Trojan Asteroids Research Articles

Asteroids and the James Webb Space Telescope

The James Webb Space Telescope (JWST) provides the opportunity for ground-breaking observations of asteroids. It covers wavelength regions that are unavailable from the ground and does so with unprecedented sensitivity. The main belt and Trojan asteroids are all observable at some point in the JWST lifetime. We present an overview of the capabilities for JWST and how they apply to the asteroids as well as some short science cases that take advantage of these capabilities.

TEMPORARY CAPTURE OF ASTEROIDS BY A PLANET: DEPENDENCE OF PROGRADE/RETROGRADE CAPTURE ON ASTEROIDS’ SEMIMAJOR AXES

ABSTRACT We have investigated the dependence of the prograde/retrograde temporary capture of asteroids by a planet on their original heliocentric semimajor axes through analytical arguments and numerical orbital integrations in order to discuss the origins of irregular satellites of giant planets. We found that capture is mostly retrograde for the asteroids near the planetary orbit and is prograde for those from farther orbits. An analytical investigation reveals the intrinsic dynamics of these dependences and gives boundary semimajor axes for the change in prograde/retrograde capture. The numerical calculations support the idea of deriving analytical formulae and confirm their dependence. Our numerical results show that the capture probability is much higher for bodies from the inner region than for outer ones. These results imply that retrograde irregular satellites of Jupiter are most likely captured bodies from the nearby orbits of Jupiter that may have the same origin as Trojan asteroids, while prograde irregular satellites originate from far inner regions such as the main-belt asteroid region.

Origin and Evolution of the Cometary Reservoirs

Comets have three known reservoirs: the roughly spherical Oort Cloud (for long-period comets), the flattened Kuiper Belt (for ecliptic comets), and, surprisingly, the asteroid belt (for main-belt comets). Comets in the Oort Cloud were thought to have formed in the region of the giant planets and then placed in quasi-stable orbits at distances of thousands or tens of thousands of AU through the gravitational effects of the planets and the Galaxy. The planets were long assumed to have formed in place. However, the giant planets may have undergone two episodes of migration. The first would have taken place in the first few million years of the Solar System, during or shortly after the formation of the giant planets, when gas was still present in the protoplanetary disk around the Sun. The Grand Tack (Walsh et al. in Nature 475:206–209, 2011) models how this stage of migration could explain the low mass of Mars and deplete, then repopulate the asteroid belt, with outer-belt asteroids originating between, and outside of, the orbits of the giant planets. The second stage of migration would have occurred later (possibly hundreds of millions of years later) due to interactions with a remnant disk of planetesimals, i.e., a massive ancestor of the Kuiper Belt. Safronov (Evolution of the Protoplanetary Cloud and Formation of the Earth and the Planets, 1969) and Fernandez and Ip (Icarus 58:109–120, 1984) proposed that the giant planets would have migrated as they interacted with leftover planetesimals; Jupiter would have moved slightly inward, while Saturn and (especially) Uranus and Neptune would have moved outward from the Sun. Malhotra (Nature 365:819–821, 1993) showed that Pluto’s orbit in the 3:2 resonance with Neptune was a natural outcome if Neptune captured Pluto into resonance while it migrated outward. Building on this work, Tsiganis et al. (Nature 435:459–461, 2005) proposed the Nice model, in which the giant planets formed closer together than they are now, and underwent a dynamical instability that led to a flood of comets and asteroids throughout the Solar System (Gomes et al. in Nature 435:466–469, 2005b). In this scenario, it is somewhat a matter of luck whether an icy planetesimal ends up in the Kuiper Belt or Oort Cloud (Brasser and Morbidelli in Icarus 225:40–49, 2013), as a Trojan asteroid (Morbidelli et al. in Nature 435:462–465, 2005; Nesvorný and Vokrouhlický in Astron. J. 137:5003–5011, 2009; Nesvorný et al. in Astrophys. J. 768:45, 2013), or as a distant “irregular” satellite of a giant planet (Nesvorný et al. in Astron. J. 133:1962–1976, 2007). Comets could even have been captured into the asteroid belt (Levison et al. in Nature 460:364–366, 2009). The remarkable finding of two “inner Oort Cloud” bodies, Sedna and 2012 $\mbox{VP}_{113}$ , with perihelion distances of 76 and 81 AU, respectively (Brown et al. in Astrophys. J. 617:645–649, 2004; Trujillo and Sheppard in Nature 507:471–474, 2014), along with the discovery of other likely inner Oort Cloud bodies (Chen et al. in Astrophys. J. Lett. 775:8, 2013; Brasser and Schwamb in Mon. Not. R. Astron. Soc. 446:3788–3796, 2015), suggests that the Sun formed in a denser environment, i.e., in a star cluster (Brasser et al. in Icarus 184:59–82, 2006, 191:413–433, 2007, 217:1–19, 2012b; Kaib and Quinn in Icarus 197:221–238, 2008). The Sun may have orbited closer or further from the center of the Galaxy than it does now, with implications for the structure of the Oort Cloud (Kaib et al. in Icarus 215:491–507, 2011). We focus on the formation of cometary nuclei; the orbital properties of the cometary reservoirs; physical properties of comets; planetary migration; the formation of the Oort Cloud in various environments; the formation and evolution of the Kuiper Belt and Scattered Disk; and the populations and size distributions of the cometary reservoirs. We close with a brief discussion of cometary analogs around other stars and a summary.

When comets get old: A synthesis of comet and meteor observations of the low activity comet 209P/LINEAR

It is speculated that some weakly active comets may be transitional objects between active and dormant comets. These objects are at a unique stage of the evolution of cometary nuclei, as they are still identifiable as active comets, in contrast to inactive comets that are observationally indistinguishable from low albedo asteroids. In this paper, we present a synthesis of comet and meteor observations of Jupiter-family Comet 209P/LINEAR, one of the most weakly active comets recorded to-date. Images taken by the Xingming 0.35-m telescope and the Gemini Flamingo-2 camera are modeled by a Monte Carlo dust model, which yields a low dust ejection speed (1/10 of that of moderately active comets), dominance of large dust grains, and a low dust production of 0.4kgs-1 at 19d after the 2014 perihelion passage. We also find a reddish nucleus of 209P/LINEAR that is similar to D-type asteroids and most Trojan asteroids. Meteor observations with the Canadian Meteor Orbit Radar (CMOR), coupled with meteoroid stream modeling, suggest a low dust production of the parent over the past few hundred orbits, although there are hints of a some temporary increase in activity in the 18th century. Dynamical simulations indicate 209P/LINEAR may have resided in a stable near-Earth orbit for ∼104yr, which is significantly longer than typical JFCs. All these lines of evidence imply that 209P/LINEAR as an aging comet quietly exhausting its remaining near surface volatiles. We also compare 209P/LINEAR to other low activity comets, where evidence for a diversity of the origin of low activity is seen.

A new method based on the subpixel Gaussian model for accurate estimation of asteroid coordinates

We describe a new iteration method to estimate asteroid coordinates, which is based on the subpixel Gaussian model of a discrete object image. The method operates by continuous parameters (asteroid coordinates) in a discrete observation al space (the set of pixels potential) of the CCD frame. In this model, a kind of the coordinate distribution of the photons hitting a pixel of the CCD frame is known a priori, while the associated parameters are determined from a real digital object image. The developed method, being more flexible in adapting to any form of the object image, has a high measurement accuracy along with a low calculating complexity due to a maximum likelihood procedure, which is implemented to obtain the best fit instead of a least-squares method and Levenberg-Marquar dt algorithm for the minimisation of the quadratic form. Since 2010, the method was tested as the basis of our CoLiTec (Collection Light Technology) software, which has been installed at several observatories of the world with the aim of automatic discoveries of asteroids and comets on a set of CCD frames. As the result, four comets (C/2010 X1 (Elenin), P/2011 NO1(Elenin), C/2012 S1 (ISON), and P/2013 V3 (Nevski)) as well as more than 1500 small Solar System bodies (including five NEOs, 21 Trojan asteroids of Jupiter, and one Centaur object) were discovered. We discuss these results that allowed us to compare the accuracy parameters of a new method and confirm its efficiency. In 2014, the CoLiTec software was recommended to all members of the Gaia-FUN-SSO network for analysing observations as a tool to detect faint moving objects in frames.

Rotation lightcurves of small jovian Trojan asteroids

Several lines of evidence support a common origin for, and possible hereditary link between, cometary nuclei and jovian Trojan asteroids. Due to their distance and low albedos, few comet-sized Trojans have been studied. We present new lightcurve information for 19 Trojans≲30km in diameter, more than doubling the number of objects in this size range for which some rotation information is known. The minimum densities for objects with complete lightcurves are estimated and are found to be comparable to those measured for cometary nuclei. A significant fraction (∼40%) of this observed small Trojan population rotates slowly (P>24h), with measured periods as long as 375h (Warner, B.D., Stephens, R.D. [2011]. Minor Planet Bull. 38, 110–111). The excess of slow rotators may be due to the YORP effect. Results of the Kolmogorov–Smirnov test suggest that the distribution of Trojan rotation rates is dissimilar to those of Main Belt Asteroids of the same size. Concerted observations of a large number of Trojans could establish the spin barrier (Warner, B.D., Harris, A.W., Pravec, P. [2009]. Icarus 202, 134–146), making it possible to estimate densities for objects near the critical period.

Hill’s approximation in a restricted four-body problem

We consider a restricted four-body problem on the dynamics of a massless particle under the gravitational force produced by three mass points forming an equilateral triangle configuration. We assume that the mass \(m_3\) of one primary is very small compared with the other two, \(m_1\) and \(m_2\), and we study the Hamiltonian system describing the motion of the massless particle in a neighborhood of \(m_3\). In a similar way to Hill’s approximation of the lunar problem, we perform a symplectic scaling, sending the two massive bodies to infinity, expanding the potential as a power series in \(m_3^{1/3}\), and taking the limit case when \(m_3\rightarrow 0\). We show that the limiting Hamiltonian inherits dynamical features from both the restricted three-body problem and the restricted four-body problem. In particular, it extends the classical lunar Hill problem. We investigate the geometry of the Poincaré sections, direct and retrograde periodic orbits about \(m_3\), libration points, periodic orbits near libration points, their stable and unstable manifolds, and the corresponding homoclinic intersections. The motivation for this model is the study of the motion of a satellite near a jovian Trojan asteroid.

Jumping mechanisms of Trojan asteroids in the planar restricted three- and four-body problems

We explore minimal dynamical mechanisms for the transport of Trojan asteroids between the vicinities of the stable Lagrange points \(L_{4}\) and \(L_{5}\) within the framework of the planar restricted three- and four-body problems. This transport, called “jumping” of Trojan asteroids, has been observed numerically in the sophisticated Solar System models. However its dynamical mechanisms have not been fully explored yet. The present study shows that invariant manifolds emanating from an unstable periodic orbit around the unstable Lagrange point \(L_{3}\) mediate the jumping of Trojan asteroids in the Sun–Jupiter planar restricted three-body problem. These invariant manifolds form homoclinic tangles and lobes when projected onto the configuration space through a discrete mapping. Thus the resulted lobe dynamics explains the mechanism for the jumping of Jupiter’s Trojan asteroids. In the Sun–Earth planar restricted three-body problem, on the other hand, invariant manifolds of an unstable periodic orbit around \(L_{3}\) do not exhibit clear homoclinic tangles nor lobes, indicating that the jumping is very difficult to occur. It is then shown that the effect of perturbation of Venus is important for the onset of the jumping of Earth’s Trojan asteroids within the framework of the Sun–Earth–Venus planar restricted four-body problem. The results presented here could shed new insights into the transport mechanism as well as trajectory design associated with \(L_{3}\), \(L_{4}\), and \(L_5\).

SIZE AND SHAPE FROM STELLAR OCCULTATION OBSERVATIONS OF THE DOUBLE JUPITER TROJAN PATROCLUS AND MENOETIUS

We present results of a stellar occultation by the Jupiter Trojan asteroid Patroclus and its nearly equal size moon, Menoetius. The geocentric mid-time of the event was 2013 October 21 06:43:02 UT. Eleven sites out of 36 successfully recorded an occultation. Seven chords across Patroclus yielded an elliptical limb fit of 124.6 by 98.2 km. There were six chords across Menoetius that yielded an elliptical limb fit of 117.2 by 93.0 km. There were three sites that got chords on both objects. At the time of the occultation we measured a separation of 664.6 km (0.247 arcsec) and a position angle for Menoetius of 2657 measured eastward from J2000 north. Combining this occultation data with previous light curve data, the axial ratios of both objects are 1.3 : 1.21 : 1, indicative of a mostly oblate ellipsoid with a slight asymmetry in its equatorial projection. The oblate shape is not an equilibrium shape for the current rotation period, but would be if it were rotating with an ~8 h period. This faster period is consistent with a pre-evolved state of the system with an orbital separation that is 50% smaller. Our best estimate of the system density is 0.88 g cm−3.

DISCRETE RESTRICTED FOUR-BODY PROBLEM: EXISTENCE OF PROOF OF EQUILIBRIA AND REPRODUCIBILITY OF PERIODIC ORBITS

We propose the discrete-time restricted four-body problem (d-R4BP), which approximates the orbits of the restricted four-body problem (R4BP). The d-R4BP is given as a special case of the discrete-time chain regularization of the general N-body problem published in Minesaki. Moreover, we analytically prove that the d-R4BP yields the correct orbits corresponding to the elliptic relative equilibrium solutions of the R4BP when the three primaries form an equilateral triangle at any time. Such orbits include the orbit of a relative equilibrium solution already discovered by Baltagiannis and Papadakis. Until the proof in this work, there has been no discrete analog that preserves the orbits of elliptic relative equilibrium solutions in the R4BP. For a long time interval, the d-R4BP can precisely compute some stable periodic orbits in the Sun–Jupiter–Trojan asteroid–spacecraft system that cannot necessarily be reproduced by other generic integrators.

Orbital dynamics of Neptune Trojans

Trojan asteroids share the same orbit with a planet, comprising together with the Sun and the planet an equilateral triangle in space. On the orbit of Jupiter, two clouds of thousands of asteroids named Greek Camp and Trojan Camp, by 60 degrees ahead and behind Jupiter respectively, have been well-known since as early as 1906. Trojan asteroids of Neptune however, was found quite late in the year of 2003. Nevertheless, evidences indicate that the Neptunes Trojan cloud is larger at least by one order of magnitude than the Jupiter Trojan cloud and the main asteroid belt, both in total number and in total mass, making itself the second largest reservoir of small bodies in the Solar system, only after the Kuiper belt. Meanwhile, the distinct orbits of Neptune Trojans that have been already observed, and the fact that they are a kind of connection between spaces within and beyond Neptune orbit, mean that they can serve as a touchstone of theories about the origin and evolution of the Solar system. We briefly present in this review the observations, the investigations on their orbital dynamics and the research on their origin.

Space weathering and the color–color diagram of Plutinos and Jupiter Trojans

The Jupiter Trojan asteroids and the Plutinos are two peculiar populations. They are dynamically resonant, therefore with heliocentric distances relatively bounded for long timescales, as a farely general rule. As a consequence, some correlation with the surface color properties of their respective members is expected. Indeed, there are apparent differences in the B-V vs. V-R color–color diagram of the two populations. Using a simple model based on the surface color due to the contribution of two components, one pristine and one altered, we find as plausible that the difference is due to the interplay of space weathering by energetic cosmic-radiation and collisional effects.

Giga-year evolution of Jupiter Trojans and the asymmetry problem

We present a series of numerical integrations of observed and fictitious Jupiter Trojan asteroids, under the gravitational effects of the four outer planets, for time-spans comparable with the age of the Solar System. From these results we calculate the escape rate from each Lagrange point, and construct dynamical maps of “permanence” time in different regions of the phase space.Fictitious asteroids in L4 and L5 show no significant difference, showing almost identical dynamical maps and escape rates. For real Trojans, however, we found that approximately 23% of the members of the leading swarm escaped after 4.5Gyrs, while this number increased to 28.3% for L5. This implies that the asymmetry between the two populations increases with time, indicating that it may have been smaller at the time of formation/capture of these asteroids. Nevertheless, the difference in chaotic diffusion cannot, in itself, account for the current observed asymmetry (∼40%), and must be primarily primordial and characteristic of the capture mechanism of the Trojans.Finally, we calculate new proper elements for all the numbered Trojans using the semi-analytical approach of Beaugé and Roig (Beaugé, C., Roig, F.V. [2001]. Icarus, 153, 391–415), and compare the results with the numerical estimations by Brož and Rosehnal (Brož, M., Rosehnal, J. [2011]. Mon. Not. R. Astron. Soc. 414, 565–574). For asteroids that were already numbered in 2011, both methods yield very similar results, while significant differences were found for those bodies that became numbered after 2011.

Dumb-bell-shaped equilibrium figures for fiducial contact-binary asteroids and EKBOs

In this work, we investigate the equilibrium figures of a dumb-bell-shaped sequence with which we are still not well acquainted. Studies have shown that these elongated and nonconvex figures may realistically replace the classic “Roche binary approximation” for modeling putative peanut-shaped or contact binary asteroids. The best-fit dumb-bell shapes, combined with the known rotational period of the objects, provide estimates of the bulk density of these objects. This new class of mathematical figures has been successfully tested on the observed light curves of three noteworthy small bodies: main-belt Asteroid 216 Kleopatra, Trojan Asteroid 624 Hektor and Edgeworth–Kuiper-belt object 2001 QG298. Using the direct observations of Kleopatra and Hektor obtained with high spatial resolution techniques and fitting the size of the dumb-bell-shaped solutions, we derived new physical characteristics in terms of equivalent radius, 62.5±5km and 92±5km, respectively, and bulk density, 4.4±0.4gcm−3 and 2.43±0.35gcm−3, respectively. In particular, the growing inadequacy of the radar shape model for interpreting any type of observations of Kleopatra (light curves, AO images, stellar occultations) in a satisfactory manner suggests that Kleopatra is more likely to be a dumb-bell-shaped object than a “dog-bone.”

Similar origin for low- and high-albedo Jovian Trojans and Hilda asteroids?

Hilda asteroids and Jupiter Trojans are two low-albedo (p$_{\rm v}$ ~ 0.07) populations for which the Nice model predicts an origin in the primordial Kuiper Belt region. However, recent surveys by WISE and the Spitzer Space Telescope (SST) have revealed that ~2% of these objects possess high albedos (p$_{\rm v}$ > 0.15), which might indicate interlopers - that is, objects not formed in the Kuiper Belt - among these two populations. Here, we report spectroscopic observations in the visible and/or near-infrared spectral ranges of twelve high-albedo (p$_{\rm v}$ > 0.15) Hilda asteroids and Jupiter Trojans. These twelve objects have spectral properties similar to those of the low- albedo population, which suggests a similar composition and hence a similar origin for low- and high-albedo Hilda asteroids and Jupiter Trojans. We therefore propose that most high albedos probably result from statistical bias or uncertainties that affect the WISE and SST measurements. However, some of the high albedos may be true and the outcome of some collision-induced resurfacing by a brighter material that could include water ice. Future work should attempt to investigate the nature of this supposedly bright material. The lack of interlopers in our sample allows us to set an upper limit of 0.4% at a confidence level of 99.7% on the abundance of interlopers with unexpected taxonomic classes (e.g., A-, S-, V-type asteroids) among these two populations.

Automated Design of Propellant-Optimal, Low-Thrust Trajectories for Trojan Asteroid Tours

The sun–Jupiter Trojan asteroid swarms are targets of interest for robotic spacecraft missions, where low-thrust propulsion systems offer a viable approach for realizing tours of these asteroids. This investigation introduces a novel scheme for the automated creation of prospective tours under the natural dynamics of a multibody regime with thrust supplied by a variable-specific-impulse engine. The procedure approximates tours by combining independently generated fuel-optimal rendezvous arcs between asteroid pairs into a series of trajectory legs. Propellant costs as well as departure and arrival times are estimated from the performance of the individual thrust arcs. Tours of interest are readily constructed in higher-fidelity models, and options for the end-to-end trajectories are easily assessed. In this investigation, scenarios where constant and varying-power sources are available to the low-thrust engine are explored. In general, the automation procedure rapidly generates a large number of potential tours and supplies reasonable cost estimates for preliminary baseline mission design. Computational aspects of the design procedure are automated such that end-to-end trajectories are generated with a minimum of human interaction after key elements associated with a proposed mission concept are specified.

THE PUZZLING MUTUAL ORBIT OF THE BINARY TROJAN ASTEROID (624) HEKTOR

Asteroids with satellites are natural laboratories to constrain the formation and evolution of our solar system. The binary Trojan asteroid (624) Hektor is the only known Trojan asteroid to possess a small satellite. Based on W.M. Keck adaptive optics observations, we found a unique and stable orbital solution, which is uncommon in comparison to the orbits of other large multiple asteroid systems studied so far. From lightcurve observations recorded since 1957, we showed that because the large Req=125-km primary may be made of two joint lobes, the moon could be ejecta of the low-velocity encounter, which formed the system. The inferred density of Hektor's system is comparable to the L5 Trojan doublet (617) Patroclus but due to their difference in physical properties and in reflectance spectra, both captured Trojan asteroids could have a different composition and origin.

Mission Analysis of Sample Return from Jovian Trojan Asteroid by Solar Power Sail

Mission Analysis of Sample Return from Jovian Trojan Asteroid by Solar Power Sail

Revised albedos of Trojan asteroids (911) Agamemnon and (4709) Ennomos

AbstractCCD‐photometry was performed for two Jupiter Trojan asteroids (911) Agamemnon and (4709) Ennomos for which the diameters were obtained from occultation events. New data on rotation periods, lightcurve amplitudes, color indices, magnitude–phase slopes, and absolute magnitudes were obtained for these asteroids. We have used the diameters from occultations (166 and 99 km) and new data on absolute magnitudes at the instant occultation (7.95 and 8.85 mag) to revise their albedos to 0.042 (911 Agamemnon) and 0.052 (4709 Ennomos).

Predictions for the detection of Earth and Mars Trojan asteroids by the Gaia satellite

The European Space Agency Gaia satellite, planned for launch in late 2013, will perform systematic astrometric observations of the whole sky over a five year period. During this mission many thousands of Solar System Objects down to magnitude V=20 will be observed including Near-Earth Asteroids and objects at Solar elongations as low as 45 degrees, which are difficult to observe with ground-based telescopes. We simulated the detection of Trojan asteroids in the orbits of Earth and Mars by Gaia. We find that Gaia will not detect the Earth Trojan 2010 TK7 although it will detect any Earth Trojans with diameters larger than 600 m. We also find that Gaia will detect the currently known Mars Trojans and could discover more than 100 new Mars Trojans as small as 400 m in diameter. The results of the Gaia mission will test the predictions about the Mars Trojan asteroid population and lead to greater understanding about the evolution of the Solar System.