Orbital Dynamics Research Articles

Near-Earth stream decoherence revisited: the limits of orbital similarity

Orbital similarity measures, such as the D values, have been extensively used in meteor science to identify meteoroid streams and associate meteorite falls with near-Earth objects (NEOs). However, the chaotic nature of near-Earth space challenges the long-term reliability of these measures for stream identification, and the increasing size of our fireball, meteorite fall, and NEO databases make random associations more common. Despite this, many researchers erroneously continue to use orbital similarity beyond its inherent limits. We aim to assess the statistical significance of using orbital similarity measures for identifying streams of meteoroids or asteroids and explore the implications of chaotic dynamics on the long-term coherence of these streams. We employed a kernel density estimation (KDE) based method to evaluate the statistical significance of orbital similarities within different datasets. Additionally, we conducted a Lyapunov characteristic lifetime analysis and simulated 300 fictitious meteoroid streams to estimate the decoherence lifetimes in near-Earth space. The orbital similarity was determined using the D$_ SH $, D', and D$_ H $ orbital similarity discriminants. Clustering analysis relied on a density-based spatial clustering of applications with noise (DBSCAN) algorithm. Our analysis found no statistically significant streams within the meteorite fall, fireball, or USG impact datasets, with orbital similarities consistent with random associations. Conversely, 12 statistically significant clusters were identified within the NEO population, likely resulting from tidal disruption events. The Lyapunov lifetime analysis revealed short characteristic lifetimes (60–200 years) for orbits in near-Earth space, emphasizing the rapid divergence of initially similar orbits. Meteoroid stream decoherence lifetimes ranged from $10^4$ to $10^5$ years, aligning with previous studies and underscoring the transient nature of such streams. The rapid decoherence of meteoroid streams and the chaotic dynamics of near-Earth orbits suggest that no reported stream or NEO associations of meteorites or fireballs are statistically significant according to orbital discriminates. Many are likely coincidental rather than indicative of a true physical link. However, several statistically significant clusters found within the NEO population are consistent with a tidal disruption formation. This contrast and lack of statistically significant associations amongst the impact datasets is likely due to the fireball databases being 2 orders of magnitude smaller than the NEO database and the higher intrinsic uncertainties of fireball observation derived orbits.

Lagrangian formulation of nuclear-electronic orbital Ehrenfest dynamics with real-time TDDFT for extended periodic systems.

We present a Lagrangian-based implementation of Ehrenfest dynamics with nuclear-electronic orbital (NEO) theory and real-time time-dependent density functional theory for extended periodic systems. In addition to a quantum dynamical treatment of electrons and selected protons, this approach allows for the classical movement of all other nuclei to be taken into account in simulations of condensed matter systems. Furthermore, we introduce a Lagrangian formulation for the traveling proton basis approach and propose new schemes to enhance its application for extended periodic systems. Validation and proof-of-principle applications are performed on electronically excited proton transfer in the o-hydroxybenzaldehyde molecule with explicit solvating water molecules. These simulations demonstrate the importance of solvation dynamics and a quantum treatment of transferring protons. This work broadens the applicability of the NEO Ehrenfest dynamics approach for studying complex heterogeneous systems in the condensed phase.

On the Andromeda-Milky Way Future Encounter: Thrice Faster Over Time

This inquiry accurately provides an analytical solution of the orbital free-falling time for the system of galaxies Andromeda-Milky Way within a non-expanding tired-light-dominated framework. The mathematical and physical background involves a two-body problem based on the orbital dynamics in which, in the first scenario, the gravitational interaction between local galaxies dominates over the expanding space. The latter is the standard astrophysical approach undertaken by public fund-based universities all over the world. However, in the second alternative scenario, Andromeda’s blueshift has to be corrected for the apparent recession velocity provided by the photon energy loss as a result of multiple interactions between photons and crystallized electrons through the intergalactic medium provided by a Tired Light, specifically, a New Tired Light process. This leads towards a substantial temporal deviation between the classic research approach and this unconventional and independent mindset. Hence, the outcome gives out a disagreement consisting in an orbital free-falling time equal to 1.7 rather than 4.5 billion years. Accordingly, the encounter of the two main galaxies of the Local Group will occur much earlier than estimated thus far. Accordingly, this implies an urgent shift in the scientific mindset as well as a course change in the application of the boundary conditions into forthcoming computational methods.

Automated Estimation of Building Heights with ICESat-2 and GEDI LiDAR Altimeter and Building Footprints: The Case of New York City and Los Angeles

Accurate estimation of building height is crucial for urban aesthetics and urban planning as it enables an accurate calculation of the shadow period, the effective management of urban energy consumption, and thorough investigation of regional climatic patterns and human-environment interactions. Although three-dimensional (3D) cadastral data, ground measurements (total station, Global Positioning System (GPS), ground laser scanning) and air-based (such as Unmanned Aerial Vehicle—UAV) measurement methods are used to determine building heights, more comprehensive and advanced techniques need to be used in large-scale studies, such as in cities or countries. Although satellite-based altimetry data, such as Ice, Cloud and land Elevation Satellite (ICESat-2) and Global Ecosystem Dynamics Investigation (GEDI), provide important information on building heights due to their high vertical accuracy, it is often difficult to distinguish between building photons and other objects. To overcome this challenge, a self-adaptive method with minimal data is proposed. Using building photons from ICESat-2 and GEDI data and building footprints from the New York City (NYC) and Los Angeles (LA) open data platform, the heights of 50,654 buildings in NYC and 84,045 buildings in LA were estimated. As a result of the study, root mean square error (RMSE) 8.28 m and mean absolute error (MAE) 6.24 m were obtained for NYC. In addition, 46% of the buildings had an RMSE of less than 5 m and 7% less than 1 m. In LA data, the RMSE and MAE were 6.42 m and 4.66 m, respectively. It was less than 5 m in 67% of the buildings and less than 1 m in 7%. However, ICESat-2 data had a better RMSE than GEDI data. Nevertheless, combining the two data provided the advantage of detecting more building heights. This study highlights the importance of using minimum data for determining urban-scale building heights. Moreover, continuous monitoring of urban alterations using satellite altimetry data would provide more effective energy consumption assessment and management.

Natural satellites database (NSDB) revisited

Any study of the dynamics of the natural planetary satellites requires as many astrometric observations as possible. This type of work is partially made by each astronomer starting this type of study but it has never been done for all the natural planetary systems. The goal of our work is to build a database of all available astrometric observations along with all the information needed for an efficient use of these data so that the astronomers interested in the dynamics of planetary satellites do not have to repeat the search for these data. To do this, we sought and carefully read all the publications containing observational data, so that we are able to include the astrometric positions of satellites, the reference frame used by the observer, the corrections and reductions made, and timescale. Direct contact with observers was sometimes necessary to obtain raw unpublished data. A new database containing about 90 <!PCT!> of all the observations that are useful for studying the dynamics of the planetary satellites is now available for the interested community of astronomers.

Analytical Second-Order Extended Kalman Filter for Satellite Relative Orbit Estimation

This study considers a relative orbit estimation problem wherein an observing spacecraft navigates with respect to a target space object at a large separation distance (several kilometers) using only the bearing angles obtained by a single onboard camera. Generally, the extended Kalman filter (EKF), which is based on linear relative motion equations such as the Clohessy–Wiltshire equation, is used for the relative navigation of satellites. The EKF linearizes the estimation error around the current estimate and applies the Kalman filter equations to this linearized system. However, it has been shown that nonlinearities of the orbit determination problem can make the linearization assumption insufficient to represent the actual uncertainty. Therefore, an analytical second-order extended Kalman filter (ASEKF) for relative orbit estimation is proposed in this study. The ASEKF, to sequentially estimate the relative states of satellites and their associated uncertainties, is formulated based on a second-order analytic relative-motion equation under J2-perturbtation, which can overcome the deficiencies of existing approaches that mainly focus on applications in two-body, near-circular, and linearized orbit dynamics. Numerical results show that the proposed method provides superior robustness and mean-square error performance compared to linear estimators under the conditions considered.

Triple trouble with PSR J1618−3921: Mass measurements and orbital dynamics of an eccentric millisecond pulsar

Context. PSR J1618−3921 is one of five known millisecond pulsars (MSPs) in eccentric orbits (eMPSs) located in the Galactic plane, whose formation is poorly understood. Earlier studies of these objects revealed significant discrepancies between observations and predictions from standard binary evolution scenarios of pulsar-helium white dwarf (HeWD) binaries, especially in the case of PSR J0955−6150, for which mass measurements ruled out most eMSP formation models. Aims. We aim to measure the masses of the pulsar and its companion, and constrain the orbital configuration of PSR J1618−3921. This facilitates understanding similarities among eMSPs and could offer hints as to their formation mechanism. Methods. We conducted observations with the L-band receiver of the MeerKAT radio telescope and the UWL receiver of the Parkes Murriyang radio telescope between 2019 and 2021. These data were added to archival Parkes and Nançay observations. We performed a full analysis on this joint data set with a timing baseline of 23 years. We also used the data from recent observations to give a brief account of the emission properties of J1618−3921, including a rotating vector model (RVM) fit of the linear polarisation position angle of the pulsar. Results. From the timing analysis, we measure a small but significant proper motion of the pulsar. The long timing baseline allowed for a highly significant measurement of the rate of advance of periastron of ω̇ = (0.00145±0.00010)°yr−1. Despite the tenfold improvement in timing precision from MeerKAT observations, we can only report a low-significance detection of the orthometric Shapiro delay parameters, h3 = 2.70−1.47+2.07 μs and ς = 0.68−0.09+0.13. Under the assumption of the validity of general relativity (GR), the self-consistent combination of these three parameters leads to mass estimates of the total and individual masses in the binary of Mtot = 1.42−0.19+0.20 M⊙, Mc = 0.20−0.03+0.11 M⊙, and Mp = 1.20−0.20+0.19 M⊙. We detect an unexpected change in the orbital period of Ṗb = −2.26−0.33+0.35 × 10−12, that is an order of magnitude larger and carries an opposite sign to what is expected from the Galactic acceleration and the Shklovskii effect, which are a priori the only non-negligible contributions expected for Ṗb. We also detect a significant second derivative of the spin frequency, f̈. The RVM fit reveals a viewing angle of ζ = (111 ± 1)°. Furthermore, we report an unexpected, abrupt change in the mean pulse profile in June 2021 of unknown origin. Conclusions. We propose that the anomalous Ṗb and f̈ we measure for J1618−3921 indicate an additional varying acceleration due to a nearby mass. The J1618−3921 binary system is likely part of a hierarchical triple, but with the third component much farther away than the outer component of the MSP in a triple star system, PSR J0337+1715. This finding suggests that at least some eMSPs might have formed in triple star systems. Although the uncertainties are large, the binary companion mass is consistent with the Pb − MWD relation, which has been verified for circular HeWD binaries and also for the two HeWDs in the PSR J0337+1715 system. Future regular observations with the MeerKAT telescope will, due to the further extension of the timing baseline, improve the measurement of Ṗb and f̈. This will help us further understand the nature of this system, and perhaps improve our understanding of eMSPs in general.

Test Mass Capture Control for Drag-Free Satellite Based on State-Dependent Riccati Equation Method

The drag-free satellite plays an important role in the space-based gravitational wave observatory. The capture control of test mass after release is a crucial technology that can affect the success of the mission. The test mass must be released to the center of the electrostatic suspension cage accurately. This paper presents a nonlinear dynamic model of drag-free satellites in Lagrange formalism. A capture control scheme for test mass release phase is proposed based on the state-dependent Riccati equation (SDRE) strategy. To deal with the actuator saturation problem, a nonlinear saturation model is introduced to the dynamics of satellite, while the SDRE strategy is applied to the non-affine system. The effectiveness of the proposed methodology is verified by the numerical simulation for the drag-free satellite.

New astrometric positions for six Jovian irregular satellites using Gaia DR3 in 2016 — 2021

The Jovian system is like a miniature solar system, with the system being more than twice as massive as all the other planets combined and having many natural satellites. Its formation and early evolution had a profound influence on our knowledge of the sculpting of the architecture of the solar system. Astrometric observations are of importance, based on these observations, its orbital dynamics, as well as its origin sometimes, of a solar system object can be determined. We aimed to obtain good astrometric positions of some irregular satellites Elara, Pasiphae, Sinope, Lysithea, Carme and Ananke to refine their orbits and ephemerides, and to understand their dynamics. We have taken, processed and reduced 964 ground-based CCD frames obtained between 2016 and 2021 by the 2.4 m telescope at the Lijiang Station of Yunnan Observatory over 27 nights. Among CCD image processing, the image subtraction technique of ISIS is employed to eliminate star images that are close to or/and almost overlapped with those of our targets in 2019. The star catalog Gaia DR3 is utilized for astrometric calibration, in which a weight scheme is applied to solve more accurate plate model. For all targets, their theoretical positions are retrieved from the Institut de Mécanique Céleste et de Calcul des Éphémérides (IMCCE) ephemeris. Our results show the mean (O - C)s (observed minus computed) of the positional residuals of all targets are −0′′.007 and 0′′.011 in R.A. and Dec., respectively. Their corresponding standard deviations are about 0′′.05 in each direction, except for Ananke (the faintest satellite) with its standard deviation about 0′′.08 in each direction.

Harnessing orbital Hall effect for efficient orbital torque in light metal vanadium

The orbital Hall effect depicts the conversion of charge current to orbital current in nonmagnetic materials without spin–orbit coupling. This absence of spin–orbit coupling enables the light metals serve as sources of orbital current exploited as the information carrier to be applied to the information technology. Here, we investigate current-induced torques in vanadium/ferromagnet (V/FM, FM = Fe, Co, Ni81Fe19) bilayers via spin-torque ferromagnetic resonance (ST-FMR) system. The sign reversal confirms that the orbital Hall effect exists in light metal V, and the orbital torque in V/Co and V/Ni81Fe19 bilayers is dominant. By performing the V thickness dependence of conversion efficiency, we determined the orbital diffusion length of 3.61 nm for V. Our experiment demonstrates that light metals can be used as novel materials in spin–orbit devices, and our research focuses on the orbital freedom of the electron and provides new content for the study of orbital dynamics.

Complex network-based multistep forecasting model for hyperchaotic time series.

We present a method for predicting hyperchaotic time series using a complex network-based forecasting model. We first construct a network from a given time series, which serves as a coarse-grained representation of the underlying attractor. This network facilitates multistep forecasting by capturing the local nonlinearity of the dynamics and offers superior accuracy over more extended periods than traditional methods. The network is formed by converting the patterns of local oscillations into sequences of numerical symbols, which are then used to create nodes and edges in a network, capturing the system's dynamical behavior at a reduced resolution. The network allows predictions up to several steps ahead without the exponential error increase usually associated with linear first-order methods. The improved predictions result from the unique ability of the network to collect identical pattern transitions in the orbit dynamics into a system of neighborhoods in the network. The effectiveness of this approach is demonstrated through its application to several high-dimensional hyperchaotic systems, where it outperforms both the linear first-order and other network-based methods in terms of prediction accuracy and horizon. Besides enhancing the predictability of chaotic systems, this methodology also outlines a procedure to develop a discrete model flow within an attractor.

Intention inference for space targets using deep convolutional neural network

Intention inference for space targets is crucial for space situational awareness. This paper introduces a rapid and precise method for recognizing the intentions of non-cooperative space targets using a deep convolutional neural network (CNN). By employing a relative orbital dynamics model, an analysis of relative motion was performed, resulting in the identification of 11 distinct motion intentions for space targets. This study also describes how to generate relative motion trajectory images to create a training set for intention inference, effectively converting the problem into one of image recognition and classification. Extensive simulations were carried out to fine-tune the network hyperparameters, and the results highlight the exceptional performance of the proposed CNN-based method, which achieved an accuracy of 99.682%. This method significantly enhances recognition accuracy over other neural network-based methods for space objects and offers considerable potential for applications like spacecraft collision avoidance and strategic maneuvers among space targets.

Tidal evolution and spin–orbit dynamics for bodies in the viscous regime

Tidal evolution and spin–orbit dynamics for bodies in the viscous regime

Impulsive maneuver strategy for multi-agent orbital pursuit-evasion game under sparse rewards

To address the subjectivity of dense reward designs for the orbital pursuit-evasion game with multiple optimization objectives, this paper proposes the reinforcement learning method with a hierarchical network structure to guide game strategies under sparse rewards. Initially, to overcome the convergence challenges in the reinforcement learning training process under sparse rewards, a hierarchical network structure is proposed based on the hindsight experience replay. Subsequently, considering the strict constraints imposed by orbital dynamics on spacecraft state space, the reachable domain method is introduced to refine the subgoal space in the hierarchical network, further facilitating the achievement of subgoals. Finally, by adopting the centralized training-layered execution approach, a complete multi-agent reinforcement learning method with the hierarchical network structure is established, enabling networks at each level to learn effectively in parallel within sparse reward environments. Numerical simulations indicate that, under the single-agent reinforcement learning framework, the proposed method exhibits superior stability in the late training stage and enhances exploration efficiency in the early stage by 38.89% to 55.56% to the baseline method. Under the multi-agent reinforcement learning framework, as the relative distance decreases, the subgoals generated by the hierarchical network transition from long-term to short-term, aligning with human behavioral logic.

Gain-controlled taming of recurrent modulation instability

We show how the recurrence phenomenon characteristic of the nonlinear stage of induced modulational instability in a passive fiber is affected by forcing. An additional linear amplification, even if extremely weak, induces separatrix crossing corresponding to critical values of the gain around which the recurrence process considerably slows down, switching between dynamical orbits of different kind. We present evidence for such phenomenon in a fiber optics experiment where the gain is finely tuned by means of Raman amplification. A theoretical explanation is also provided that matches almost perfectly with our experimental results. Published by the American Physical Society 2024

Decay time estimate for LEO spacecraft

The growing concerns posed by orbital debris represent a serious threat to the future of space operations in low Earth orbit. With the goal of limiting the formation of new debris, space agencies are proposing international guidelines that satellites should be able to deorbiting within 25 years of the end of their operational life. Orbital decay is typically caused by atmospheric drag, so estimating the decay time of a satellite subject to drag is critical to assessing whether the guidelines are met. However, such estimate is a very challenging task because of the difficulty of accurately modeling atmospheric properties and because of the coupling of orbital dynamics with spacecraft attitude. In this paper, a simplified algorithm based on the King-Hele formulation is proposed to rapidly estimate the decay time of an orbiting satellite without imposing any assumptions on the spacecraft’s nominal size, mass, geometry or attitude. The algorithm accounts for the effect of solar activity level variations on atmospheric properties and drag coefficient through an iterative procedure and can be applied to any object in orbit. Numerical tests show that the predictions in terms of decay times are very accurate for satellites that are quite different in size and geometry, including the presence of an aerodynamic drag augmentation system such as a drag sail.

Drag sail attitude tracking via nonlinear control

A drag sail is a propellantless device suitable for passive deorbiting of satellites after their end-of-life. It exploits atmospheric drag to gradually reduce the kinetic energy of the decommissioned satellite and cause it to lose altitude over time. It is well known that the braking effect of the atmosphere is greater the surface exposed to the flow of the atmospheric particles relative to the satellite. For this reason, a drag sail is essentially a large and lightweight membrane, which is deployed by the satellite when it is to begin orbital decay. For given environmental/initial conditions and inertial characteristics of the deployed system, the braking effect of a drag sail is more intense if its perpendicular axis is constantly aligned with the direction of the relative particle flow. For this purpose, a sliding mode control strategy is adopted. The reference to follow is obtained by propagating the spacecraft orbital dynamics along with its attitude dynamics. Various orbital perturbations and the disturbance torque due to atmospheric drag are implemented in the numerical code to verify the robustness of the proposed control law. It is also assumed that the spacecraft control torque vector is bounded in magnitude and always belongs to the plane of the braking device. The results show that the proposed strategy is effective in accurately tracking the reference attitude and that it is robust, being able to track a reference that varies unpredictably due to both orbital and attitude perturbations.

Dynamic low earth orbit multi satellite hopping beam resource allocation considering load and dynamic coverage balance (LDCB-MSHBRA)

A dynamic low earth orbit multi satellite hopping beam resource allocation method based on time slicing is proposed to address the issue of changing coverage and beam interference caused by satellite mobility in multi satellite and multi beam communication scenarios. The method involves six processes: (1) Establishing a low earth orbit satellite system with three identical configuration parameters and motion speed parameters; (2)Assign a value to the time slicing weight coefficient and use the principle of load balancing to minimize the difference in demand for dual star services as the optimization objective; (3) Obtain initial power resource allocation with maximum system capacity as the optimization objective; (4) Considering the mobility of low earth orbit satellites, updating weight coefficients and dynamically allocating power resources, a time resource dynamic allocation matrix and the optimal service cell set are obtained; (5) Update the independent coverage cell set of the third low earth orbit satellite, use the Lagrange equation of the weighted fair objective function to obtain the time resource allocation optimization matrix, and use one-way search to determine the optimal service cell set; (6) With the goal of maximizing system capacity, the optimal solution of the power resource allocation matrix for the third low earth orbit satellite is obtained. The system throughput is introduced to intuitively measure system performance, and adjustments are made based on the overlap of Samsung coverage. The resource allocation method is based on a fairness model, considering load balancing and dynamic coverage range changes. On the basis of improving the overall system throughput, it ensures the fairness of resource allocation and allocates time, frequency, and power resources to multiple satellites with overlapping coverage, which helps to improve the throughput and resource utilization of satellite systems.

Autonomous Lunar rendezvous trajectory planning and control using nonlinear MPC and Pontryagin’s principle

This paper explores the application of Nonlinear Model Predictive Control (NMPC) techniques, based on the Pontryagin Minimum Principle, for a minimum-propellant autonomous rendezvous maneuver in non-Keplerian Lunar orbits. The relative motion between the chaser and the target is described by the nonlinear dynamics of the circular restricted three body-problem, posing unique challenges due to the complex and unstable dynamics of near-rectilinear halo orbits. Key aspects of the proposed NMPC include trajectory optimization, maneuver planning, and real-time control, leveraging on its ability to satisfy complex mission requirements while ensuring safe and efficient spacecraft operations and in the presence of input and nonlinear/non-convex state constraints. The proposed formulation allows the design of a minimum-propellant controller, whose optimal control signal results to be bang–bang in time. A case study based on the Artemis III mission – where the docking of the Orion spacecraft to the Gateway station is planned – is illustrated in order to demonstrate the efficiency of the proposed approach, showcasing its potential for enhancing target tracking accuracy, while reducing propellant consumption.

Revisiting WASP-19b’s Orbital Evolution: New TESS Data and Apsidal Precession Analysis

Due to the ongoing debate of whether WASP19b is experiencing orbital decay or apsidal precession, I reexamine the orbital evolution of the hot Jupiter WASP-19b using new TESS data from sectors 09, 36, 62, and 63. My comprehensive analysis of transit and occultation timing variations compares models of constant period, orbital decay, and apsidal precession. Results show no significant preference between orbital decay and apsidal precession models. I find a period change rate of −1.40 ± 0.54 ms yr−1, slower than some previous studies but consistent with others. My apsidal precession analysis yields an eccentricity of 0.00178 and a precession rate of 0.036 deg day−1, differing from recent literature. These findings underscore the complexity of WASP-19b’s orbital dynamics and the need for continued long-term monitoring.