Orbital Motion Research Articles

Emergence of collective oscillations in massive human crowds

Dense crowds form some of the most dangerous environments in modern society1. Dangers arise from uncontrolled collective motions, leading to compression against walls, suffocation and fatalities2, 3–4. Our current understanding of crowd dynamics primarily relies on heuristic collision models, which effectively capture the behaviour observed in small groups of people5,6. However, the emergent dynamics of dense crowds, composed of thousands of individuals, remains a formidable many-body problem lacking quantitative experimental characterization and explanations rooted in first principles. Here we analyse the dynamics of thousands of densely packed individuals at the San Fermín festival (Spain) and infer a physical theory of dense crowds in confinement. Our measurements reveal that dense crowds can self-organize into macroscopic chiral oscillators, coordinating the orbital motion of hundreds of individuals without external guidance. Guided by these measurements and symmetry principles, we construct a mechanical model of dense-crowd motion. Our model demonstrates that emergent odd frictional forces drive a non-reciprocal phase transition7 towards collective chiral oscillations, capturing all our experimental observations. To test the robustness of our findings, we show that similar chiral dynamics emerged at the onset of the 2010 Love Parade disaster and propose a protocol that could help anticipate these previously unpredictable dynamics.

Orbital motion and epicyclic oscillations around a black hole with magnetic charge

Orbital motion and epicyclic oscillations around a black hole with magnetic charge

Explicit solution for the attitude motion of a bias momentum satellite under Bdot magnetic damping

Explicit solution for the attitude motion of a bias momentum satellite under Bdot magnetic damping

Structure Functions of Rotation Measures Revealing the Origin of Fast Radio Bursts

Abstract Structure function (SF) analysis is a powerful tool for studying plasma turbulence. Theoretically, the SF of Faraday rotation measure (RM) is expected to include a geometric component due to the relative orientation of sight lines through an ordered magnetic field. However, observational evidence for this component remains elusive. Here, we report that the SFs of the binary PSR B1744–24A and the repeating fast radio burst (FRB) 20201124A exhibit both a periodic geometric component, caused by binary orbital motion, and a flat statistical component. The statistical component, induced by stochastic fluctuations in electron density and magnetic field, aligns with RM scatter derived from pulse depolarization. These findings indicate that FRB 20201124A has a binary origin and suggest that the periodic geometric component can serve as a diagnostic tool to identify binary companions.

An In-depth Investigation of the Primordial Cluster Pair ASCC 19 and ASCC 21

Abstract Utilizing Gaia data from the literature, we report a new young (∼8.9 Myr) cluster pair, ASCC 19 and ASCC 21, located near the Orion star-forming complex. The clusters are separated by a 3D distance of 27.00 ± 7.51 pc. Both clusters share a common age (Log(age) = 6.95 ± 0.05), similar radial velocities (RV = 21.34 ± 4.47 km s−1 for ASCC 19 and RV = 20.05 ± 3.86 km s−1 for ASCC 21), and comparable metallicities ([Fe/H] = −0.14 ± 0.25 dex for ASCC 19 and [Fe/H] = −0.12 ± 0.04 dex for ASCC 21, from LAMOST-DR11). These similarities suggest that the clusters likely originated from the fragmentation of the same molecular cloud, forming a primordial cluster pair. Furthermore, the formation of the two clusters is attributed to the coalescence of multiple subclusters, as inferred from the distribution analysis between metal abundances and distances to clusters’ centers. Neither cluster shows significant mass segregation. Their members with RVs exceeding 100 km s−1 are young variables. Additionally, a tidal interaction between the clusters is observed. Comparisons of the Roche radius with tidal radii, as well as velocity difference with orbital velocity, suggest that the pair is an unbound system, that is, a double cluster. Finally, orbital motion simulations show that the clusters will not merge into a single system.

Determination of the Electric Field by Particle Tracking in a Plasma Sheath Region during Free Fall

In this work we present an experiment in which we injected microspheres at low pressure into a capacitively coupled argon plasma chamber. The setup was located in the top point of the Einstein-Elevator drop tower in Hannover, Germany, where the microparticles reached their equilibrium position above the lower electrode during 1g. During the fall, the trajectories of the microparticles, which were driven by the electric force, the neutral drag force and some residual gravitational force, were recorded. In addition, simulations of the plasma conditions were performed with commercial software to determine the microparticle charges via an orbital motion limit theory approach, taking into account the charge exchange in ion-neutral collisions. Based on the calculated position dependence of the microparticle charges and the electric force, the electric field present in the plasma sheath region was finally determined.

Evidence for magneto-gravitational processes in supermassive black hole binary PG 1553+113

ABSTRACT PG 1553+113 has drawn significant attention for its quasi-periodic oscillation (QPO) in $\gamma$-ray variability, though the origin of its variability remains uncertain. In this study, we propose a physical mechanism to explain the observed $\gamma$-ray variability within the framework of a supermassive black hole binary (SMBHB) system, supported by a newly identified component hidden in the light curve. A detailed analysis for its $\sim$16-yr light curve obtained from Fermi-LAT observations is performed by Gaussian process. As anticipated, the QPO of 2.1 yr ($771\pm 8$ d) is effectively captured by the stochastically driven damped simple harmonic oscillator kernel within the underdamped regime, and the overall stochastic nature of the variability is described by the damped random walk (DRW) kernel albeit with an unconstrained damping time-scale. Additionally, our results reveal a previously unrecognized component in active galactic nuclei variability, characterized by the Mat$\acute{\rm e}$rn$-3/2$ kernel, which is typically associated with systems undergoing abrupt energy release. These findings can be consistently interpreted within the SMBHB framework. The QPO of $\sim$2.1 yr is likely attributed to the orbital motion in a SMBHB system. The Mat$\acute{\rm e}$rn$-3/2$ component is interpreted as resulting from magnetic reconnection events triggered by gravitational perturbations of the magnetic field within the jet, occurring as one black hole approaches the other. Meanwhile, in this case, the damping time-scale of the common DRW kernel remains unconstrained due to the influence of new perturbations within the system.

ERROR ANALYSIS OF THE MULTI-STAGE METHOD OF DETERMINING THE TRAJECTORY PARAMETERS OF LOW-ORBITAL SPACE OBJECTS DURING EXPERIMENTAL TESTING OF INFORMATION AND COMMUNICATION CONTROL SYSTEMS AND SPACE ENVIRONMENT ANALYSIS

The repulsion of large-scale Russian aggression and other existing threats in the sphere of national security and defense of Ukraine require the accelerated development of space information technologies in the state and determine the urgent need to improve the organization of the use of space technologies in the interests of defense, the creation of the necessary organizational structures, the deployment of modern information and communication systems with the aim of increasing space situational awareness. One of the main tasks of space situational awareness is the necessary level of knowledge about outer space, the characteristics of space objects of various origins, previous, current and projected knowledge about the parameters of their orbital motion. This task becomes particularly relevant due to the adversary's use of its space means of special and radio- technical intelligence and means of commercial organization, including microsatellites, as a result of which there is a need to control the routes of the passage of surveillance satellites with the subsequent development of plans for camouflage and other types of countermeasures and protection of troops. The article formulates the task of evaluating the effectiveness of information and communication systems that are being improved as part of conducting experimental tests as part of the System of Control and Analysis of the Space Situation, which are based on algorithms for processing the results of optical observations for maintaining a catalog of space objects. The value of the systematic errors of the initial determination of the motion parameters of a low-orbit circum-circular space object based on the results of optical observations using a multi-stage method based on the approximation of measurements by a circular model and consistent evaluation of planar and in-plane parameters of the orbit was evaluated. Methodological errors introduced when describing the circular motion model of a low-orbit space object along an elliptical trajectory with a small eccentricity are: according to the parameters of the orbit plane, up to 0,80; by period - up to 4 minutes; by the latitude argument – 0,2. In the case when the observation interval does not exceed 1 minute, the maximum errors in angular parameters do not exceed 0,1, which is quite acceptable for solving practical tasks of determining the orbits of small space objects. The systematic error of the period estimation can be compensated by joint processing of the results of optical observations on different turns of the flight.

Analytic four-body limaçon choreography

The trajectories and interaction forces of four bodies with equal masses are analytically described. The bodies follow a choreographic motion in a trisectrix limax periodic orbit without collisions. The curve is similar to a numerical curve of a folded figure of eight. The center of mass is fixed at the origin. The moment of inertia, the non-zero angular momentum as well as the kinetic and potential energies of the system are constant. The interaction forces are not Newtonian but linear attractive and repulsive forces along the lines joining the bodies. To the best of our knowledge, this is the first analytical solution to a four-body choreography in a curve other than the circle.

Unlocking ultra-deep wide-field imaging with sidereal visibility averaging

abstract Producing ultra-deep high-angular-resolution images with current and next-generation radio interferometers introduces significant computational challenges. In particular, the imaging is so demanding that processing large datasets, accumulated over hundreds of hours on the same pointing, is likely infeasible in the current data reduction schemes. In this paper, we revisit a solution to this problem that was considered in the past but is not being used in modern software: sidereal visibility averaging (SVA). This technique combines individual observations taken at different sidereal days into one much smaller dataset by averaging visibilities at similar baseline coordinates. We present our method and validated it using four separate 8-hour observations of the ELAIS-N1 deep field, taken with the International LOw Frequency ARray (LOFAR) Telescope (ILT) at 140 MHz. Additionally, we assessed the accuracy constraints imposed by Earth's orbital motion relative to the observed pointing when combining multiple datasets. We find, with four observations, data volume reductions of a factor of 1.8 and computational time improvements of a factor of 1.6 compared to standard imaging. These factors will increase when more observations are combined with SVA. For instance, with 3000 hours of LOFAR data aimed at achieving sensitivities of the order of μJy beam^-1 at sub-arcsecond resolutions, we estimate data volume reductions of up to a factor of 169 and a 14-fold decrease in computing time using our current algorithm. This advancement for imaging large deep interferometric datasets will benefit current generation instruments, such as LOFAR, and upcoming instruments such as the Square Kilometre Array (SKA), provided the calibrated visibility data of the individual observations are retained. abstract

Evolution of parsec-scale jet directions in active galaxies

Abstract We analyze the variability of the parsec-scale jet directions in active galactic nuclei (AGNs). Our analysis involves 317 AGNs at frequencies ranging from 2 to 43 GHz, and is made possible by developing an automatic jet direction measurement procedure. We find strong significant variations in a one quarter of these AGNs; the effect is likely ubiquitous, and not detected in the rest due to a limited sensitivity and observations epoch coverage. Apparent jet rotation speeds range from 0.21 deg yr−1 at 2 GHz to 1.04 deg yr−1 at 43 GHz. This strong frequency dependence indicates that the variability cannot be explained by jet components propagating ballistically without acceleration: more complex jet shapes or motion patterns are required. Still, we demonstrate that the apparent direction changes are predominantly caused by the jet nozzle rotations, and not by individual components propagating transversely to the jet. In this work, we focus on variability scales much longer than the times of observations, that is ≳ 50 years. Using our measurements, we bound potential periods to less than 1000 years in the source rest frame for 90% AGNs in the sample. These timescales constrain jet direction variation mechanisms, with the most likely explanations being the plasma instabilities, the precession caused by the accretion disk with density ∼r−1, and the orbital motion of binary systems.

Understanding and Modeling the Dynamics of Storm‐Time Atmospheric Neutral Density Using Random Forests

AbstractAtmospheric neutral density is a crucial component to accurately predict and track the motion of satellites. During periods of elevated solar and geomagnetic activity atmospheric neutral density becomes highly variable and dynamic. This variability and enhanced dynamics make it difficult to accurately model neutral density leading to increased errors which propagate from neutral density models through to orbit propagation models. In this paper we investigate the dynamics of neutral density during geomagnetic storms. We use a combination of solar and geomagnetic variables to develop three Random Forest machine learning models of neutral density. These models are based on (a) slow solar indices, (b) high cadence solar irradiance, and (c) combined high‐cadence solar irradiance and geomagnetic indices. Each model is validated using an out‐of‐sample data set using analysis of residuals and typical metrics. During quiet‐times, all three models perform well; however, during geomagnetic storms, the combined high cadence solar iradiance/geomagnetic model performs significantly better than the models based solely on solar activity. The combined model capturing an additional 10% in the variability of density and having an error up to six times smaller during geomagnetic storms then the solar models. Overall, this work demonstrates the importance of including geomagnetic activity in the modeling of atmospheric density and serves as a proof of concept for using machine learning algorithms to model, and in the future forecast atmospheric density for operational use.

An Approach to Near-Optimal Continuous-Thrust Solution for Plane Constellation Deployment

Paving the way in satellite constellation deployment, this article presents the Comprehensive Program (GCP) for planning constellation deployment missions by introducing a near-optimal solution for continuous-thrust maneuvers. The GCP establishes time constraints, enabling appropriate time scheduling and eliminating reconfiguration phases. It considers various cases of satellite departure and arrival sequences, collision avoidance constraints, and time limitations. A near-optimal solution for the continuous-thrust trajectory of each satellite is introduced, relying on the Fourier series approximation of the thrust pointing angle. The Fourier series with constant coefficients replaces the thrust angle in the satellite’s orbital motion equations in polar coordinates. The primary advantage of this near-optimal approach lies in its simplicity in accommodating space perturbations, posing no challenges in problem-solving. Additionally, the approach is beneficial due to its straightforward implementation and simple mathematical computations. This approach does not require pre-determining the revolution number of the transfer trajectory, unlike shape-based methods. The proposed method’s flexibility allows it to adapt and optimize the trajectory without prior assumptions about the number of revolutions required for the mission. Analyses demonstrate the proposed algorithm’s versatility and precision across various scenarios involving different orbital eccentricities, thrust forces, and thrust pointing angles. The constant coefficients of the Fourier series are determined by defining a set of objective functions and minimizing them using the Multi-Objective Particle Swarm Optimization algorithm (MOPSO). The first and second objective functions ensure that the transfer orbit reaches the desired deployment point, while the third and fourth ones guarantee the tangential conditions between the transfer orbit and the final orbit. An additional objective function minimizes the trajectory time. As a perturbation of interest, the effect of Earth’s oblateness is considered.

Orbital Eccentricity Study of Planets: A Comparative Analysis of Manual Simulation and Digital Visualization

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.

N-dimensional Lomb Scargle Periodogram analysis of traveling ionospheric disturbances using ionosonde data

There is a multitude of wave-like phenomena in Earth’s ionosphere and thermosphere such as acoustic waves, gravity waves, planetary waves, tides, and Traveling Ionospheric Disturbances (TIDs) which are the ionospheric manifestation of atmospheric waves. These phenomena are often difficult to study since measurements are typically irregular in time and space due to geographic constraints for deploying ground instruments and the natural orbital motion of satellites. This frequently precludes Fourier methods such as the Fast Fourier Transform (FFT) from being used. The Lomb-Scargle Periodogram (LSP) provides FFT-like analysis when measurements are irregular. To our knowledge, all prior use of the LSP in space science has been one-dimensional. This paper uses a N-Dimensional extension of the LSP (ND LSP) to study traveling ionospheric disturbances in four dimensions on a quiescent day near solar minimum. We use an exquisite dataset consisting of 12 ionosondes over Australia on June 29, 2019. The ND LSP resolves the full 3-dimensional wave vector as well as the period for many discrete TIDs. To the degree possible, we validate our findings from ionosonde data processed with the ND LSP by using an FFT-based method on line-of-sight TEC data from the same period and find similar wavelengths and periods for the large TIDs. We show that TIDs occur preferentially near 70o elevation and could be missed or mischaracterized if using TEC data in the thin-shell approximation.

Probing the Equation of State of Neutron Stars with Captured Primordial Black Holes

Gravitational waves (GWs) from primordial black holes (PBHs) inspiraling within neutron stars (NSs)—should they exist—are detectable by ground-based detectors and offer a unique insight into the internal structure of NSs. To provide accurate templates for GW searches, we solve Einstein’s equations within NSs and calculate the orbital motion of the captured PBH by considering dynamical friction, accretion, and gravitational radiation. Equipped with precise GW waveforms for PBHs inspiraling inside NSs, we find that the Einstein Telescope can differentiate between various equations of state for NSs. As PBHs inspiral deeper into NSs, the GW frequency rises near the surface, then decreases to a constant value deeper within NSs. The distinctive characteristics of GW frequency serve as the smoking gun for GW signals emitted by PBHs inspiraling inside NSs and can be used to probe the nuclear matter in the crust and core of NSs.

Three Years of High-contrast Imaging of the PDS 70 b and c Exoplanets at Hα with MagAO-X: Evidence of Strong Protoplanet Hα Variability and Circumplanetary Dust

We present 3 yr of high-contrast imaging of the PDS 70 b and c accreting protoplanets with the new extreme AO system MagAO-X as part of the MaxProtoPlanetS survey of Hα protoplanets. In 2023 and 2024, our sharp (25–27 mas FWHM), well-AO-corrected (20%–26% Strehl), deep (2–3.6 hr) images detected compact (r ∼ 30 mas; r ∼ 3 au) circumplanetary disks (CPDs) surrounding both protoplanets. Starlight scattering off the front edge of these dusty CPDs is the likely source of the bright compact continuum light detected within ∼30 mas of both planets in our simultaneously obtained continuum 668 nm filter images. After subtraction of contaminating continuum and point-spread function residuals with pyKLIP angular differential imaging and spectral differential imaging, we obtained high-contrast ASDI Hα images of both planets in 2022, 2023, and 2024. We find the Hα line flux of planet b fell by (8.1 ± 1.6) × 10−16 erg s−1 cm−2, a factor of 4.6 drop in flux from 2022 to 2023. In 2024 March, planet b continued to be faint with just a slight 1.6× rise to an Hα line flux of (3.64 ± 0.87) × 10−16 erg s−1 cm−2. For c, we measure a significant increase of (2.74 ± 0.51) × 10−16 erg s−1 cm−2 from 2023 to 2024, which is a factor of 2.3 increase. So both protoplanets have recently experienced significant Hα variability with ∼1 yr sampling. In 2024, planet c is brighter than b: as c is brightening and b generally fading. We also tentatively detect one new point source “CC3” inside the inner disk (∼49 mas; at PA ∼ 295°; 2024) with orbital motion roughly consistent with a ∼5.6 au orbit.

Pre-calculated space-ground integrated structure (P-SGIS) against link cut set (LCS) failures in space-ground integrated optical networks.

Fiber link failure is a common and frequent failure type in terrestrial optical networks (TONs). To guarantee the stable operation of the TON against single or multi-link failures, various kinds of survivability technologies have been proposed. Although these survivability technologies are effective in many cases, a link cut set (LCS), which is a set of fiber links whose simultaneous failures can disconnect the TON, presents an extreme situation of network partitioning that these technologies cannot address. Recently, the satellite network has obtained rapid development and various types of satellite constellations are being constructed. Moreover, the laser inter-satellite link (LISL) is studied deeply and verified widely. The satellite optical network (SON) is gradually formed and can be integrated with the TON together into the space-ground integrated optical network (SGION). In the SGION, the LCS failure in the TON can be addressed by the SON. This paper focuses on space-ground integrated protection. A pre-calculated space-ground integrated structure (P-SGIS) is designed. "Pre-calculated" refers to extracting reliable, low-redundant backup protection structures in advance from the physical topology of the SGION, based on prior knowledge, such as satellite movement regularity, failure distribution, and so on. Heuristic algorithms are developed for P-SGIS construction and backup resource reservation. Numerical results show that the P-SGIS-based protection scheme has high resource efficiency and protection success rate.

Enhancing System Capacity Through Joint Space‐Ground Multi‐Beam Coordination for LEO Satellite Systems

ABSTRACTDue to the long transmission distance of the constellation network represented by the low‐orbit satellite system, the satellite‐to‐ground link is subject to large path loss and limited communication performance. This paper uses multi‐satellite and multi‐beam joint transmission technology to form a virtual multiplex network with ground multi‐antenna terminals (Multiple‐Input Multiple‐Output [MIMO] system). However, due to the high‐speed movement of satellites, the topology of the MIMO system is unstable, which in turn affects the stability of the system throughput. This article proposes two inter‐satellite cooperation modes to improve the stability of MIMO system capacity. The first method is to optimize the channel capacity by rationally allocating the beam power of the gateway station so that the gateway station can achieve transparent forwarding through satellites. The second method rotates the angle of the user's receiving antenna to combat channel changes caused by changes in satellite position. Simulation results show that both methods can effectively improve the minimum channel capacity. Transparent forwarding can increase the capacity by about 22.7%, while the rotating antenna can still improve the performance gain by at least 36.3% even with a limited rotation angle. This research contributes to the development of stable and efficient communication systems in satellite‐ground cooperative networks.

ESPRESSO reveals a single but perturbed broad-line region in the supermassive black hole binary candidate PG 1302-102

In this work, we present a new, fully Bayesian analysis of the highest-resolution optical spectrum of the supermassive black hole (SMBH) binary candidate PG 1302-102, obtained with ESPRESSO at the VLT ( R ). Our methodology, based on robust Bayesian model selection, reveals the presence of multiple narrow emission lines at the expected redshift of the source and confirms (for Hbeta ) and detects (for Hgamma ) the clear presence of redshifted broad components. Additionally, we have discovered a ``very broad'' and, if it is associated with the Hbeta , ``very redshifted'' component at $ We evaluate two scenarios for explaining the observed broad emission line (BEL) features in PG 1302-102. In the case in which the redshifted BEL asymmetry arises from the orbital motion of a putative binary, our measurements coupled with simple estimates of the broad-line region (BLR) sizes suggest that the individual black hole BLRs are either settled in a single BLR or in the process of merging and, therefore truncated and highly disturbed. Alternatively, in the scenario of a single SMBH, we explain the distorted emission of the BELs with a nonsymmetric distribution of the BLR clouds; namely, a thin disk with a spiral perturbation. This BLR configuration is statistically preferred over any empirical multi-Gaussian fit and simultaneously explains the asymmetric emission of the Hbeta and Hgamma close to the bulk of the line and any additional excess (or the lack of it, in the case of the Hgamma ) at much longer wavelengths. The physical origins of the perturbation are still unclear and a connection with the possible presence of a black hole binary cannot be ruled out. Given the growing evidence from theoretical and observational works demonstrating the common presence of disturbed BLRs in active galactic nuclei, we argue that an origin related to self-gravitating instabilities may be more plausible.