provide a correction to standard models of lunar orbital evolution relevant for astrophysical applications. We use the reconstructed history of ice thickness, paleotopography, and sea level change since the last glacial cycle (∼122,000 yr ago) and adopt a revised tidal dissipation model to argue that the climate-induced changes in the lunar orbit might not be negligible and have likely altered the Earth–Moon distance by variable rates as large as ∼0.9 mm yr −1 , which occur on top of the background trend of ∼38.3 mm yr −1 . However, this is currently absent from dynamical models of lunar evolution. Our results suggest that lunar orbit ephemerides might need to be revised by at least ∼1.5%–2.3% in order to obtain a more accurate representation of the tidal dynamics and orbital motions. The model proposed in this paper might also be relevant for other astrophysical bodies, such as exoplanetary satellites.

Abstract Tidal flats worldwide are undergoing accelerated regime shifts from accretion to erosion, undermining their natural capacity for coastal protection and threatening the sustainability of adjacent urban areas. Although the influences of climate change and reduced sediment supply on tidal flat morphodynamics are widely acknowledged, the intrinsic sediment dynamic mechanisms behind these shifts remain poorly understood. Based on multi‐year in situ observations of Jiangsu tidal flat—once known for rapid accretion but now undergoing erosion under multiple stressors—we show that the regime shift occurs progressively, with erosion expanding from the lower to the upper intertidal zone over several years. Episodic high‐energy wave events dominated near‐bed boundary‐layer hydrodynamics in this shallow‐water environment. Wave orbital motions penetrated efficiently to the seabed, producing high wave‐current shear stresses that caused net erosion, whereas tidal currents played a secondary role. Erosion was highly sensitive to wave height; a threshold of approximately 0.22 m triggered the shift from accretion to erosion. This wave‐dominated erosion led to bed lowering, which further amplified wave energy and erosion rates, establishing a self‐reinforcing feedback. We propose a conceptual morphodynamic model illustrating this mechanism of accretion–erosion transition, which may also apply to other sediment‐starved coastal systems such as subaqueous deltas. These insights support improved adaptive management of vulnerable coastal sedimentary systems under growing climatic and anthropogenic pressures.