Light is dispersive in gravitational field. It results in that, under the condition of strong gravitational field, the observed numbers, size, distance and spectrogram of a celestial object is different from the real ones. Therefore, the observed jets of the Sgr A* and M87 need be understood further with the orbit of the stars around them. And, the observed orbits of the S-stars around the Sgr A* is different from the real ones. It implies that the observed optical images of the distant celestial body with strong gravitational field need be further understood with other observations and physics laws to accurately and precisely know the real physical configuration of it.

The Direction-of-Arrival (DoA) estimation methods are highly versatile and find extensive applications in satellite communication. The DoA methods are employed across a range of orbits, from Low Earth Orbits (LEO) to Geostationary Earth Orbits (GEO). They serve multiple applications, including altitude determination, geolocation and estimation accuracy, target localization, and relative and collaborative positioning. This paper presents a novel approach for modeling the DoA angle using a closed-form expression, incorporating the boresight angle and satellite and Earth station position data. The method uses the geographic coordinate system in the satellite communication system, precisely the latitude and longitude of the Earth station and altitude parameters of the satellite stations, to calculate the Earth station’s elevation angle and accurately model the DoA angle. Furthermore, this paper performs a comprehensive comparative analysis of various DoA methods to gain deeper insights into the performance of DoA estimation in multi-antenna systems operating under spatially correlated channels. Accordingly, this paper evaluates DoA estimation performance using root-mean-square-error (RMSE) statistics for uplink and downlink conditions through extensive Monte Carlo simulations. The simulation’s effectiveness is validated against the Cramer-Rao Bound (CRB) performance metric for the Additive white Gaussian noise (AWGN) case. (i.e., thermal noise). The simulation results demonstrate improved RMSE performance in satellite systems by incorporating spatial correlation into the system model.

The rapid advancement of Earth observation systems and satellite networks driven by commercial space has led to a significant increase in the number of remote sensing satellites, thereby establishing the groundwork for all-weather, continuous cluster collaborative observation. Following anti-irradiation hardening measures, low-cost commercial off-the-shelf (COTS) devices are effectively operated within intricate space environments, leading to substantial enhancements in on-orbit computing capabilities of individual satellites. Leveraging the on-board distributed processing framework, it fully utilizes wide-area scattered space computing resources and automatically establishes a network of neighboring satellites through inter-satellite communication links to construct a spatially distributed and computationally cooperative space cloud computing environment. This enables the sharing of space computing resources and facilitates satellite-based mission coordination, reducing reliance on ground-based remote sensing satellite services while enhancing the response efficiency of remote sensing application services. The present paper pro-vides a comprehensive review of the current development status, existing challenges, and problems faced by space-based remote sensing on-orbit processing platforms and on-board intelligent processing algorithms, starting from the immediate application requirements of remote sensing satellite in-orbit processing. In view of the anticipated surge in large-scale computing resources in space, a distributed remote sensing satellite data processing architecture based on large-scale on-board computing power is constructed, and the architecture is designed in detail from the aspects of physical architecture, software architecture, workflow and key technologies. Finally, three real-time service scenarios that align with the construction content of an ultra-low orbit satellite constellation and 6G technology have been designed to provide solutions and references for subsequent development of space-based intelligent remote sensing constellations.

Exact sequential state estimation of orbiting objects in space can be found by predicting the state using Fokker Planck Kolmogorov Equation (FPKE) and measurement correction using Bayes’ conditional/posterior Probability Density Function (PDF). Posterior PDF can be expressed as Gaussian density expanded in terms of Hermite polynomials named as Gram Charlier Series (GCS). This research is an extension of an earlier work on second order linearized solution to nonlinear Bayesian filtering using Taylor series and third order GCS expansion of posterior PDF. In this new extension, Bayes’ posterior PDF is approximated by a mixture of GCS functions for which the parameters are propagated using linear propagation theory. The update of weights of different components of GCS mixture model uses the FPKE error as feedback to adapt for the amplitude of different GCS components while solving a quadratic programming problem earlier used for Gaussian Mixture Model (GMM) PDF. Proposed filtering method is applied on tracking of space debris. The simulation results for the filter shows performance is moderately better than single GCS filter, Extended Kalman Filter (EKF) and Gaussian Sum Filter (GSF) under space debris’ highly uncertain initial conditions and sparse measurement availability.

Complexes of triply positive europium ion with organic ligands are popular objects for studying photophysical properties. This is related not only to the bright red emission of this 4f element, but also to some spectroscopic peculiarities of its luminescence: the first excited spin-orbit level (7F1) lies only about 300 cm−1 above the ground state (7F0), so that at room temperature its population is around 25–30%. However, such electronic structure of Eu(III) provides its paramagnetism under ordinary conditions. This fact is often ignored by researchers, which is shortsighted from the materials science point of view. A comprehensive and systematic study of the magnetic behavior for the Eu(III) molecular coordination compounds is a challenging task for the development of new polyfunctional materials. The present work presents synthesis, single crystal XRD analysis results, and a magnetic study for the firstly prepared europium(III) complexes with two neutral scorpionate ligands: trispyrazolylmethane (HCPz3) and its methylated analog, tris(3,5-dimethyl-1-pyrazolyl)methane (HC(PzMe2)3). The values of the spin-orbit coupling parameter obtained for Eu-trication by a theoretical approximation of the experimental magnetic susceptibility data are compared with those known for the scarce amount of the magnetically studied molecular compounds.

To address the issue of reduced orbit estimation accuracy resulting from discrepancies between in-orbit measured geomagnetic field values and IGRF model values in autonomous orbit estimation of microsatellites based on geomagnetic field measurements, this study introduces an adaptive cubature H-infinity filtering algorithm. Firstly, it presents the low-altitude orbital dynamics model and geomagnetic field measurement model for microsatellites. Subsequently, within the adaptive cubature H-infinity filtering algorithm, a spherical simplex rule and a second-order Gaussian-Legendre quadrature criterion are employed to compute the spherical surface integral and radial integral. Additionally, a spherical simplex-radial quadrature rule is proposed to enhance the approximation accuracy of nonlinear Gaussian weighted integrals. Furthermore, by integrating extended H-infinity filtering based on game theory with the cubature quadrature rule, an inverse proportional relationship between constraint level and filtering innovation is established. This allows for adaptive adjustment of the constraint level to enhance robustness against model errors. Finally, through semi-physical simulation experiments, it is demonstrated that compared with traditional algorithms, the proposed algorithm improves autonomous orbit estimation position accuracy of microsatellites by 7.49%, while also enhancing velocity accuracy by 3.1%, thus validating its effectiveness.

This study investigates the fixed-time consensus-based attitude control problem for large telescope on-orbit construction subject to discrete-time communication, unknown tiny disturbance torque, model uncertainty, and actuator saturation under an undirected communication graph. Motivated by the need to save wireless communication resources, the communication scheme was designed to exploit interference, which can save communication resources in proportion to the number of modular unit mirrors. Then, a fixed-time observer with discrete-time communication was proposed, which also handles the unknown channel attenuation problem when exploiting information interference. Moreover, based on the backstepping procedure and the suitably defined adaptive compensation law, the fixed-time attitude consensus control law was proposed to handle unknown tiny disturbance torque, model uncertainty, and actuator saturation. Finally, comparative simulation results were provided to verify the effectiveness of the fixed-time observer and proposed fixed-time control law.

Aiming at the development of the application of massive and heterogeneous LEO constellations, the influence of typical perturbation forces on the orbit prediction of LEO satellites at different altitudes is analyzed. Firstly, the main perturbation force model of LEO satellites is introduced. Then experiments for analyzing the influence of orbit prediction on LEO satellites at different altitudes are designed. Finally, the influence of typical perturbation forces on the orbit prediction under different prediction durations by numerical analysis is assessed systematically, and the orbit prediction of LEO satellites with different non-spherical gravitational field orders, ocean tide orders and atmospheric density models were compared and calculated. The research results show that different orders of non-spherical gravitational fields should be considered when the altitude of satellites is different, the reasonable gravitational field orders for LEO satellites at 500km, 1000km, 1500km and 2000km under 1-hour forecast time are 140x140, 80x80, 60x60 and 40x40 orders, the reasonable orders of ocean tide perturbation for 1500km and 2000km satellites are 20x20 orders. Under the 24-hour forecast time, atmospheric resistance has a great influence on the precision of LEO satellites at orbit altitude below 1,000km. The forecast deviation of the LEO satellites orbit at 500km reaches 8751.576m. The difference of orbit precision between different atmospheric density models is in the meter level. The orbit deviation by the Standard Atmosphere 1976 and NRLMSISE 2000 atmospheric models respectively reaches 25.494m. Relevant conclusions provide support for the optimization and selection of dynamical models in high precision orbit determination and fast orbit prediction of LEO satellites.

The attitude dynamics and orbit dynamics of large rigid space structures are coupled with each other under gravity gradient, which may affect the stability of the large rigid space structures. In this paper, the gravity gradient stability of a large rigid space structure is studied under both small and large disturbances. Based on the rigid body dynamics and orbit dynamics, an accurate dynamic model without any linearization of the large rigid space structure is established via the natural coordinate formulation (NCF), which is able to describe the large overall motions of the structures. By using the generalized-α algorithm, the gravity gradient stability of the large rigid space structure is simulated and analyzed via various examples, including the influence of large disturbance angles, the positions at the stabilization and unstabilization regions. Finally, the relationship between spinning stability and gravity gradient stability is also investigated via a large spinning space structure.

Intercalation of noble metals can produce giant Rashba-type spin-orbit splittings in graphene. The spin-orbit splitting more than 100 meV has not yet been achieved in graphene on a metallic or a semiconductor substrate. Here, we report the p-type graphene obtained by Pt intercalation of zero-layer graphene on SiC substrate. The spin splitting of ∼200 meV was observed at a wide range of binding energies. Comparing the results of theoretical studies of different models with the experimantal ones measured by spin-ARPES, XPS and STM methods, we came to the conclusion that inducing giant spin-orbit splitting requires not only a fairly close arrangement of graphene to Pt layer, but also the presence of graphene corrugation caused by non-flat Pt layer. This makes it possible to find a compromise between strong hybridization and increased spin-orbit interaction. In our case, this is achieved by forming Pt submonolayer ordered on a nanometer scale under graphene.

In recent, Chae found that, at weak gravitational acceleration g_N≲10⁻⁹ms⁻², the observed orbit of the wide binary stars is not accordant with current theory of binary star. Here, we present, this finding should be an observational evidence for that Newtonian theory of orbit perturbation is still valid in galactic scale.

Suppose G is a graph with vertex-orbits O1,1 O2, . . . ,Ot, and jOi j denotes the cardinallity of Oi. Then OG (x) = åt 2 i=1 xjOi j is called as orbit polynomial. It is well-known that this polynomial 3 has a unique positive zero d in the interval [0, 1]. The aim of this paper is to study the specific 4 properties of this polynomial and then we determine the location of this root for several classes of 5 complex networks to compare with other graphical measures. Besides, we compare the unique 6 positive zero measure with several well-known centrality graph measures.

The current emphasis in the advancement of space-based synthetic aperture radar (SAR) is on lightweight payloads under 100kg with resolutions surpassing 1m. This focus is directed towards meeting the launch criteria for multiple satellites on a single rocket and cutting costs. This article discusses the creation and progress of a Ku-band SAR payload for the Taijing-4(03) Satellite, launched on January 23, 2024 accompanied by four other satellites. The SAR payload design was customized to meet the demands of a micro-nano satellite platform, resulting in a lightweight, flat design weighing less than 80kg, seamlessly integrated with the plate-shaped satellite platform. The article also introduces a beam optimization strategy for the phased array SAR antenna, significantly boosting the SAR system’s performance. The SAR payload provides various operating modes like slide-spot, strip, scan 1, scan 2, and others, with a maximum achievable resolution exceeding 1m. Extensive in-orbit testing of the payload produced numerous high-quality SAR images with potential uses in emergency disaster mitigation, safeguarding ecosystems, monitoring forests, managing crops, tracking sea ice, and more.

Orbital fractures are a common finding in facial trauma and serious complications may arise when orbital reconstruction is not done properly. The virtual planning can be used to manufacture patient-specific titanium orbital implants (PSI) through the process of selective laser melting. This method is currently considered the most accurate technique for orbital reconstruction. Even with the most accurate tehniques of bone reconstruction, there are still situations where enophthalmos is present after reconstruction which may be produced by intraorbital soft tissue atrophy. The aim of this paper was to evaluate the orbital soft tissue after postraumatic reconstruction of the orbital walls fractures. 10 patients diagnosed with unilateral orbital fractures were included in this study. A CT scan of the head region with thin slices (0.6mm) and soft and bone tissue windows was done. After data processing, the STL files were exported and the intraorbital fat tissue volume and the muscular tissue volume were masured. The volumes of affected orbit tissues were compared with the volumes of the healthy orbit tissues for each patient. Our findings conclude that a higher or a lower grade of fat and muscular tissue loss is present in all cases of reconstructed orbital fractures.

The usual equation for both motions of a single planet around the sun and electrons in the deterministic Rutherford-Bohr atomic model is conservative with a singular potential at the origin. When a dissipation is added, new phenomena appear which were investigated thoroughly by R. Ortega and his co-authors between 2014 and 2017, in particular all solutions are bounded and tend to $0$ for $t$ large, some of them with asymptotically spiraling exponentially fast convergence to the center. We provide explicit estimates for the bounds in the general case that we refine under specific restrictions on the initial state, and we give a formal calculation which could be used to determine practically some special asymptotically spiraling orbits. Besides, a related model with exponentially damped central charge or mass gives some explicit exponentially decaying solutions which might help future investigations. An atomic contraction hypothesis related to the asymptotic dying off of solutions proven for the dissipative model might give a solution to some intriguing phenomena observed in paleontology, familiar electrical devices and high scale cosmology

The usual equation for both motions of a single planet around the sun and electrons in the deterministic Rutherford-Bohr atomic model is conservative with a singular potential at the origin. When a dissipation is added, new phenomena appear. It is shown that whenever the momentum is not zero, the moving particle does not reach the center in finite time and its displacement does not blow-up either, even in the classical context where arbitrarily large velocities are allowed. Moreover we prove that all bounded solutions tend to $0$ for $t$ large, and some formal calculations suggest the existence of special orbits with an asymptotically spiraling exponentially fast convergence to the center.

Space-based gravitational wave detection is extremely sensitive to disturbances. The Keplerian configuration cannot accurately reflect the variations in spacecraft configuration. Planetary gravitational disturbances are one of the main sources. Numerical simulation is an effective method to investigate the impact of perturbation on spacecraft orbits. This study shows that, in the context of the Taiji project, Earth’s gravity is an essential factor in the change in heliocentric formation configuration, contributing to the relative acceleration between spacecrafts in the order of O(10−6)m·s−2. Considering 00:00:00 on October 27, 2032 as the initial orbiting moment, under the influence of Earth’s gravitational perturbation, the maximum relative change in armlengths and variation rates of armlengths for Taiji is 1.6×105km, 32m·s−1 respectively, compared with the unperturbed Keplerian orbit. Additionally, by considering the gravitational perturbations of Venus and Jupiter, the armlength and relative velocity for Taiji are reduced by 16.01% and 17.45%, respectively, compared with when only considering that of Earth. The maximum amplitude of the formation motion indicator changes with the orbit entry time. Results show that the relative velocity increase between the spacecrafts is minimal when the initial orbital moment occurs in July. Moreover, the numerical simulation results are inconsistent when using different ephemerises. The differences between ephemeris DE440 and DE430 are smaller than those between DE440 and DE421.

The application of space robotic manipulators and heightened autonomy for ios represents a paramount pursuit for leading space agencies, given the substantial threat posed by space debris to operational satellites and forthcoming space endeavors. This work presents a guidance algorithm based on drl to solve for the space manipulator path-planning during the motion synchronization phase with the mission target. The goal is the trajectory generation and control of a spacecraft equipped with a 7-dof robotic manipulator, such that its end effector remains stationary with respect to the target point of capture. The ppo drl algorithm is used to optimize the manipulator’s guidance law, and the autonomous agent generates the desired joints rates of the robotic arm, which are then integrated and passed to a model-based feedback linearization controller. The agent is first trained to optimize its guidance policy and then tested extensively to validate the results against a simulated environment representing the motion synchronization scenario of an ios mission.

The purpose of this paper is to investigate the effect of a varying moment on the rotation angle of a large tethered satellite that is orbiting a planet. Two different types of orbits were investigated: a simple circular orbit and an elliptical orbit. Cases with zero and non-zero initial angular rotation velocity were investigated as well. This investigation will assist satellite docking missions. The large rigid tethered satellite is a futuristic concept, and this investigation is meant to assist possible docking missions to the satellite. To simplify the problem, the rotation is constrained to the orbital plane.

After proposing the Principle of Minimum Gravitational Potential, in a pursuit to find the explanation behind the correction to Newton's gravitational potential that accounts for Mercury's orbit, by finding all the higher-order corrections it is shown that the consequences of the existence of speed of light for gravity are not yet fully explored.

We investigate emergent conductive phenomena triggered by collinear antiferromagnetic orderings. We show that an up-down-zero spin configuration in a triangle cluster leads to linear and nonlinear spin conductivities even without the relativistic spin–orbit coupling; the linear spin conductivity is characterized by the Drude-type one, while the nonlinear spin conductivity is characterized by the Hall-type one. We demonstrate the emergence of both spin conductivities in the breathing kagome system consisting of a triangle cluster. The nonlinear spin conductivity becomes larger than the linear one when the Fermi level lies near the region where a small partial band gap opens. Our results indicate that collinear antiferromagnets with the triangle geometry give rise to rich spin conductive phenomena.

There are gravitational field and baryonic matter (star, planet, gases etc.) in our world; gravitational field is much more fundamental for that the relativistic mass of the gravitational field of a neutron star is almost 10²¹ times the mass of the neutron star. And, it is astonishing that the relativistic mass density of the gravitational field on the surface of a neutron star can be larger than the mass density of the neutron star. It is well known that, in the weak gravitational field a light line appears a straight line while in the strong field it is a curved line. It is stressed that the result measured in the strong field is more fundamental for that in a galaxy the measurable object is generally with strong field. It results in that the way that the result measured on the Earth with weak field is used as the universal standard need be revised as gravity is studied in the scale of a galaxy. It seems that a new theory of gravity need be developed for the new observations.

The electron of magnetic spin −1/2 is a Dirac fermion of a complex four-component spinor field. Though it is effectively addressed by relativistic quantum field theory, an intuitive form of the fermion still remains lacking. In this novel undertaking, the fermion is examined within the boundary posed by a recently proposed MP model of a hydrogen atom into 4D space-time. Such unorthodox process conceptually transforms the electron to the four-component spinor of non-abelian in both Euclidean and Minkowski space-times. Supplemented by several postulates, the relativistic and non-relativistic applications of the model are explored from an alternative perspective. The outcomes have important implications towards defining the spin-orbit coupling of particles from external light interactions. These findings, if considered could consolidate properly the fundamentals of the quantum state of matter from an alternative perspective using quantum field theory application and they warrant further investigations.

Distant Retrograde Orbits in the Earth-Moon system are gaining in popularity as stable `parking' orbits for various conceptual missions. To investigate the stability of potential Distant Retrograde Orbits, simulations were executed, with propagation running over a thirty-year period. Initial conditions for the vehicle state were limited such that the position and velocity vectors were in the Earth-Moon orbital plane, with the velocity oriented such that it would produce retrograde motion about Moon. The resulting trajectories were investigated for stability against the eccentric relative orbits of Earth and Moon in an environment that also included gravitational perturbations from Sun, Jupiter, and Venus, and the effects of radiation pressure. The results appear to indicate that stability is enhanced for certain resonant states within the Earth-Moon system.

The idea of an extension of life for CubeSats is proposed to reduce space debris in a low-earth orbit. In this work, a gripper is designed for geometry-based grasping in berthing tasks. The grasping operation is outlined for square- and rectangle-profiled CubeSats. Equilibrium conditions are used to choose fingertips shape and parameters for grasping the CubeSat body. A design scheme is proposed to provide the required accuracy. A design concept is developed into a lab prototype by using low-cost 3D printing technique, and a mock-up grasping task that is representative of the berthing operation is evaluated with the lab prototype. Center-mass hanging setup for the prototype and grasped body is used to evaluate the impact of grasping, partially replicating the conditions in space by reducing the effect of gravity on the system.

The most commonly used real-time augmentation services in China are International GNSS Service (IGS) real-time service, PPP-B2b service, and BeiDou Satellite-Based Augmentation System (BDSBAS) dual-frequency augmentation service. However, the research on the performance evaluation, comparison and application scope of these three products is still unknown and unrevealed. This article introduces methods for obtaining real-time augmentation information and real-time orbit and clock offset recovery. Based on real-time orbit and clock offset accuracy, positioning accuracy, and positioning availability, it systematically evaluates the performance of CNES, PPP-B2b, and BDSBAS augmentation information. The results indicate that the radial accuracy of CNES and PPP-B2b real-time orbit products is consistent, and the Root Mean Square (RMS) is better than 5 cm. CNES can achieve centimeter-level accuracy in both along-track and cross-track components, surpassing the decimeter-level accuracy of PPP-B2b. Both services demonstrate consistent accuracy in real-time clock offset, with PPP-B2b showing similar standard deviations (STD) of 0.16 ns for different satellites. However, for CNES, the STD of real-time clock offset varies for GPS, BDS-3 MEO, and BDS-3 IGSO satellites, with values of 0.10 ns, 0.19 ns, and 0.60 ns, respectively. The accuracy and availability of the two PPP services exhibit the same levels, with centimeter-level accuracy achieved after convergence and positioning availability exceeding 99%. Therefore, the difference between the two services in application areas depends on the acquisition of augmentation information. However, BDSBAS, which concentrates on code observations, demonstrates lower accuracy in real-time orbit and clock offset, positioning accuracy, and positioning availability compared to the other two services. Its primary application is in the aviation and maritime domains, where there is a greater need for service integrity, continuity, and reliability.

In order to monitor the diversity of terrestrial biomes, the Earth Exploration Satellite Services demand a high data rate for downlink transmissions while sharing their frequency spectrum with, and suffering interferences from, cellular Base Stations. Both highlight the dilemmas of spectral efficiency (bps/Hz) and spectral coexistence. Our research aims to mitigate interference on low orbit satellite downlinks using Cognitive Radio (CR) and Adaptive MODulation and CODing (MODCOD) techniques. To fulfill this: 1) we present CR approaches to enhance spectrum exploitation. Next, 2) we detail Adaptive MODCOD (ACM) technique to increase RF power and spectral efficiencies. Then, 3) we suggest the solution by combining 1) and 2). Afterwards, 4) we analyze it by monitoring the signal to interference plus noise ratio and the CR/MODCOD strategy. Finally, 5) we provide case studies to demonstrate the strategy’s effectiveness through the practical operation of satellite services, and 6) we conduct a bench test of the communication system.

Galactic rotation curve was formulated before the Sgr A* had been confirmed. The action of the Sgr A* on the rotation curve has not been considered. Now, it was observed that the fastest stars in the Milky Way is in the distance less than 0.5pc from the Sgr A*. It is contradicted with the current galactic rotation curve in which the orbital velocity near the center of the galaxy is the smallest. And, because of the advance of technology, it was observed that the circular velocity curve of the Milky Way from 5 to 30 kpc is with a significantly faster decline (Keplerian decline) compared to the inner parts. It is contradicted with the current curve in which the out parts could be larger or no decline. And, it was observed that the fast galaxy bar continue challenge the standard cosmology. For the reasons, we present an improved galactic rotation curve.

Using the orbit decomposition, a new enumerative polynomial P(x) is introduced for abstract (simplicial) complexes of a given type, e.g., trees with a fixed number of vertices or triangulations of the torus with a fixed graph. The polynomial has the following three useful properties. (I) The value P(1) is equal to the total number of unlabeled complexes (of a given type). (II) The value of the derivative P'(1) is equal to the total number of nontrivial automorphisms when counted across all unlabeled complexes. (III) The integral of P(x) from 0 to 1 is equal to the total number of vertex-labeled complexes, divided by the order of the acting group. The enumerative polynomial P(x) is demonstrated for trees and then is applied to the triangulations of the torus with the vertex-labeled complete four-partite graph G = K_{2,2,2,2}, in which specific case P(x) = x^{31}. The graph G embeds in the torus as a triangulation, T(G). The automorphism group of G naturally acts on the set of triangulations of the torus with the vertex-labeled graph G. For the first time, by a combination of algebraic and symmetry techniques, all vertex-labeled triangulations of the torus (twelve in number) with the graph G are classified intelligently without using computing technology, in a uniform and systematic way. It is helpful to notice that the graph G can be converted to the Cayley graph of the quaternion group Q_8 with the three imaginary quaternions i, j, k as generators.

Orbit and clock products are used in real-time GNSS precise point positioning without knowing their quality. This study develops a new approach to detect orbit and clock errors through comparing geometry-free and geometry-based wide-lane ambiguities in PPP model. The reparameterization and estimation procedures of the geometry-free and geometry-based ambiguities are described in detail. The effects of orbit and clock errors on ambiguities are given in analytical expressions. The numerical similarity and differences of geometry-free and geometry-based wide-lane ambiguities are analyzed using different orbit and clock products. Furthermore, two types of typical errors in orbit and clock are simulated and their effects on wide-lane ambiguities are numerically produced and analyzed. The contribution discloses that the geometry-free and geometry-based wide-lane ambiguities are equivalent in terms of their formal errors. Although they are very close in terms of their estimates when the used orbit and clock for geometry-based ambiguities are precise enough, they are not the same, in particular, in the case that the used orbit and clock, as a combination, contain significant errors. It is discovered that the discrepancies of geometry-free and geometry-based wide-lane ambiguities are coincided with the actual time-variant errors in the used orbit and clock at the line-of-sight direction. This provides a quality index for real-time users to detect the errors in real-time orbit and clock products, which potentially improves the accuracy of positioning.

Living organisms are active open systems far from thermodynamic equilibrium. The ability to behave actively corresponds to dynamical metastability: minor but supercritical internal or external effects may trigger major substantial actions such as gross mechanical motion, dissipating internally accumulated energy reserves. Gaining selective advantage from beneficial use of activity requires a consistent combination of sensual perception, memorised experience, statistical or causal prediction models, and resulting favourable decisions on actions. This information processing chain originated from mere physical interaction processes prior to life, here denoted as structural information exchange. From there, the self-organised transition to symbolic information processing marks the beginning of life, evolving by novel purposivity of trial-and-error feedback and accumulation of symbolic information. The emergence of symbols and prediction models can be described as a ritualisation transition, a symmetry-breaking kinetic phase transition of the 2^nd kind previously known from behavioural biology. The related new symmetry is the neutrally stable arbitrariness, conventionality or code invariance of symbols with respect to their meaning. The meaning of such symbols is given by the structural effect they ultimately unleash, directly or indirectly, by deciding on which actions to take. The early genetic code represents the first symbols. The genetically inherited symbolic information is the first prediction model for activities sufficient for survival under the condition of environmental continuity, sometimes understood as a “final causality” property of the model.

The concept of geostationary VHTS (Very High Throughput Satellites) is based on multibeam coverage with intensive frequency and polarization reuse in addition to the use of larger bandwidths in the feeder links, in order to provide high capacity satellite links at a reduced cost per Gbps in orbit. The dimensioning and design of satellite networks based on VHTS imposes the analysis of multiple trade-offs to achieve an optimal solution in terms of cost, capacity and figure of merit of the user terminal. In this paper, we propose a new method for sizing VHTS satellite networks based on an analytical expression of the forward link CINR (Carrier-to-Interference-plus-Noise Ratio) that is used to evaluate the trade-off of different combinations of system parameters. The proposed method considers both technical and commercial requirements as inputs including the constraints to achieve the optimum solution in terms of the user G/T, the number of beams and the system cost. The cost model includes both satellite and ground segments. Exemplary results are presented with feeder links using Q/V bands, DVB-S2X and transmission methods based on CCM and VCM (Constant and Variable Coding and Modulation, respectively) in two scenarios with different service areas.

In the bar of our Milky Way, there should be another supermassive black hole B which is with the mass almost 10−2~10−5 the Sgr A* and with a distance almost 10,000 lightyears from the Sgr A*. The bar is formed by the stars that are orbiting around the two black holes Sgr A* and B. And, in the bar, a lots of stars orbit around B while another lots of stars around Sgr A*. The two orbits form the peanut shape with “x-shaped structure” in the bar, while the boxy core is formed with all of the three orbits. And, the orbits of the stars out of the bar could be repulsed to a distant place by the black hole B to form the galactic spiral arms.

In this paper, an attempt has been made to analyze the effect of spool port/ groove geometry on the pressure drop and chamber pressures which effect the performance parameters of the flow distributor valve. The work mainly involves formulation of detailed mathematical model of the valve and compare them on the same platform. For mathematical modelling, Matlab has been used. The size of the orifices is considered same throughout the model for better comparison. Initially the construction and functioning of flow distributor valve along with working principles of hydrostatic motor (Rotary Piston) is shown. Next shown the analytical analysis of area change and pressure drops due to different geometry of the spool valve ports. After that the computational fluid dynamics (CFD) analysis has been shown. A complete mathematical model to describe such flow distributor valve is developed after having a comprehensive knowledge of orifice characteristics, flow interactions based on valve geometry. Equations of flow through different orifices (fixed and variable area) of the valve have been developed based on the relationships obtained earlier.

Satellite communication is expected to play a vital role in realizing Internet of Remote Things (IoRT) applications. This article considers an intelligent reflecting surface (IRS)-assisted downlink low Earth orbit (LEO) satellite communication network, where IRS provides additional reflective links to enhance the intended signal power. We aim to maximize the sum-rate of all the terrestrial users by jointly optimizing the satellite’s precoding matrix and IRS’s phase shifts. However, it is difficult to directly acquire the instantaneous channel state information (CSI) and optimal phase shifts of IRS due to the high mobility of LEO and the passive nature of reflective elements. Moreover, most conventional solution algorithms suffer from high computational complexity and are not applicable to these dynamic scenarios. A robust beamforming design based on graph attention networks (RBF-GAT) is proposed to establish a direct mapping from the received pilots and dynamic network topology to the satellite and IRS’s beamforming, which is trained offline using the unsupervised learning approach. The simulation results corroborate that the proposed RBF-GAT can achieve approximate performance compared to the upper bound with low complexity.

When the formation flying consists of satellites that are independent from each other and forms a virtual synthetic aperture telescope that replaces a single large telescope with all of its optical elements it is required mutual coordination between the satellites with high accuracy in order to achieve good optical observations. In this paper we consider the problem of developing a control system for a tetrahedral satellite formation flying representing a synthetic aperture telescope in the geostationary orbit for high resolution monitoring of fire in the forest area in infrared spectrum. Synthesizing the image with good quality requires to keep the configuration of formation with µm-class accuracy. Study of dynamics of passive uncontrolled motion of formation flying showed a significant deviation of the configuration from the required shape with a high frequency due to the action of gravitational forces. To keep the configuration in the required form with µm accuracy the analysis of efficiency of various controllers was carried out in the process of numerical simulation. The simulation results made it possible to highlight the features of using various approaches to the development of control system for the satellite formation flying representing a synthetic aperture telescope.

In this paper, the problem of autonomous optimal absolute orbit keeping for a satellite mission in Low Earth Orbit using electric propulsion is considered. The main peculiarity of the approach is to support small satellite missions in which the platform is equipped with a single thruster nozzle which provides acceleration on a single direction at a time. This constraint implies that an attitude maneuver is necessary before or during each thrusting arc to direct the nozzle into the desired direction. In this context, an attitude guidance algorithm specific for the orbit maneuver has been developed. A Model Predictive Control scheme is proposed, where the attitude kinematics are coupled with the orbital dynamics in order to obtain the optimal guidance profiles in terms of satellite state, reference attitude, and thrust magnitude. The proposed control scheme is developed exploiting Formation Flying techniques where the reference orbit is that of a virtual spacecraft that the main satellite is required to rendezvous with. In addition to the controller design, the closed loop configuration is presented supported by numerical simulations. The efficacy of the proposed autonomous orbit keeping approach is shown in several application scenarios.

We summarize the results on electron transport in hybrid superconducting S/B/S' mesa-structure consisted of the oxide epitaxial S/B heterostructures, where S is the cuprate YBa2Cu3O 7-x superconductor, B – an interlayer with the spin dependent characteristics, and S’ is the Nb top superconductor. Josephson effect was observed manifested in appearance of oscillating Shapiro steps amplitudes with microwave signal power due to synchronization of junction self-generation of electromagnetic radiation and the external microwave probe signal. Triplet component of superconducting correlations emerged when the interlayer comprised two magnetic materials SrRuO3 and La0.7Sr0.3MnO3 with non-collinear magnetizations as well in the case of antiferromagnetic insulator Sr2IrO4 characterized by strong spin-orbit interaction. Thickness of the interlayer in the both cases considerably exceeded the coherence length of the magnetic spin active interlayer hinting on appearance of long-range proximity effect and spin-triplet superconducting current. Magnetic field dependences measured at dc, and the existence of the second harmonic in superconducting current–phase relation revealed by measurements at microwave frequencies will be discussed.

For Interferometry Synthetic Aperture Radar (InSAR), the normal baseline is one of the main factors that affect the accuracy of the ground elevation. For Gaofen-3 (GF-3) InSAR processing, the poor accuracy of the real-time orbit determination resulting in a large baseline error, leads to the modulation error in azimuth and the slope error in range for timely Digital Elevation Model (DEM) generation. In order to address this problem, a baseline estimation method based on external DEM is proposed in this paper. Firstly, according to the characteristic of the real-time orbit of GF-3 images, orbit fitting is executed to remove the non-linear error factor. Secondly, the height errors are obtained in slant-range plane between Shuttle Radar Topography Mission (SRTM) DEM and the GF-3 generated DEM after orbit fitting. At the same time, the height errors are used to estimate the baseline error which has a linear variation. In this way, the orbit error can be calibrated by the estimated baseline error. Finally, DEM generation is performed by using the modified baseline and orbit. This procedure is implemented iteratively to achieve a higher accuracy DEM. Based on the results of GF-3 interferometric SAR data for Hebei, the effectiveness of the proposed algorithm is verified and the accuracy of GF-3 real-time DEM products can be improved extensively.

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other. According to Kepler’s 1^st Law, “orbit of a planet with respect to the Sun is an ellipse, with the Sun at one of the two foci.” Orbit of the Moon with respect to Earth is also distinctly elliptical, but this ellipse has a varying eccentricity as the Moon comes closer to and goes farther away from the Earth in a harmonic style along a full cycle of this ellipse. In this paper, our research results are summarized, where it is first mathematically shown that the “distance between points around any two different circles in three dimensional space” is equivalent to the “distance of points around a vector ellipse to another fixed or moving point, as in two dimensional space”. What is done is equivalent to showing that bodies moving on two different circular orbits in space vector wise behave as if moving on an elliptical path with respect to each other, and virtually seeing each other as positioned at an instantaneously stationary point in space on their relative ecliptic plane, whether they are moving with the same angular velocity, or different but fixed angular velocities, or even with different and changing angular velocities with respect to their own centers of revolution. This mathematical revelation has the potential to lead to far reaching discoveries in physics, enabling more insight into forces of nature, with a formulation of a new fundamental model regarding the motions of bodies in the Universe, including the Sun, Planets, and Satellites in the Solar System and elsewhere, as well as at particle and subatomic level. Based on the demonstrated mathematical analysis, as they exhibit almost fixed elliptic orbits relative to one another over time, the assertion is made that the Sun, the Earth, and the Moon must each be revolving in their individual circular orbits of revolution in space. With this expectation, individual orbital parameters of the Sun, the Earth, and the Moon are calculated based on observed Earth to Sun and Earth to Moon distance data, also using analytical methods developed as part of this research to an approximation. This calculation and analysis process have revealed additional results aligned with observation, and this also supports our assertion that the Sun, the Earth, and the Moon must actually be revolving in individual circular orbits.

The new observations, including the fastest star, the circular velocity curve of the Milky Way and the fast galaxy bar, should imply that the mass of the center of the Milky Way is almost 10¹¹ times the mass of the Sun.

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other, whereas objects follow parabolic escape orbits while moving away from Earth and bodies asserting a gravitational pull, and some comets move in near-hyperbolic orbits when they approach the Sun. In this article, it is first mathematically proven that the “distance between points on any two different circles in three-dimensional space” is equivalent to the “distance of points on a vector ellipse from another fixed or moving point, as in two-dimensional space.” Then, it is further mathematically demonstrated that “distance between points on any two different circles in any number of multiple dimensions” is equivalent to “distance of points on a vector ellipse from another fixed or moving point”. Finally, two special cases when the “distance between points on two different circles in multi-dimensional space” become mathematically equivalent to distances in “parabolic” or “near-hyperbolic” trajectories are investigated. Concepts of “vector ellipse”, “vector hyperbola”, and “vector parabola” are also mathematically defined. The mathematical basis derived in this Article is utilized in the book “Everyhing Is A Circle: A New Model For Orbits Of Bodies In The Universe” in asserting a new Circular Orbital Model for moving bodies in the Universe, leading to further insights in Astrophysics.

The three-axis stabilization geostationary remote sensing satellite features high time resolution and plays a significant role in weather forecasting and environmental monitoring. With the future development of satellite technology, we propose a rapid geolocation algorithm for three-axis stabilization geostationary remote sensing satellites from the perspective of software algorithms. The method assesses conventional remote sensing data geolocation methods and the coordination group for meteorological satellites (CGMS, Coordination Group for Meteorological Satellites) nominal grid publishing format. First, the initial incident viewing vector of each detector on the sensor was constructed. Then, by reflecting the satellite platform's east-west and north-south mirrors, the outgoing vector of the payload coordinate system was obtained. This vector was converted to the satellite body coordinate system and, subsequently, to the satellite orbit coordinate system. The conversion of the earth-fixed coordinate system and the mirror rotation angle under ideal CGMS grid conditions were obtained, and the mirror rotation angle was converted to the corresponding CGMS nominal grid position to complete data positioning. The algorithm omits the complex process of calculating the intersection point between the viewing vector and the geodetic ellipsoid sphere from the earth-fixed coordinate system, resulting in an 83.3% improvement in computational efficiency without compromising positioning accuracy compared with conventional geolocation methods. This algorithm greatly improves the processing efficiency of geostationary meteorological satellite positioning, but its limitation is that the data processing results must be released in the CGMS nominal grid format.

In space application, hybrid pixel detectors of the Timepix family have been considered mainly for measurement of radiation levels and radiation dosimetry in low earth orbits. By the example of the Space Application of Timepix Radiation Monitor (SATRAM), we demonstrate the unique capabilities of Timepix-based miniaturized radiation detectors for particle separation. Using a novel method for proton spectrum reconstruction, we were able to measure the spectrum of protons trapped in the inner Van-Allen radiation belt, for the first time with a single-layer detector. We assess the measurement stability and the resiliency of the detector to the space environment demonstrating that, even though degradation is observed, data quality has not been affected significantly over more than 10 years. Based on the SATRAM heritage and the capabilities of the latest-generation Timepix-series chips, we discuss their applicability for use in a compact magnetic spectrometer for deep-space mission or in the high radiation environment of the Jupiter radiation belts, and their capability for use as single-layer X- and γ-ray polarimeter. The latter was supported by measurement of the polarization of scattered radiation in a laboratory experiment, where a modulation of 80% was found.

Signal-to-noise ratio (SNR) is an important index to evaluate radiation performance and image quality of optical imaging systems under low illumination background. Under the nighttime lighting condition, the illumination of remote sensing objects is low and varies greatly, usually ranging from several lux to tens of thousands of lux. Nighttime light remote sensing imaging requires high sensitivity and large dynamic range of detectors. Luojia 1-01 is the first professional nighttime light remote sensing satellite in the world. In this paper, we took the nighttime light remote sensing camera carried on the satellite as research object, proposed an in-orbit SNR test method based on time series images to overcome the problem of low spatial resolution. We first analyzed the process of luminous flux transmission between objects and satellite and established a radiative transfer model. By combining the parameters of large relative aperture optical system and high sensitivity CMOS device, we established SNR model and specially analyzed the effect of exposure time and quantization bits on SNR. Finally we used the proposed in-orbit test method to calculate SNR of lighting images acquired by satellite. And the measured result is in good agreement with the model predicted data. Under the condition of 10lx illumination, the SNR of typical objects can reach 27.02dB, which is much better than the requirement of 20dB for engineering application.

Pure orbital blowout fractures occur within the confines of the internal orbital wall. Restoration of orbital form and volume is paramount to prevent functional and esthetic impairment. The anatomical peculiarity of the orbit has encouraged surgeons to develop implants with customized features to restore its architecture. This has resulted in worldwide clinical demand for patient-specific implants (PSIs) designed to fit precisely in the patient's unique anatomy. Fused filament fabrication (FFF) three-dimensional (3D) printing technology has enabled the fabrication of implant-grade polymers such as Polyetheretherketone (PEEK), paving the way for a more sophisticated generation of biomaterials. This study evaluates the FFF 3D printed PEEK orbital mesh customized implants with a metric considering the relevant design, biomechanical, and morphological parameters. The performance of the implants is studied as a function of varying thicknesses and porous design constructs through a finite element (FE) based computational model and a decision matrix based statistical approach. The maximum stress values achieved in our results predict the high durability of the implants, and the maximum deformation values were under one-tenth of a millimeter (mm) domain in all the implant profile configurations. The circular patterned implant (0.9 mm) had the best performance score. The study demonstrates that compounding multi-design computational analysis with 3D printing can be beneficial for the optimal restoration of the orbital floor.

This article presents a concise survey of basic discrete and semi-discrete nonlinear models which produce two- and three-dimensional (2D and 3D) solitons, and a summary of main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ⁽²⁾) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of basic species of multidimensional discrete modes, including fundamental and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.

Spin-orbit coupling and nonparaxiality effects during propagation of vortex vector light beams in a cylindrical graded-index waveguide are investigated by solving the full three-component field Maxwell’s equations. Symmetry breaking effects for left- and right-handed circularly polarized vortex light beams propagating in a rotationally symmetric graded-index optical fiber are considered. The mode-group delay in a graded-index fiber due to spin-orbit interaction is demonstrated. It is shown that the relative delay times between vortex pulses of opposite circular polarizations of the order of 10 ps/km can be observed in graded-index fibers for high-order topological charges.

We examine here characteristics of electromagnetic waves that propagate through an unbounded space filled with a homogeneous isotropic chiral medium. Resulting characters are compared to those of the electromagnetic waves propagating through an achiral free space. To this goal, we form energy conservation laws for key bilinear parameters in a chiral case. Due to a nonzero medium chirality, conservation laws turn out to contain extra terms that are linked to the spin-orbit coupling, which is absent for an achiral case. As an example, we take a plane wave for achiral case to evaluate those bilinear parameters. Resultantly, the conservation laws for a chiral case are found to reveal inconsistencies among several bilinear parameters that constitute the con-servation laws , thereby prompting us to establish partial remedies for formulating proper wave-propagation problems.

A particular challenge in the conceptual design of direct-from orbit delivery systems is the seemingly well-known kinematics retain fallacies whose efficacies are reduced over great distances. Rotation about the local wing of an aerospace vehicle is almost never the pitch angle, yet modern application of kinematics often assumes such (with accompanying angular error). The same assertion is usually true about the nature of roll and yaw angles. Expressing motion in coordinates of rotating reference frames necessitates transformation between reference frames, and one such transformation is embodied in the Direction Cosine Matrices (DCM) formed by a sequence of three successive frame rotations. One of two ubiquitous sequences of three rotations used to construct the DCM involves first a rotation around the inertial z-axis, then intermediate y-axis, then finally about the body’s x-axis; a sequence commonly called the “aerospace sequence” or the a “3-2-1 rotation sequence”. The second ubiquitous sequence is the so-called “orbital sequence” or “3-1-3 rotation sequence” with rotations about the inertial z axis first, then about the intermediate x-axis, then finally about the body z-axis. This manuscript evaluates which sequence is the most advantageous for an object starting in space and then travels through the atmosphere to a target on the Earth’s surface. Six degrees of freedom of vehicle motion were simulated starting in orbit with a given thrust and commanded maneuver. The simulation performs all twelve possible rotation sequences (transforming inertial coordinates to body coordinates) with comparison by computational burden and error representing rotations about body axes (roll, pitch, and yaw respectively). Simulation precision is validated using the quaternion normalization condition indicating near machine precision (0.9\times{10}^{-15}) and reveals the so-called 132 rotation is the most accurate with an average error of 0.14° and a computational time of 0.013 seconds: resulting in a 97.95% increase in accuracy over the so-called 321 rotation and a 99.84% increase over the so-called 313 rotation.

To keep the global navigation satellite system functional during extreme conditions, it is a trend to employ autonomous navigation technology with inter-satellite link. As in the newly built BeiDou system (BDS-3) equipped with Ka-band inter-satellite links, every individual satellite has the ability of communicating and measuring distances among each other. The system also has less dependence on the ground stations and improved navigation performance. Because of the huge amount of measurement data, centralized data processing algorithm for orbit determination is suggested to be replaced by a distributed one in which each satellite in the constellation is required to finish a partial computation task. In current paper, the balanced extended Kalman filter algorithm for distributed orbit determination is proposed and compared with whole-constellation centralized extended Kalman filter, iterative cascade extended Kalman filter, and increasing measurement covariance extended Kalman filter. The proposed method demands a lower computation power however yields results with a relatively good accuracy.