Identical Orbits Research Articles

Symmetric twin paradox for free-falling frames: Argument against the relativistic time dilation?

The twin paradox, a classical puzzle in Special Relativity (SR), is typically resolved by acknowledging the asymmetry introduced by the acceleration of one twin's frame, associated with a rocket's motion through space. A similar paradox arises without any accelerated system, involving three or more inertial systems. This is commonly resolved by employing the relativistic concepts of clock synchronization and simultaneity. Here, we reformulate the paradox for two free-falling systems, where the twins traverse identical circular orbits in opposite directions around a central mass with a spherically symmetric gravitational field. This redefined version of the paradox eliminates asymmetry inherent in the original problem. Since both frames are free-falling, they can be viewed as locally inertial according to Einstein's Equivalence Principle. Additionally, no synchronization with clocks in other frames is needed. We explore a potential resolution to the paradox and highlight that there may be a misinterpretation of the Lorentz transformation in SR.

Neural Network-Based Formation Flying Using Aerodynamic Forces via Variable Shape Function

Conventional formation flying Earth-orbiting satellites control their orbits to perform their missions using thrusters, but the amount of propellant loaded into a satellite is limited. Therefore, the use of aerodynamic forces for orbit control has been attracting attention, particularly in low Earth orbit. The orbit control can be achieved by appropriately changing the state of satellite, such as attitude and shape, to meet the aerodynamic requirements. In modeling the relationship between satellite state and aerodynamic forces, conventional methods ignore the shielding caused by the nonconvexity of the satellite’s appearance. Ignoring the shielding creates a gap between the modeled and the real aerodynamic forces, resulting in poor control performance. To solve this problem, we propose an aerodynamic force modeling method that incorporates a neural network to estimate the shielding. We train the neural network using data from an aerodynamics simulator. The optimal state that not only generates the required aerodynamic forces but also improves controllability under various mechanical constraints is obtained by solving an optimization problem that incorporates the proposed aerodynamic model. We conduct numerical simulations for establishing and maintaining general circular orbit formations. The results show convergence and continuous stable control of the deputy satellite to the ideal orbit.

Cooperative learning event‐triggered control for discrete‐time nonlinear multi‐agent systems by internal and external interaction topology

AbstractThis paper investigates distributed cooperative learning event‐triggered control for discrete‐time strict‐feedback nonlinear multi‐agent systems with an identical system structure and different recurrent reference orbits. A clever system decomposition method is firstly proposed to divide every ‐order agent system into first‐order subsystems, which makes it possible to solve the tough problem that every estimated neural weight cannot converge to an unique ideal value based on the existing control scheme. By constructing two interaction typologies, a novel distributed cooperative weight updating law is designed by the introduction of the internal interaction terms between subsystems of every agent, the external interaction terms between agents, and the triggering mechanism between agents. With the combination of the graph multiplication operation, the consensus theory and the matrix null space property, the proposed cooperative event‐triggered control scheme guarantees that every agent can track their corresponding recurrent reference trajectories. And further the exponential convergence of all agents' neural estimated weights to a close vicinity around their mutual and unique ideal weights is verified under the condition that the directed interaction topology between agents is strongly connected and balanced. Such a weight convergence makes the proposed scheme has some significant advantages including the small data storage space, the convenient knowledge reuse, the good generalization ability, and the low communication burden. By reinvoking the saved constant weights, a static learning controller is presented for the high‐performance control of similar diversified tracking tasks. Simulation studies and some comparisons are given to show the advantages and effectiveness of the presented scheme.

Emergence and evolution of unusual inhomogeneous limit cycles displacing hyperchaos in three quorum-sensing coupled identical ring oscillators

We demonstrate that strongly asymmetric limit cycles can be observed in the system of three identical ring oscillators (3-gene networks known as Repressilators) globally coupled by signal molecule diffusion added to the model in a way like the known bacterial “quorum-sensing” mechanism. These cycles are stable over a wide interval of the coupling strengths where they expel the dominant hyperchaotic regime existing in three Repressilators in very large areas of parameters. The bifurcations of the inhomogeneous limit cycle, with a high-amplitude orbit for one oscillator and two low-amplitude identical orbits for the other two, are traced. Bifurcation analysis reveals an unusual cascade of bifurcations ended in the appearance of a new limit cycle with splitted (slightly nonidentical) low-amplitude orbits. Both cycles lose stability giving birth inhomogeneous chaos in the small parameter interval. Hyperchaos dominates in the parameter plane around the “island” with inhomogeneous limit cycles, and this accounts for very long hyper chaotic transients when the system is returning to stable asymmetric cycles after their perturbations. In turn, it is the cycles that contribute the asymmetric and often rather long pieces in hyperchaotic trajectories. The presented cycles differ from the known asymmetric attractors: inhomogeneous limit cycles born from “oscillation death” and the cycles observing in “smallest chimeras”.

Spin-Orbit versus Hyperfine Coupling-Mediated Intersystem Crossing in a Radical Pair.

While spin-orbit coupling (SOC) is typically the dominant interaction that couples singlet and triplet states within individual chromophores, hyperfine coupling (HFC) becomes important in multichromophoric systems, particularly in relation to the radical pair mechanism. Here, we use TD-DFT to calculate the spin-orbit coupling and hyperfine coupling between the first singlet and triplet charge transfer states of the radical pair 2Pyrene- and 2N,N-dimethylaniline+. We show that, as the intermolecular donor-acceptor distance grows, SOC decays to zero (as one would expect) because singlet and triplet states are characterized by identical orbitals in space, while the HFC remains comparatively constant. The switching region occurs around 4 Å, beyond which HFC dominates over SOC as far as defining the rate of intersystem crossing (ISC).

Optimization of Multispacecraft Maneuvers for Mobile Target Tracking from Low Earth Orbit

This paper presents a method of planning spacecraft maneuvers for mobile target tracking. Agile, maneuverable spacecraft have been proposed as a means of modifying satellite orbits to observe discrete targets on the Earth on demand. This work adapts this concept to propose a method of using maneuverable spacecraft to observe a mobile target as it moves across the Earth. Previous work has shown the potential of such an approach to increase persistence of coverage of a moving target. This work applies a suitable optimizer to select possible maneuvers for a spacecraft, or a constellation of spacecraft, to repeatedly observe a moving target. A biased random key genetic algorithm is used, which adjusts the for each maneuver to minimize the total used and maximize target coverage over the full sequence of maneuvers. The developed method is applied to two case studies concerning monitoring of tropical storms. The results indicate that, using relatively small maneuvers, spacecraft orbits can be adjusted to improve the quantity and quality of views of a moving target. In the Typhoon Megi case study, a single spacecraft using less than is shown to double the access time and provide two additional observations of the storm eye compared with a nonmaneuvering spacecraft in an identical initial orbit. Opportunities for observations increase as the number of maneuverable spacecraft are increased, with a three-spacecraft constellation able to provide five complete observations of the storm eye for a total change in velocity of 12 m/s.

Mixed-Sensitivity Control for Drag-Free Spacecraft Based on State Space

This paper investigates a mixed-sensitivity control method for a class of drag-free spacecraft-needed frequency-separation control, which overcomes the coupled problem of a multiple-in multiple-out (MIMO) system with multiple sensitive-axes and disturbances of actuators. Firstly, the relative dynamics equation is established based on the character of displacement error, which is separated by that test-mass (TMs) tracking ideal orbit with high-frequency displacement and cavity of spacecraft tracking TMs with low-frequency displacement. Secondly, the feedback gain matrix is obtained by the LMI/SDP, which is devised by a general system containing a weight function. Finally, the simulation results demonstrate the performance of the proposed method.

Change Detection for Monostatic Pursuit SAR GMTI—Theories and Experimental Results

Monostatic pursuit refers to the operating mode formed by two monostatic SAR systems that follow an identical orbit with a separation in time of several seconds. The detected changes between SAR scenes with several seconds time difference are most likely the changes caused by ground moving targets. Hence, this operating mode opens an opportunity to detect ground moving targets by SAR change detection methods. The paper investigates this possibility to detect ground moving targets using change detection and to combine change detection and GMTI for GMTI. In this combination, a GMTI method will help to classify the detected changes obtained with a change detection method. Some GMTI results are provided in the paper based on the measurements in the monostatic pursuit mode with deployed targets, conducted by TerraSAR-X and TanDEM-X in Sweden in early 2015.

Sixth Order Numerov-Type Methods with Coefficients Trained to Perform Best on Problems with Oscillating Solutions

Numerov-type methods using four stages per step and sharing sixth algebraic order are considered. The coefficients of such methods are depended on two free parameters. For addressing problems with oscillatory solutions, we traditionally try to satisfy some specific properties such as reduce the phase-lag error, extend the interval of periodicity or even nullify the amplification. All of these latter properties come from a test problem that poses as a solution to an ideal trigonometric orbit. Here, we propose the training of the coefficients of the selected family of methods in a wide set of relevant problems. After performing this training using the differential evolution technique, we arrive at a certain method that outperforms the other ones from this family in an even wider set of oscillatory problems.

On formation flying in low earth mirrored orbits — A case study

Spacecraft formation flying in co-planar identical orbits with oppositely directed apse lines (eccentricity vectors) allows simultaneous in-situ measurements in different altitudes and time-sequential measurements in a limited altitude range (rapid revisit); a key enabling factor in understanding many poorly understood phenomena in our atmosphere and its interaction with the magnetosphere. The dynamics and control problem for flying formations in mirrored orbits are investigated using the Mechanisms of Energetic Mass Ejection - Explorer (MEME-X) mission concept as a case study. It is determined that the proposed two-craft and four-craft configurations require routine maintenance to correct their relative motion. The formation maintenance costs are quantified for both configurations and determined to be within the capabilities of small satellites. A high-fidelity end-to-end simulation is developed to model the entire two-craft mission concept, from orbit insertion to decommissioning, providing an approximate baseline for the flight dynamics costs of similar missions using multiple spacecraft flying in mirrored orbits.

Equilibrium, Regular Polygons, and Coulomb-Type Dynamics in Different Dimensions

The equation of motion in ℝ d of n generalized point charges interacting via the s -dimensional Coulomb potential, which contains for d = 2 a constant magnetic field, is considered. Planar exact solutions of the equation are found if either negative n − 1 > 2 charges and their masses are equal or n = 3 and the charges are different. They describe a motion of negative charges along identical orbits around the positive immobile charge at the origin in such a way that their coordinates coincide with vertices of regular polygons centered at the origin. Bounded solutions converging to an equilibrium in the infinite time for the considered equation without a magnetic field are also obtained. A condition permitting the existence of such solutions is proposed.

First-principles investigation on the bonding mechanism between graphyne and the (111) surface of Cu, Ag and Au

A series of adsorption configurations with less than 2% lattice mismatch of graphyne adsorbed at different sites on the (111) surface of Cu, Ag and Au are obtained by a systematic rotation of the graphyne sheet. Besides, all the non-equivalent adsorption configurations of graphyne on metal surfaces are obtained by a structure screening method based on the translation of graphyne sheet and the calculation of the atomic overlapping area at the interface. The most stable adsorption configuration of graphyne on each metal surface is obtained by optimizing these non-equivalent adsorption configurations with a small computational cost. Then the adsorption energy, differential charge density, and partial density of states are calculated using a first-principles method in order to investigate the bonding mechanism between graphyne and the (111) surface of these three metals. The results show that the adsorption types of graphyne on the (111) surface of Cu, Ag and Au are chemisorption, chemical and physical mixed adsorption and pure physisorption, respectively. In detail, when a metal (Cu or Ag) atom is below a C atom, the C-pz orbital will interact with the s and d orbitals of the metal atom and then form a covalent bond with the metal atom. In particular, when a Cu atom lies below two carbon atoms joined by an acetylene bond, the s and d orbitals of the Cu atom hybridize with each other to form two identical sd orbitals and then form two covalent bonds with two C-pz orbitals. Our results not only provide a structure screening method for obtaining the most stable configuration with a very small lattice mismatch but also reveal the interface bonding mechanism between graphyne and metals, which will provide help for the preparation of graphyne and its application in composite materials.

Synthetic Aperture Radar Flood Detection under Multiple Modes and Multiple Orbit Conditions: A Case Study in Japan on Typhoon Hagibis, 2019

Flood detection using a spaceborne synthetic aperture radar (SAR) has become a powerful tool for organizing disaster responses. The detection accuracy is increased by accumulating pre-event observations, whereas applying multiple observation modes results in an inadequate number of observations with the same mode from the same orbit. Recent flood detection studies take advantage of the large number of pre-event observations taken from an identical orbit and observation mode. On the other hand, those studies do not take account of the use of multiple orbits and modes. In this study, we examined how the analysis results suffered when pre-event observations were only taken from a different orbit or mode to that of the post-event observation. Experimental results showed that inundation areas were overlooked under such non-ideal conditions. On the other hand, the detection accuracy could be recovered by combining analysis results from possible alternate datasets and became compatible with ideal cases.

Gravitational Effects in Electrostatic Storage Rings and the Search for the Electric Dipole Moments of Charged Particles

Spurious signals induced by curved spacetime in the gravity field of the rotating Earth in experiments on the search for the electric dipole moment of charged particles manifested by the spin rotation in pure electrostatic storage rings have been analyzed with the focus on effects of Earth’s rotation. It has been found that the rotation of the plane of an electrostatic storage ring together with the Earth generates a nonzero magnetic field. Locally in the storage ring, the spin precession frequency linear in Earth’s rotation is much higher than the frequency of the spin precession caused by the electric dipole moments. It has been argued that the integral spurious spin rotation for a particle on an ideal orbit is strongly suppressed because the contribution from Earth’s rotation is sign-alternating along the storage ring. A background signal quadratic in Earth’s rotation is finite but small.

An Adaptive Real-Time Detection Algorithm for Dim and Small Photoelectric GSO Debris.

Geosynchronous orbit (GSO) is the ideal orbit for communication, navigation, meteorology and other satellites, but the space of GSO is limited, and there are still a large number of space debris threatening the safety of spacecraft. Therefore, real-time detection of GSO debris is necessary to avoid collision accidents. Because radar is limited by transmitting power and operating distance, it is difficult to detect GSO debris, so photoelectric detection becomes the mainstream way to detect GSO debris. This paper presents an adaptive real-time detection algorithm for GSO debris in the charge coupled device (CCD) images. The main work is as follows: An image adaptive fast registration algorithm and an enhanced dilation difference algorithm are proposed. Combining with mathematical morphology, threshold segmentation and global nearest neighbor (GNN) multi-target tracking algorithm, the functions of image background suppression, registration, suspected target extraction and multi-target tracking are realized. The processing results of a large number of measured data show that the algorithm can detect dim geostationary earth orbit (GEO) and non-GEO debris in GSO belt stably and efficiently, and the processing speed meets the real-time requirements, with strong adaptive ability, and has high practical application value.

Non-orthogonal determinants in multi-Slater-Jastrow trial wave functions for fixed-node diffusion Monte Carlo.

The accuracy and efficiency of ab initio Quantum Monte Carlo (QMC) algorithms benefit greatly from compact variational trial wave functions that accurately reproduce ground state properties of a system. We investigate the possibility of using multi-Slater-Jastrow trial wave functions with non-orthogonal determinants by optimizing identical single particle orbitals independently in separate determinants. As a test case, we compute variational and fixed-node diffusion Monte Carlo (FN-DMC) energies of a C2 molecule. For a given multi-determinant expansion, we find that this non-orthogonal orbital optimization results in a consistent improvement in the variational energy and the FN-DMC energy on the order of a few tenths of an eV. In some cases, fewer non-orthogonal determinants are required compared to orthogonal ones in order to achieve similar accuracy in FN-DMC. Our calculations indicate that trial wave functions with non-orthogonal determinants can improve computed energies in a QMC calculation when compared to their orthogonal counterparts.

Relative positioning of formation-flying spacecraft using single-receiver GPS carrier phase ambiguity fixing

In recent years, differential carrier phase-based relative positioning (or “baseline determination”) with precision at the millimeter and submillimeter levels has been demonstrated for the GRACE, TanDEM-X and Swarm missions in offline processing. Specific features of such missions have included the use of spacecraft of similar shapes placed in almost identical orbits as well as the use of consistent geodetic-class GPS receivers. These elements have proven to be advantageous for the computation of baseline solutions with such precision levels. Particularly, they have allowed to fully leverage the use of differential GPS techniques, including the estimation and use of carrier phase integer ambiguities. Similarly, the aforementioned spacecraft and orbit characteristics have made it possible to tightly constrain the relative dynamics of formations in the generation of reduced-dynamic solutions. Other than the former examples, prospective formation-flying mission proposals, such as SAOCOM-CS and PICOSAR, may comprise spacecraft with very different characteristics, including dissimilar GPS/GNSS receivers. Such cases may no longer provide favorable conditions for relative orbit determination strategies. As an alternative, absolute orbit solutions may be computed individually for each spacecraft and used for the generation of precise baseline products. This study aims at the assessment of the potential of single-receiver ambiguity fixing for the generation of precise baseline solutions. Results using flight data from the GRACE, TanDEM-X and Swarm missions exhibit baseline accuracy better than 5 mm (3D RMS) for a one-month test period in June 2016. As such, the presented solutions may be considered for prospective formation-flying remote sensing missions with baseline precision requirements at the subcentimeter level. Likewise, the method is considered of particular interest for future multi-spacecraft formations and swarms that require efficient determination of a large number of individual baselines.

Generalized Image Navigation & Registration Algorithms for Ground and Space Segments

Ground segment image navigation and registration algorithms and space segment image motion compensation algorithm are presented. The fundamental ground algorithm is based on Kalman filter instead of least squares and does not require ranging or accurate orbit to be provided by flight dynamics. Kalman filter is used to estimate attitude correction angles, orbit position and velocity relative to ideal geostationary orbit, and internal misalignments of imagers with single mirror or two mirrors. Kalman filter measurements consist of landmarks extracted from the imaging instrument level 1A data blocks, maneuver delta V or coarse orbit from flight dynamics, and spacecraft attitude telemetry inserted in the imager wideband data. The ground algorithm is then shown how to be applied to systems with star and landmark measurements, systems with star only measurements with accurate orbit provided by flight dynamics or by the global positioning system, and systems with spacecraft inertial angular rate. Pixel location transformation from imager line of sight reference frame to GOES and CGMS fixed grid frames is also provided for on-ground image registration using resampling.

Phase Correction of Single-Look Complex Radar Images for User-Friendly Efficient Interferogram Formation

We present a new interferometric synthetic aperture radar processing approach that removes topography–dependent phase from single-look complex (SLC) radar images, making interferogram formation more efficient. We first adopt motion compensation techniques to resample SLC images with respect to an ideal reference orbit and then separate the residual topographic phase contributions into parts dependent only on individual SLC acquisitions, and generate topography-compensated images directly in latitude–longitude coordinates. Since the number of interferograms is typically much larger than the number of SLC images, our approach greatly reduces needed computational resources. Furthermore, we move the need for precise knowledge of imaging geometry upstream from the end user to the data provider. We demonstrate our approach for both preprocessed SLC images and raw data using COSMO-SkyMed L1A and ALOS L0 products. The performance of our method depends on the quality of the digital elevation model (DEM) used—DEM error affects the correction phase proportionally to the baseline between radar scenes and the reference orbital path. With a 1000-m baseline and a nominal 30° incidence angle, we find that the uncertainty of estimated deformation increases by approximately 1 cm with every 3 m increase in the DEM error.

Burst Misalignment Evaluation for ALOS-2 PALSAR-2 ScanSAR-ScanSAR Interferometry

This paper reports the validation results of burst misalignment for ScanSAR-ScanSAR interferometry of the Phased Array-type L-band Synthetic Aperture Radar-2 (PALSAR-2) aboard the Advanced Land Observing Satellite-2 (ALOS-2, “DAICHI-2”). After the internal software modification on 8 February 2015, ALOS-2 ScanSAR observation mode archives have been available for use in interferometric analysis, as it was planned. However, it has not been reported whether its burst misalignment satisfies the mission requirements: 90% or higher burst overlap ratio. The validation results in this paper confirm that the expected observation misalignment satisfies the required range, including minimal seasonal and orbital dependencies. The results in this paper are obtained directly from the azimuth offset of the single look complex (SLC) data and are not derived from the orbit records. Nine identical orbits and frame numbers are chosen and evaluated to investigate the average burst misalignment and orbital dependency.