Orbital Dynamics Research Articles

Saturn's F ring is intermittently shepherded by Prometheus.

One of the stranger planetary rings is Saturn's narrow, clumpy F ring, lying just outside the main rings, in a region disturbed by chaotic orbital dynamics. We show that the F ring has a stable "true core" that dominates its mass and is confined into discontinuous short arcs of particles larger than a few millimeters in radius. The more obvious micron-size particles seen in images, outlining and obscuring the true core, contribute only a small fraction of its mass. We found that these arcs of large particles orbit Saturn in a specific corotational resonance with the nearby 100-kilometer diameter ringmoon Prometheus, which stabilizes the F ring material and allows it to persist within the disturbed region for decades or longer. Toward the end of the observing period, a small chaotic glitch in the orbit of Prometheus temporarily disrupted the confinement, but the arcs seem to be able to adapt.

RBFNN-based angles-only orbit determination method for non-cooperative space targets

Angles-only orbit determination during space situational awareness missions for non-cooperative targets such as space debris is subject to the well-known observability problem, that is, the orbital state is weakly observable or even unobservable because of missing range measurements. The key point to solve this problem is how to quickly capture the nonlinearity of orbit dynamics if only one space-based passive sensor is available to observe the target and translational maneuvers are not executed. To solve the short-arc angles-only problem, this study develops a simple and fast orbit determination method by exploiting the advantages of radial basis function neural network (RBFNN). Emphasis was placed on the design of the RBFNN, which was trained to construct a mapping network model from line-of-sight (LOS) measurements to the relative orbit. First, the perturbed relative orbit dynamics considering the Earth's non-spherical J2 term and air drag was established with the LOS measurement model. Second, a RBFNN-based angles-only orbit determination frame was developed, in which the generator of the training dataset, data preprocessing algorithm, and RBF network structure were designed. Finally, the proposed method was verified and tested using a set of numerical simulations of low-Earth orbit cases. The anti-noise and generalization performance of the designed network and the sensitivity of the solution accuracy to the measurement frequency and span were presented and discussed. Additionally, the advantages of the RBFNN-based method were confirmed by comparison with the results obtained using the BPNN (Back Propagation Neural Network)-based method. The simulation results show that the average orbit prediction error for LEO scenarios is approximately 0.08% using the index of initial relative distance, where only three sets of LOS angles are measured within a span of 24 s.

Anderson localization and quenched induced dynamics of spin orbit coupled Bose–Einstein condensate in a random potential

We consider the localization and dynamical properties of a one dimensional spin orbit coupled Bose–Einstein condensate trapped by a disordered speckle potential. We numerically solve coupled Gross–Pitaevskii equation to obtain ground sate solutions. The effects of spin–orbit coupling and detuning parameter on localization are investigated. It is found that the increase of spin–orbit coupling delocalizes the condensate while the increase of detuning favors localization. After achieving the numerical ground state solutions, we examine the quench induced dynamics of the condensate by the complete cessation of the spin–orbit coupling. We show that at parameters where the ground state is not localized, the dynamics of the system is chaotic.

Loss of FAM210A in Satellite Cell Drives Mitochondrial Dysfunction and Muscle Weakness in Experimental Peripheral Artery Disease

Introduction: Peripheral artery disease (PAD) affects approximately 200 million people globally. Chronic limb-threatening ischemia (CLTI) represents the most advanced clinical phenotype of PAD. Mitochondrial metabolism defects are apparent in the satellite cells of CLTI patients, and the muscle regeneration process demands increased energy, with satellite cell mitochondrial metabolism and dynamics playing a crucial role. However, our current understanding of the role of satellite cells and muscle regeneration in PAD pathology is notably inadequate. Recent studies have shown that the absence of FAM210A, a newly identified mitochondrial protein, can trigger morphological and energetic abnormalities in mitochondria, resulting in muscle function deterioration and promoting muscle wasting. Given the impaired mitochondrial function in satellite cells in CLTI patients and the heightened energy demand regulated by mitochondrial dynamics during muscle regeneration in satellite cell, it is therefore essential to exploring the role of FAM210A in satellite cells in CLTI limb pathology. The objective of this study was to investigate the impact of the loss of FAM210A in satellite cells in mice with experimental PAD. Methods: Male and female conditional FAM210A satellite cell knock out (FAM210ASCKO) and FAM210A floxed (FAM210Afl/fl) mice (N=3-5) were used for this project. Femoral artery ligation surgery was performed to induce PAD. Tamoxifen was administered for 5 days intraperitoneally one week prior to the surgery. Mice were euthanized twenty-eight days after surgery. Outcome measures included limb perfusion assessment, muscle weight, muscle force production, and mitochondrial respiration. Results: FAM210ASCKO mice had significantly decreased muscle mass of the tibialis anterior and extensor digitorum longus ( p<0.0001 and p=0.0004 respectively). More importantly, maximal muscle force with in-situ contraction in tibialis anterior was significantly lower in FAM210ASCKO mice compared to FAM210Afl/fl mice (FAM210Afl/fl mice: 1085.16 ± 331.08 mN; FAM210ASCKO mice: 430.77 ± 467.91 mN; p=0.0139). Furthermore, analysis of mitochondrial oxidative phosphorylation (OXPHOS) revealed that FAM210ASCKO mice had a significant reduction compared to FAM210Afl/fl mice (48%) in skeletal muscle mitochondrial bioenergetic function at various levels of energy demand mimicking from resting to maximal exercise when carbohydrate was used to energize mitochondria ( p=0.034). Importantly, the analysis of mitochondrial membrane potential consistently reveals a substantial reduction in FAM210ASCKO mice compared to FAM210Afl/fl mice, which can partially explain the diminished mitochondrial bioenergetic function observed in ischemic FAM210ASCKO mice. Conclusion: The results of this study indicate that the loss of FAM210A in satellite cells exacerbates ischemic muscle pathology evidenced by muscle weakness and mitochondrial failure in FAM210ASCKO mice with PAD. Future work is needed to elucidate the mechanisms by which FAM210A regulate ischemic satellite cell function and the therapeutic potential of preventing ischemia-induced loss of FAM210A in PAD. This study was supported by National Institutes of Health (NIH) grant R01-HL149704 (to Dr Ryan). Mr Thome was supported by NIH grant F31-DK128920. This is the full abstract presented at the American Physiology Summit 2024 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

High Specific-Impulse Electrospray Explorer Trajectory Guidance and Control Air Bearing Demonstration

As small satellite-mission concepts that require travel farther from their traditional domain of low-Earth orbit are being considered, there is a growing need to develop small-scale propulsion systems that can provide the necessary net impulse to enable deep-space operation. The High Specific-Impulse Electrospray Explorer for Deep-Space (HiSPEED) project is an example concept considered for this paper, as it would be a small satellite that uses electrospray thrusters to navigate along a low-thrust spiral trajectory from Earth to a near-Earth asteroid. The NASA Jet Propulsion Laboratory Small Satellite Dynamics Testbed operates simulation and air- bearing testing environments. This paper focuses on its planar air-bearing platform used to create a nearly frictionless environment in three degrees of freedom: two translational and one rotational. The platform maneuvers using eight compressed air thrusters controlled by an onboard single-board computer using position feedback from a motion-capture system. This paper discusses the design, development, and testing of a closed-loop controller for this platform that enables trajectory following with position error less than 4 cm. The paper presents data from tests representative of HiSPEED spiral escape trajectories and operations in proximity to an asteroid, along with implications for HiSPEED and similar concepts.

Multiple-arc optimization of low-thrust Earth–Moon orbit transfers leveraging implicit costate transformation

This work focuses on minimum-time low-thrust orbit transfers from a prescribed low Earth orbit to a specified low lunar orbit. The well-established indirect formulation of minimum-time orbit transfers is extended to a multibody dynamical framework, with initial and final orbits around two distinct primaries. To do this, different representations, useful for describing orbit dynamics, are introduced, i.e., modified equinoctial elements (MEE) and Cartesian coordinates (CC). Use of two sets of MEE, relative to either Earth or Moon, allows simple writing of the boundary conditions about the two celestial bodies, but requires the formulation of a multiple-arc trajectory optimization problem, including two legs: (a) geocentric leg and (b) selenocentric leg. In the numerical solution process, the transition between the two MEE representations uses CC, which play the role of convenient intermediate, matching variables. The multiple-arc formulation at hand leads to identifying a set of intermediate necessary conditions for optimality, at the transition between the two legs. This research proves that a closed-form solution to these intermediate conditions exists, leveraging implicit costate transformation. As a result, the parameter set for an indirect algorithm retains the reduced size of the typical set associated with a single-arc optimization problem. The indirect heuristic technique, based on the joint use of the necessary conditions and a heuristic algorithm (i.e., differential evolution in this study) is proposed as the numerical solution method, together with the definition of a layered fitness function, aimed at facilitating convergence. The minimum-time trajectory of interest is sought in a high-fidelity dynamical framework, with the use of planetary ephemeris and the inclusion of the simultaneous gravitational action of Sun, Earth, and Moon, along the entire transfer path. The numerical results unequivocally prove that the approach developed in this research is effective for determining minimum-time low-thrust Earth–Moon orbit transfers.

Density-based in-orbit collision risk model valid for any impact geometry

Neglecting small fragments in space debris evolutionary models can lead to a significant underestimation of the collision risk for operational satellites. However, when scaling down to the millimetre range, the debris population grows to over a hundred million objects, making deterministic approaches too computationally expensive. On the contrary, probabilistic models provide a more efficient alternative, which however typically works under some simplifying assumptions on the dynamics, limiting their field of applicability. This work proposes an extension of the density-based collision risk models to any orbital dynamics and impact geometry. The impact rate with a target satellite is derived from a multi-dimensional phase space density function in orbital elements, which discretely varies over both phase space and time. The assumption of a bin-wise constant cloud density allows for the analytical transformation of the six-dimensional distribution in orbital elements into the three-dimensional spatial density function, guaranteeing an efficient and accurate evaluation of the fragments flux. The proposed method is applied to the assessment of the collision risk posed by occurred fragmentation events in different orbital regions on a high-risk target object. The effect on the impact rate of the modelling improvements, compared to previous probabilistic formulations, is discussed.

Orbital dynamics of smart dust with Poynting–Robertson and solar wind drag

Smart dust devices are tiny systems-on-a-chip platforms capable of sensing, storing and transmitting data wirelessly as part of a large network with distributed capabilities. Previous works investigated the long-term orbital evolution of smart dust in space by studying the combined effect of gravitational perturbations, solar radiation pressure (SRP) and atmospheric drag. In the current work, the problem of finding long-term orbital equilibria conditions for smart dust is recast and extended to include Poynting–Robertson and Solar Wind (PRSW) drag. By including the PRSW effects and defining new equilibrium conditions on the orbital orientation, some additional partial equilibrium solutions are found. Moreover, it is shown that even though PRSW is not dominant compared to SRP or J2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J_2$$\\end{document}, it still influences the evolution of the relative Sun-orbit orientation. For orbits with higher initial perigee altitudes, where drag and J2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J_2$$\\end{document} effects subside, it is shown that PRSW influences long-term orbital behavior, and should be considered in the orbit design scheme of smart dust devices.

Spacecraft Formation Keeping and Reconfiguration Using Optimal Visual Servoing

This paper proposes a direct visual servoing system for spacecraft guidance in formation flying scenarios. The proposed image-based visual servoing system uses image information for planning and executing formation acquisition, reconfiguration, and maintenance maneuvers. The system assumes that LEDs are located at specific points on the satellites, enabling the visual servoing controller to rely on continuous tracking of these features in the camera’s image plane. Analytical developments demonstrate that the proposed optimal visual control system is stable and optimal, and it acts on both the orbital and attitude dynamics of the spacecraft, considering circular and elliptical reference orbits. The distributed image-based controller defines a cost function that minimizes control efforts, and the paper proses an optimal framework for developing controllers that address the issue. A ROS-based simulation tool was used to test the proposed visual servoing controller in a realistic small-sat formation flying scenario. Results indicate that the proposed distributed control strategy is viable and robust against environmental perturbations and disturbances in sensing and actuation.

Stable Orbiting Around Small Moons Using J2-Perturbed Elliptic Restricted Problem

Confirmed small-body missions Martian Moons eXploration (MMX) and Hera are set to explore Martian moons and the binary asteroid Didymos’s moon Dimorphos, respectively. Orbital dynamics around these small moons differ substantially from those around previously visited targets. Simplified models, such as the circular-restricted three-body problem, cannot yield accurate predictions for orbits and their stability in real-world operations. To be specific, the orbit of the small moon and its vicinity are significantly perturbed by the oblateness of the planet and their relative positions. Realistic control constraints and the unstable 3:1 resonance of retrograde orbits further complicate orbit maintenance around a small moon. Therefore, minimizing the dynamical perturbation on baseline orbits resulting from model mismatches is crucial. This paper introduces the J2-ER3BP+GH model dedicated to describing the orbital dynamics around the small moon. It incorporates the J2 perturbation of the planet on the elliptic-restricted three-body problem and can accommodate a nonspherical gravity field of the moon. Bounded orbits can still be identified without much effort in this sophisticated model. Baseline orbits around Phobos and Dimorphos from the J2-ER3BP+GH model become much easier to maintain, as verified in the high-fidelity dynamic and control environments.

Dynamics of small precession orbit of a massive-charged particle in five-dimensional Reissner-Nordström spacetime model

Abstract This report discusses the dynamics of the small precession orbit of a massive-charged particle by using the Reissner-Nordström metric with an additional spatial dimension. The event horizon of a massive-charged object in the 5–dimension was smaller than that in the 4–dimension. The difference in the size of the massive-charged object event horizon has implications for the spacetime region that can trap massive-charged particles in bound orbits. The spacetime region in the 5–dimension was narrower than that in the 4–dimension. Based on a specific condition, we found that the small precession orbital formalism of massive-charged particles in the 5–dimension implies smaller orbital precession fluctuations than those in the 4–dimension. We applied a dynamical system approach to analyze the dynamics of related small precession motions.

Quantifying the orbital-to-spin moment ratio under dynamic excitation

The orbital component of magnetization dynamics, e.g., excited by ferromagnetic resonance (FMR), may generate “orbitronic” effects in nanomagnetic devices. Yet, distinguishing orbital dynamics from spin dynamics remains a challenge. Here, we employ x-ray magnetic circular dichroism (XMCD) to quantify the ratio between the orbital and spin components of FMR-induced dynamics in a Ni80Fe20 film. By applying the XMCD sum rules at the Ni L3,2 edges, we obtain an orbital-to-spin ratio of 0.108 ± 0.005 for the dynamic magnetization. This value is consistent with 0.102 ± 0.008 for the static magnetization, probed with the same x-ray beam configuration as the dynamic XMCD experiment. The demonstrated method presents a possible path to disentangle orbitronic effects from their spintronic counterparts in magnetic media.

Numerical Study on the Effects of Re on the Unsteady Behaviors in a Transonic Axial-Fan Under Inlet Distortion

Abstract The dynamic response of a compression system is the complex dynamic behaviors reacted by the compressor subject to non-uniform inflow excitation. However, in a real operating condition, the compressor would work at a wide range of altitudes within the flight envelope, which forces us to consider how Re additionally affects the compressor performance loss and dynamic response characteristic due to inlet distortion. To explore this issue, a full-annulus unsteady 3D simulation has been used to calculate the performance of a transonic axial fan with a 180-deg distortion at different Re. The results show that Re has additional detrimental effects on the fan aerodynamic performance with non-uniform inflow. To further explore the mechanisms of Re effects on fan–distortion interaction, the spatial and temporal distribution of the rotor blade response is discussed. The temporal distribution of the fan–distortion interaction is not changed with Re by analyzing the dynamic response orbit of the fan rotor. However, the spatial distribution of Re effects is highly related to the blade profile loaded mode at different spanwise locations. The results indicate that the time constant of fan dynamic response decreases by 17% at the mid-loaded region in the middle of the blade and increases by 40% at the aft-loaded region near the blade tip. Further analysis reveals that due to the low Re and flow separation of the suction surface, the thickness variation of blade boundary layer is the main cause for varying the blade time constant.

Orbital dynamics of a binary system composed of a massive star and a black hole companion

In this work, we consider a binary system composed of a massive star and a black hole companion. By monitoring the mass transfer from the star to the black hole, we perform a thorough and systematic orbit classification for determining the final states of a test particle moving inside the gravitational field of the binary system. For this purpose, we deploy the theory of the time-independent restricted three-body problem for modeling the motion of the test particle. Our analysis strongly suggests that escaping, collisional and bounded motion dominate in different phases of the mass transport, while the overall orbital dynamics of the test particle become very intricate for larger differences between the masses of the two primaries. Moreover, the bounded motion is further classified into regular, sticky, and chaotic by using the SALI chaos indicator.

Minimal Quantization Model in Pilot-Wave Hydrodynamics.

Investigating how classical systems may manifest dynamics analogous to those of quantum systems is a broad subject of fundamental interest. Walking droplets, which self-propel through a resonant interaction with their own wave field, provide a unique macroscopic realization of wave-particle duality that exhibits behaviors previously thought exclusive to quantum particles. Despite significant efforts, elucidating the precise origin and form of the wave-mediated forces responsible for the walker's quantumlike behavior remained elusive. Here, we demonstrate that, owing to wave interference, the force responsible for orbital quantization originates from waves excited near stationary points on the walker's past trajectory. Moreover, we derive a minimal model with the essential ingredients to capture quantized orbital dynamics, including quasiperiodic and chaotic orbits. Notably, this minimal model provides an explicit distinction between local forces, which account for the walker's preferred speed and wave-induced added mass, and spatiotemporal nonlocal forces responsible for quantization. The quantization mechanism revealed here is generic, and will thus play a role in other hydrodynamic quantum analogs.

Transient grating spectroscopy on a DyCo5 thin film with femtosecond extreme ultraviolet pulses.

Surface acoustic waves (SAWs) are excited by femtosecond extreme ultraviolet (EUV) transient gratings (TGs) in a room-temperature ferrimagnetic DyCo5 alloy. TGs are generated by crossing a pair of EUV pulses from a free electron laser with the wavelength of 20.8 nm matching the Co M-edge, resulting in a SAW wavelength of Λ = 44 nm. Using the pump-probe transient grating scheme in reflection geometry, the excited SAWs could be followed in the time range of -10 to 100 ps in the thin film. Coherent generation of TGs by ultrafast EUV pulses allows to excite SAW in any material and to investigate their couplings to other dynamics, such as spin waves and orbital dynamics. In contrast, we encountered challenges in detecting electronic and magnetic signals, potentially due to the dominance of the larger SAW signal and the weakened reflection signal from underlying layers. A potential solution for the latter challenge involves employing soft x-ray probes, albeit introducing additional complexities associated with the required grazing incidence geometry.

Beyond Point Masses. III. Detecting Haumea’s Nonspherical Gravitational Field

The dwarf planet Haumea is one of the most compelling trans-Neptunian objects to study, hosting two small, dynamically interacting satellites, a family of nearby spectrally unique objects, and a ring system. Haumea itself is extremely oblate due to its 3.9 hr rotation period. Understanding the orbits of Haumea’s satellites, named Hi’iaka and Namaka, requires detailed modeling of both satellite–satellite gravitational interactions and satellite interactions with Haumea’s nonspherical gravitational field (parameterized here as J 2). Understanding both of these effects allows for a detailed probe of the satellites’ masses and Haumea’s J 2 and spin pole. Measuring Haumea’s J 2 provides information about Haumea’s interior, possibly determining the extent of past differentation. In an effort to understand the Haumea system, we have performed detailed non-Keplerian orbit fitting of Haumea’s satellites using a decade of new, ultra-precise observations. Our fits detect Haumea’s J 2 and spin pole at ≳2.5σ confidence. Degeneracies present in the dynamics prevent us from precisely measuring Haumea’s J 2 with the current data, but future observations should enable a precise measurement. Our dynamically determined spin pole shows excellent agreement with past results, illustrating the strength of non-Keplerian orbit fitting. We also explore the spin–orbit dynamics of Haumea and its satellites, showing that axial precession of Hi’iaka may be detectable over decadal timescales. Finally, we present an ephemeris of the Haumea system over the coming decade, enabling high-quality observations of Haumea and its satellites for years to come.

The “Drake Equation” of Exomoons—A Cascade of Formation, Stability and Detection

After 25 years of the prediction of the possibility of observations, and despite the many hundreds of well-studied transiting exoplanet systems, we are still waiting for the announcement of the first confirmed exomoon. We follow the “cascade” structure of the Drake equation but apply it to the chain of events leading to a successful detection of an exomoon. The scope of this paper is to reveal the structure of the problem, rather than to give a quantitative solution. We identify three important steps that can lead us to discovery. The steps are the formation, the orbital dynamics and long-term stability, and the observability of a given exomoon in a given system. This way, the question will be closely related to questions of star formation, planet formation, five possible pathways of moon formation; long-term dynamics of evolved planet systems involving stellar and planetary rotation and internal structure; and the proper evaluation of the observed data, taking the correlated noise of stellar and instrumental origin and the sampling function also into account. We highlight how a successful exomoon observation and the interpretations of the expected further measurements prove to be among the most complex and interdisciplinary questions in astrophysics.

Ultrafast Chiral Precession of Spin and Orbital Angular Momentum Induced by Circularly Polarized Laser Pulse in Elementary Ferromagnets.

Despite spin (SAM) and orbital (OAM) angular momentum dynamics being well-studied in demagnetization processes, their components receive less focus. Here, we utilize real-time time-dependent density functional theory (rt-TDDFT) to unveil significant x and y components of SAM and OAM induced by circularly left (σ+) and right (σ-) polarized laser pulses in ferromagnetic Fe, Co, and Ni. Our results show that the magnitude of the OAM is an order of magnitude larger than that of the SAM, highlighting a stronger optical response from the orbital degrees of freedom of electrons. Intriguingly, σ+ and σ- pulses induce chirality in the precession of SAM and OAM, respectively, with clear associations with laser frequency and duration. Finally, we demonstrate the time scale of the OAM and SAM precession occurs even earlier than that of the demagnetization process and the OISTR effect. Our results provide detailed insight into the dynamics of SAM and OAM during and shortly after a polarized laser pulse.

Chaotic tides as a solution to the Hyperion problem

The dynamics of the outer regular satellites of Saturn are driven primarily by the outward migration of Titan, but several independent constraints on Titan’s migration are difficult to reconcile with the current resonant orbit of the small satellite Hyperion. We argue that Hyperion’s rapid irregular tumbling greatly increases tidal dissipation with a steep dependence on orbital eccentricity. Resonant excitation from a migrating Titan is then balanced by damping in a feedback mechanism that maintains Hyperion’s eccentricity without fine-tuning. The inferred tidal parameters of Hyperion are most consistent with rapid Titan migration enabled by a resonance lock with an internal mode of Saturn, but a scenario with only equilibrium dissipation in Saturn is also possible.