Temporary Capture Research Articles

Investigating temporary capture in the Sun-Jupiter three-body system via Lagrangian coherent structures

Abstract The temporary capture (TC) of Jupiter-family objects has long been a pivotal focus in celestial mechanics research. This study investigates the temporary capture of objects near Jupiter within the context of the planar circular restricted three-body problem (PCRTBP), employing Lagrangian coherent structures (LCSs) and periapsis Poincaré maps. Initially, LCSs are identified via periapsis Poincaré maps and applied to segment the phase space. Parameter scanning enables a detailed analysis, classifying the orbital behaviors of objects in the proximity of Jupiter into three distinct categories: temporary capture, low-energy flyby, and collision, each designating specific regions in phase space. Subsequently, a novel method for screening potential TC objects within the Jupiter system is proposed and validated, informed by the dynamic characteristics of TC motions. The efficacy of this method is illustrated by the reidentification of six known TC comets and the prediction of a prospective TC asteroid, 2002 GV28. Within the framework of the PCRTBP, analogous TC trajectories for these comets and asteroids are identified, offering novel insights into the dynamics of temporary capture events.

Capture Efficiency Analysis in the Circular Restricted Three-body Problem

Temporary capture efficiency is studied in the framework of the circular restricted three-body problem in two steps. First, a non-uniform distribution of test particles around the secondary’s orbit is obtained by fully accounting the secondary’s gravitational influence. Second, the capture efficiency is computed based on the non-uniform distribution. Several factors influencing the result are discussed. By studying the capture efficiency in the circular restricted three-body problem of different mass ratios, a power-law relation between the capture efficiency (p) and the mass ratio (μ) is established, which is given by p ≈ 0.27 × μ 0.53, within the range of 3.0035 ×10−6 ≤ μ ≤ 3.0034 × 10−5. Taking the Sun–Earth system as an example, the influence from the orbit eccentricity of the secondary on the non-uniform distribution and the capture efficiency is studied. Our studies find that the secondary’s orbit eccentricity has a negative influence on the capture efficiency.

Temporary capture of a small body into a geocentric orbit

Temporary capture of a small body into a geocentric orbit

Designing Low-Energy Low-Thrust Flight to the Moon on a Temporary Capture Trajectory

Designing Low-Energy Low-Thrust Flight to the Moon on a Temporary Capture Trajectory

Designing Low-Energy Low-Thrust Flight to the Moon on a Temporary Capture Trajectory

The study considers the problem of calculating the low-energy trajectories of a low-thrust spacecraft to the Moon during the ballistic capture. The transfer is carried out using a transit trajectory in the vicinity of one of the collinear libration points L1 or L2 of the Earth-Moon system. Using a transit trajectory allows us to reduce fuel consumptions for the transfer by applying spacecraft dynamic in the Earth-Moon system. After exit from the orbit of ballistic capture, depending on the goal of mission the required lunar orbit can be formed, or the maneuver can be completed for inserting into the required interplanetary trajectory. A method for solving the problem is proposed, which consists in selecting the suitable transit trajectory to ensure sufficiently long duration of staying a spacecraft in the sphere of influence of the Moon, and in calculating the optimal low-thrust trajectories from initial lunar orbit to the transit trajectory to the Moon. To solve the problem of optimal control and calculate the optimal exit point to the transit trajectory, the Pontryagin’s maximum principle is used in combination with the continuation method by parameter. Numerical examples are given for calculating low-energy trajectories to the Moon during the ballistic capture with the optimization of exit point to the transit trajectory.

Low-Thrust Lunar Capture Leveraging Nonlinear Orbit Control

Nonlinear orbit control with the use of low-thrust propulsion is proposed as an effective strategy for autonomous guidance of a space vehicle directed toward the Moon. Orbital motion is described in an ephemeris model, with the inclusion of the most relevant perturbations. Unfavorable initial conditions, associated with weak, temporary lunar capture, are considered, as representative conditions that may be encountered in real mission scenarios. These may occur when the spacecraft is released in nonnominal flight conditions, which would naturally lead it to impact the Moon or escape the lunar gravitational attraction. To avoid this, low-thrust propulsion, in conjunction with nonlinear orbit control, is employed, to drive the space vehicle toward two different, prescribed, low-altitude lunar orbits. Nonlinear orbit control leads to identifying a saturated feedback law (for the low-thrust magnitude and direction) that is proven to enjoy global stability properties. The guidance strategy at hand is successfully tested on three different mission scenarios. Then, the capture region is identified, and includes a large set of initial conditions for which nonlinear orbit control with low-thrust propulsion is effective to achieve lunar capture and final orbit acquisition. For the purpose of achieving lunar capture, low-thrust propulsion is shown to be more effective if ignited at aposelenium.

Energy analysis of the single impulsive Earth–Moon transfer with the temporary lunar capture

The single impulsive planar Earth–Moon transfer strategy is investigated by analyzing the energy change of the lunar capture. A planar bicircular model of the restricted four-body problem is applied to define the single impulsive trajectory to the Moon from the Earth. Then analytical expressions are derived to describe the energy changes of the lunar capture in the Sun–Earth rotating frame. Accordingly, the eccentricity at the perilune of the single impulsive transfer trajectory can be calculated analytically to explore the lunar escape and capture conditions. The error analysis shows that the theoretical solutions serve as good approximations of the energy changes of the single impulsive transfer. Furthermore, it has been found that the perilune angle and the perilune radius are the critical factors for lunar capture. Finally, the theoretical results are successfully employed to find a series of single impulsive planar Earth–Moon transfers.

Necessary condition for temporary asteroid capture

Abstract Asteroid capture holds great significance in understanding the origins of asteroids, the source of life, and the exploration of planetary mineral resources. To ensure the success of a mission aimed at capturing asteroids, it is crucial to choose asteroids that can be naturally captured by Earth. This article focuses on the orbital characteristics of temporarily captured asteroids. Through a statistical simulation of asteroid motion and an analytical derivation of the Jacobian integral, the necessary conditions for the temporary capture of asteroids by Earth are calculated. The analysis results show an approximately linear relationship between the orbit elements of temporarily captured asteroids. This condition is used to screen the currently observed near-Earth asteroids and has identified asteroids such as 2006 RH120 and 2020 CD3, which have been temporarily captured by Earth. These findings provide important suggestions for future asteroid capture missions and target selection.

Effect of the inclination in the passage through the 5/3 mean motion resonance between Ariel and Umbriel

The orbits of the main satellites of Uranus are expected to slowly drift away owing to tides raised in the planet. As a result, the 5/3 mean motion resonance between Ariel and Umbriel was likely encountered in the past. Previous studies have shown that, in order to prevent entrapment in this resonance, the eccentricities of the satellites must be larger than ~0.01 at the epoch, which is hard to explain. On the other hand, if the satellites experience some temporary capture and then escape, the inclinations rise to high values that are not observed today. We have revisited this problem both analytically and numerically focussing on the inclination, using a secular two-satellite model with circular orbits. We show that if the inclination of Umbriel was around 0.15° at the time of the 5/3 resonance encounter, capture can be avoided in about 60% of the cases. Moreover, after the resonance crossing, the inclination of Umbriel drops to a mean value around 0.08°, which is close to the presently observed one. The final inclination of Ariel is distributed between 0.01° and 0.25° with a nearly equal probability, which includes the present mean value of 0.02°.

Trojan asteroids and the co-orbital dust ring of Venus

Context. Co-orbital asteroids have been thought to be the possible source of the zodiacal dust ring around the orbit of Venus, but the conclusions about the orbital stability and thus about the existence of Venus Trojans are inconsistent in the literature. Aims. We present a systematic survey of the orbital stability of Venus Trojans that takes the dynamical influences from General Relativity and the Yarkovsky effect into account. Methods. The orbits of thousands of fictitious Venus Trojans were simulated numerically. Using a frequency analysis, we describe their orbital stabilities and the dynamical mechanisms behind them. The influences of General Relativity and of the Yarkovsky effect, which were previously either neglected or oversimplified, were investigated in long-term numerical simulations. Results. The stability maps on the (a0, i0) plane and (a0, e0) plane are depicted, and the most stable Venus Trojans are found to occupy low-inclination horseshoe orbits with low eccentricities. The resonances that carve the fine structures in the stability map are determined. General Relativity decreases the stability of orbits only little, but the Yarkovsky effect may drive nearly all Venus Trojans out of the Trojan region in a relatively short time. Conclusions. The Venus Trojans have a poor orbital stability and cannot survive to the age of the Solar System. The zodiacal dust ring found around the orbit of Venus is more likely a sporadic phenomenon, as the result of a temporary capture into the 1:1 mean motion resonance of dust particles that were probably produced by passing comets or asteroids, but not by Venus Trojans.

How to Become a Mini-moon: Some Hints from 2022 NX1

Low-velocity encounters between our planet and any near-Earth object (NEO) in an Earth-like orbit may induce its temporary capture as a mini-moon. Such mini-moon episodes could lead the NEO to complete one or more revolutions around Earth when gravitationally bound, a temporarily-captured orbiter, like in the cases of 2006 RH120 and 2020 CD3; sometimes not even one revolution is completed, a temporarily-captured flyby, like in the case of 1991 VG. Asteroid 2022 NX1 experienced a temporarily-captured flyby in 1981, has had another one in 2022, and will become a temporarily-captured orbiter in 2051. This object occupies the edge of Earth’s co-orbital space and sometimes it approaches us following a horseshoe path.

Are there long‐living Hilda‐like asteroids between Jupiter and Saturn?

AbstractTo clarify the question of asteroids between Jupiter and Saturn a numerical study of the stability of orbits of fictitious bodies in this region has been undertaken. There are almost no minor planets moving there with the exception of 61 faint asteroids. After determining the mean motion resonances and the three‐body resonances, we have studied orbits for inclinations from 1 to 91 degrees to find out stable regions from 6.8 to 8.0 au. This was done up to 100 Myrs in the dynamical model Sun–Jupiter–Saturn and massless fictitious asteroids. In a study with a finer grid in inclination from 1 to 31 degrees and semi‐major axes from 6.88 to 7.30 au, we integrated ten thousand orbits up to the moment of their escape. These results showed a region in semi‐major axes with stable orbits in the interval from 7.12 to 7.23 au for moderate inclinations. Nevertheless, being a temporary capture there could be these objects much larger than the tiny ones discovered up to now in the region between Jupiter and Saturn.

Transient Retention of Floating Particles Captured by Emergent Vegetation Through Capillarity

AbstractThis work presents and discusses a series of experiments focusing on the transport of floating particles, mimicking seeds and propagules, within an array of randomly arranged cylinders mimicking emergent vegetation stems. The focus is on the temporary capture process by which particles colliding with a cylinder are trapped by surface tension for finite but relatively long retention times, thus promoting a large mechanical dispersion. Video analysis of the particle paths within the array shows that the probability of particles being captured, either temporarily or permanently, as well as the mean retention time, vary with flow velocity while being weakly affected by stem density. On the contrary, stem density plays a significant role in determining the frequency of the temporary captures; in particular, the probability of having temporary, rather than permanent, captures increases with vegetation density. We also propose some relationships to predict the probability of having temporary capture events and their mean duration based on experimental results.

A dedicated Lunar Trojan Asteroid Survey with small ground-based telescopes

ABSTRACT A co-orbital asteroid shares the orbit of a secondary body about its primary. Though more commonly encountered as an asteroid that shares a planet’s orbit around the Sun, a co-orbital asteroid could similarly share the orbit of the Moon around the Earth. Though such asteroids would be close to the Earth and so relatively bright, their rapid on-sky motion is such that they might escape detection by near-Earth asteroid surveys. The discovery of such lunar co-orbital asteroids (which we will refer to generically here as Lunar Trojans or LTs) would advance our understanding of inner Solar System orbital dynamics and would provide research opportunities for the growing number of missions slated for cislunar space. No LT asteroids are currently known and the last published survey dedicated to these asteroids was conducted nearly 40 yr ago. It has been theoretically determined that orbits near the Earth–Moon L4 and L5 points could survive for several million years. Although this time-scale is shorter than the lifetime of the Solar System, it introduces the possibility of the temporary capture of asteroids into the LT state. This project aims to observationally evaluate the population of LTs with modern techniques. Using four small ground-based telescopes from the iTelescope network, 8340 deg2 on the sky were surveyed down to 15th mag. Though one fast-moving near-Earth object was detected, no LTs were observed. We deduce an upper limit of ≲5 LTs with H < 26.

Free-free Gaunt factors of hydrogen-like ions in dense quantum plasmas

The free-free Gaunt factors as functions of the initial electron energy εi of hydrogen-like ions are investigated, for a typical photon absorption energy of ω= 10 Ry in strongly coupled quantum plasmas, where the screened Coulomb interactions are modeled as the cosine-Debye–Hückel potentials. The free-free Gaunt factors in the strongly coupled quantum plasmas exhibit remarkably different features from the ones in the weakly coupled classical plasmas. The results of the free-free processes are featured with the resonances when the screening length κ is close to the critical screening length κnlc(the corresponding bound state |nl〉 merges into the continuum state when the screening length approaches the value). It is found that these resonances can be roughly classified into two types: the enhanced broad resonance and the shape-type narrow resonance. The former one appears when κ→κnsc, where a virtual state |ns〉 with near-zero-energy exists, while the latter one (κ→κnlc, l≥1) is formed by the temporary capture of a continuous electron by an effective short-range potential. Note that when the screening length is close to both κnpc and κn sc, the Gaunt factors would exhibit a superimposition of a narrow shape-type resonance and a broad resonance. Given that the free-free Gaunt factor is a summation over the angular momentum, the main contributions of different partial waves to the resonance behavior are further analyzed.

The Removal Efficiencies of Several Temperate Tree Species at Adsorbing Airborne Particulate Matter in Urban Forests and Roadsides

Although urban trees are proposed as comparatively economical and eco-efficient biofilters for treating atmospheric particulate matter (PM) by the temporary capture and retention of PM particles, the PM removal effect and its main mechanism still remain largely uncertain. Thus, an understanding of the removal efficiencies of individual leaves that adsorb and retain airborne PM, particularly in the sustainable planning of multifunctional green infrastructure, should be preceded by an assessment of the leaf microstructures of widespread species in urban forests. We determined the differences between trees in regard to their ability to adsorb PM based on the unique leaf microstructures and leaf area index (LAI) reflecting their overall ability by upscaling from leaf scale to canopy scale. The micro-morphological characteristics of adaxial and abaxial leaf surfaces directly affected the PM trapping efficiency. Specifically, leaf surfaces with grooves and trichomes showed a higher ability to retain PM as compared to leaves without epidermal hairs or with dynamic water repellency. Zelkova serrata (Thunb.) Makino was found to have significantly higher benefits with regard to adsorbing and retaining PM compared to other species. Evergreen needle-leaved species could be a more sustainable manner to retain PM in winter and spring. The interspecies variability of the PM adsorption efficiency was upscaled from leaf scale to canopy scale based on the LAI, showing that tree species with higher canopy density were more effective in removing PM. In conclusion, if urban trees are used as a means to improve air quality in limited open spaces for urban greening programs, it is important to predominantly select a tree species that can maximize the ability to capture PM by having higher canopy density and leaf grooves or trichomes.

Charged dust close to outer mean-motion resonances in the heliosphere

We investigate the dynamics of charged dust close to outer mean-motion resonances with planet Jupiter. The importance of the interplanetary magnetic field on the orbital evolution of dust is clearly demonstrated. New dynamical phenomena are found that do not exist in the classical problem of uncharged dust. We find changes in the orientation of the orbital planes of dust particles, an increased amount of chaotic orbital motions, sudden 'jumps' in the resonant argument, and a decrease in time of temporary capture due to the Lorentz force. Variations in the orbital planes of dust grain orbits are found to be related to the angle between the orbital angular momentum and magnetic axes of the heliospheric field and the rotation rate of the Sun. These variations are bound using a simplified model derived from the full dynamical problem using first order averaging theory. It is found that the interplanetary magnetic field does not affect the capture process, that is still dominated by the other non-gravitational forces. Our study is based on a dynamical model in the framework of the inclined circular restricted three-body problem. Additional forces include solar radiation pressure, solar wind drag, the Poynting-Robertson effect, and the influence of a Parker spiral type interplanetary magnetic field model. The analytical estimates are derived on the basis of Gauss' form of planetary equations of motion. Numerical results are obtained by simulations of dust grain orbits together with the system of variational equations. Chaotic regions in phase space are revealed by means of Fast Lyapunov Chaos Indicators.

The use of Design of experiments to calculate the influence of planet oblateness in the temporary gravitational capture

This paper presents the study of the influence of the oblateness of one planet in the temporary gravitational capture of a particle (or a spacecraft) around the main celestial body of the system. The gravitational capture is a physical phenomenon where a celestial body (or a spacecraft), initially in a hyperbolic orbit with positive energy with respect to the main body of the system, is captured by another celestial body, changing the energy of the orbit to negative during a determined time. In this way, we have a temporary capture of this body or spacecraft. In the case of a spacecraft, it is possible to make this capture permanent by the application of a propulsion system to the spacecraft. This technique is done with savings over the traditional maneuvers performed without the support of the temporary capture, so it can help mission designers in the planning of the mission. As an example, the system used in the present paper is composed by the Sun-Jupiter-particle, and this system is modeled by the circular restricted three-body problem (CR3BP) plus the oblateness of Jupiter. To determine the effects of the oblateness in the dynamics of the particle, it is used the design of experiments to generate the data for a global analysis of the model. The oblateness of the planet is varied to show the effects of this parameter.

Orbital stability of ensembles of particles in regions of magnetic reconnection in Earth's magneto-tail

We investigate the collective behavior of particle orbits in the vicinity of magnetic reconnection in Earth's magneto-tail. Various regions of different kinds of orbital stability of particle motions are found. We locate regimes of temporary capture of particle orbits in configuration space as well as locations, where strong particle accelerations take place. With this study, we are able to provide a detailed map, i.e., the topology, of high and low acceleration centers close to the reconnection site. Quasiregular and chaotic kinds of motions of elementary particles can be determined as well. The orbital stability of particle orbits is obtained by a statistical analysis of the outcome of the system of variational equations of particle orbits within the framework of particle-in-cell simulations. Using the concept of Lyapunov characteristic numbers to ensembles of particle orbits, we introduce Lyapunov ensemble averages to describe the response of particle orbits to local perturbations induced by the electromagnetic field.

The emotional attentional blink is robust to divided attention.

The emotional attentional blink (EAB) refers to a temporary impairment in the ability to identify a target when it is preceded by an emotional distractor. It is thought to occur because the emotional salience of the distractor exogenously captures attention for a brief duration, rendering the target unattended and preventing it from reaching awareness. Here we tested the extent to which the EAB can be attenuated by inducing a diffuse top-down attentional state, which has been shown to improve target identification in an analogous attentional phenomenon, the attentional blink. Rapid sequences of landscape images were presented centrally, and participants reported the orientation of a ± 90° rotation of a landscape target. To induce a diffuse state of attention, participants were given a secondary task of monitoring for the appearance of a colored dot in the periphery. We found that emotional distractors impaired target recognition performance to comparable extents, regardless of whether or not participants concurrently performed the peripheral-monitoring task. Moreover, we found that performance of the secondary task led to an impaired ability to ignore neutral distractors. Subjective ratings of target vividness mirrored the behavioral accuracy, with frequent reports of intermediate levels of vividness suggesting that the EAB might impair target visibility in a graded manner. Our results demonstrate that the EAB is robust to manipulations of top-down attention, suggesting that the temporary capture of attention by emotionally salient stimuli involves processes that are distinct from those that produce the attentional blink.