We introduce a new method for analyzing sparse photometric data of asteroids and apply it to Zwicky Transient Facility observations of the Jupiter Trojan asteroids. The method relies on the creation of a likelihood model that includes the probability distribution of rotational brightness variations at an unknown rotation phase. The likelihood model is analyzed via a Markov Chain Monte Carlo to quantify the uncertainty in our parameter estimates. Using this method, we provide color, phase parameter, absolute magnitude and amplitude of rotation measurements for 1049 Jupiter Trojans. We find that phase parameter is correlated with color and the distribution of Trojan asteroid rotational amplitudes is indistinguishable from that of main-belt asteroids.
Earth Trojan Asteroids are an important but elusive population that co-orbit with Earth at the L4 and L5 Lagrange points. There is only one known, but a large population is theoretically stable and could provide insight into our solar system's past and present as well as planetary defense. In this paper, we present the results of an Earth Trojan survey that uses a novel shift-and-stack detection method on two nights of data from the Dark Energy Camera. We find no new Earth Trojan Asteroids. We calculate an upper limit on the population that is consistent with previous searches despite much les…
The Jupiter Trojan asteroid 128383 (2004 JW52) was recently reported to have optical colors that are incongruous with its dynamical class. New and archival observations show that this is not the case. This is a reminder that we must always rule out the possibility that the Point Spread Function (PSF) of a minor planet is blended with that of a background sidereal source in survey images before its colors in the associated survey catalog can be considered reliable.
The existence of Earth's Trojan asteroids is not well constrained and represents a major gap in our inventory of small bodies in near-Earth space. Their discovery would be of high scientific and human interest.
In a previous paper we simulated the orbital evolution of dust particles from the Jupiter Trojan asteroids ejected by the impacts of interplanetary particles, and evaluated their overall configuration in the form of dust arcs. Here we compare the orbital properties of these Trojan dust particles and the Trojan asteroids. Both Trojan asteroids and most of the dust particles are trapped in the Jupiter 1:1 resonance. However, for dust particles, this resonance is modified because of the presence of solar radiation pressure, which reduces the peak value of the semi-major axis distribution. We find…
The Lucy Mission accomplishes its science during a series of five flyby encounters with seven Trojan asteroid targets. This mission architecture drives a concept of operations design that maximizes science return, provides redundancy in observations where possible, features autonomous fault protection and utilizes onboard target tracking near closest approach. These design considerations reduce risk during the relatively short time-critical periods when science data is collected. The payload suite consists of a color camera and infrared imaging spectrometer, a high-resolution panchromatic imag…
Aims. The surfaces of the Trojan asteroids are steadily bombarded by interplanetary micrometeoroids, which releases ejecta of small dust particles. These particles form the faint dust arcs that are associated with asteroid clouds. Here we analyze the particle dynamics and structure of the arc in the region of the $L_4$ Trojan asteroids. Methods. We calculate the total cross section of the $L_4$ Trojan asteroids and the production rate of dust particles. The motion of the particles is perturbed by a variety of forces. We simulate the dynamical evolution of the dust particles, and explore the ov…
Jupiter has nearly 8000~known co-orbital asteroids orbiting in the L4 and L5 Lagrange points called Jupiter Trojan asteroids. Aside from the greater number density of the L4 cloud the two clouds are in many ways considered to be identical. Using sparse photometric data taken by the Asteroid Terrestrial-impact Last Alert System (ATLAS) for 863 L4 Trojans and 380 L5 Trojans we derive the shape distribution for each of the clouds and find that, on average, the L4 asteroids are more elongated than the L5 asteroids. This shape difference is most likely due to the greater collision rate in the L4 cl…
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 encou…
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 Trojan…
We describe ZStreak, a semi-real-time pipeline specialized in detecting small, fast-moving near-Earth asteroids (NEAs) that is currently operating on the data from the newly-commissioned Zwicky Transient Facility (ZTF) survey. Based on a prototype originally developed by Waszczak et al. (2017) for the Palomar Transient Factory (PTF), the predecessor of ZTF, ZStreak features an improved machine-learning model that can cope with the $10\times$ data rate increment between PTF and ZTF. Since its first discovery on 2018 February 5 (2018 CL), ZTF/ZStreak has discovered $45$ confirmed new NEAs over a…
Trojan asteroids are minor planets that share the orbit of a planet about the Sun and librate around the L4 or L5 Lagrangian points of stability. They are important solar-system fossils because they carry information on early Solar System formation, when collisions between bodies were more frequent. Discovery and study of terrestrial planet Trojans will help constrain models for the distribution of bodies and interactions in the inner Solar System. Since the discovery of the first outer planet Trojan in 1906, several thousand Jupiter Trojans have been found. Of the terrestrial planets there ar…
To date, reflectance spectra of Jupiter Trojan asteroids have revealed no distinctive absorption features. For this reason, the surface composition of these objects remains a subject of speculation. Spectra have revealed, however, that the Jupiter Trojan asteroids consist of two distinct sub-populations which differ in the optical to near-infrared colors. The origins and compositional differences between the two sub-populations remain unclear. Here we report the results from a 2.2-3.8 $μ$m spectral survey of a collection of 16 Jupiter Trojan asteroids, divided equally between the two sub-popul…
The Trojan asteroids orbit about the Lagrangian points of Jupiter and the residence times about their present location are very long for most of them. If these bodies originated in the outer Solar System, they should be mainly composed of water ice, but, in contrast with comets, all the volatiles close to the surface would have been lost long ago. Irrespective of the rotation period, and hence the surface temperature and ice sublimation rate, a dust layer exists always on the surface. We show that the timescale for resurfacing the entire surface of the Trojan asteroids is similar to that of th…
Due to their strong resonances with their host planet, Trojan asteroids can remain in stable orbits for billions of years. As a result, they are powerful probes for constraining the dynamical and chemical history of the solar system. Although we have detected thousands of Jupiter Trojans and dozens of Neptune Trojans, there are currently no known long-term stable Earth Trojans. Dynamical simulations show that the parameter space for stable Earth Trojans in substantial, so their apparent absence poses a mystery. This work uses a large ensemble of N-body simulations to explore how the Trojan pop…
Trojan asteroids are minor planets that share the orbit of a planet about the Sun and librate around the L4 or L5 Lagrangian points of stability. Although only three Mars Trojans have been discovered, models suggest that at least ten times this number should exist with diameters >= 1 km. We derive a model that constrains optimal sky search areas and present a strategy for the most efficient use of telescope survey time that maximizes the probability of detecting Mars Trojans. We show that the Gaia space mission could detect any Mars Trojans larger than 1 km in diameter, provided the relative m…
Trojan asteroids are minor planets that share the orbit of a planet about the Sun and librate around the L4 or L5 Lagrangian points of stability. They are important because they carry information on early Solar System formation, when collisions between bodies were more frequent. Discovery and study of terrestrial planet Trojans will help constrain models for the distribution of bodies and interactions in the inner Solar System. We present models that constrain optimal search areas, and strategies for survey telescopes to maximize the probability of detecting inner planet Trojans. We also consi…
We report on the discovery of new Martian Trojans within the Minor Planet Center list of asteroids. Their orbital evolution over 10^8 yr shows characteristic signatures of dynamical longevity (Scholl et al, 2005) while their average orbits resemble that of the largest known Martian Trojan, 5261 Eureka. The group forms a cluster within the region where the most stable Trojans should reside. Based on a combinatorial analysis and a comparison with the Jovian Trojan population, we argue that both this feature and the apparent paucity of km-sized Martian Trojans (Trilling et al, 2006) as compared t…
We obtained near-infrared (0.8 - 2.5 micron) spectra of seven Jovian Trojan asteroids that have been formerly reported to show silicate-like absorption features near 1 micron. Our sample includes the Trojan (1172) Aneas, which is one of three Trojans known to possess a comet-like 10 micron emission feature, indicative of fine-grained silicates. Our observations show that all seven Trojans appear featureless in high signal-to-noise ratio spectra. The simultaneous absence of the 1 micron band and presence of the 10 micron emission can be understood if the silicates on (1172) Aneas are iron-poor.…
We study orbital and physical properties of Trojan asteroids of Jupiter. We try to discern all families previously discussed in literature, but we conclude there is only one significant family among Trojans, namely the cluster around asteroid (3548) Eurybates. It is the only cluster, which has all of the following characteristics: (i) it is clearly concentrated in the proper-element space; (ii) size-frequency distribution is different from background asteroids; (iii) we have a reasonable collisional/dynamical model of the family. Henceforth, we can consider it as a real collisional family. We …
The Gaia satellite, planned for launch by the European Space Agency (ESA) in 2013, is the next generation astrometry mission following Hipparcos. While mapping the whole sky, the Gaia space mission is expected to discover thousands of Solar System Objects. These will include Near-Earth Asteroids and objects at Solar elongations as low as 45 degrees, which are difficult to observe with ground-based telescopes. We present the results of simulations for the detection of Trojan asteroids in the orbits of Earth and Mars by Gaia.
We present an analysis of lifetimes and resonances of Earth Trojan Asteroids (ETAs) in the MEGASIM data set (Yeager & Golovich 2022). Trojan asteroids co-orbit the Sun with a planet but remain bound to the Lagrange points, L4 (60° leading the planet) or L5 (60° trailing). In the circular three-body approximation, the stability of a Trojan asteroid depends on the ratio of the host planet mass and the central mass. For the inner planets, the range of stability becomes increasingly small, so perturbations from the planets have made primordial Trojans rare. To date there have been just two ETAs (2…
Seven of the nine known Mars Trojan asteroids belong to an orbital cluster named after its largest member 5261 Eureka. Eureka is likely the progenitor of the whole cluster, which formed at least 1 Gyr ago. It was suggested that the thermal YORP effect spun-up Eureka resulting with fragments being ejected by the rotational-fission mechanism. Eureka's spectrum exhibits a broad and deep absorption band around 1 μm, indicating an olivine-rich composition. Here we show evidence that the Trojan Eureka cluster progenitor could have originated as impact debris excavated from the Martian mantle. We pre…
Near-Earth asteroids (NEAs) are organized into five main classes: Amor, Apollo, Aten, Atira and 'Ayló'chaxnim. Asteroids belonging to the 'Ayló'chaxnim class are located entirely within the orbit of Venus making them difficult to detect by ground-based observatories. The first-known asteroid of this class, (594913) 'Ayló'chaxnim, was discovered by the Zwicky Transient Facility (ZTF) in 2020 January during a twilight search for asteroids at small solar elongations that ran between September 2019 and January 2020. Due to its large diameter of $\sim$2 km, the discovery of (594913) 'Ayló'chaxnim i…
We have used the XSHOOTER echelle spectrograph on the European Southern Obseratory (ESO) Very Large Telescope (VLT) to obtain UVB-VIS-NIR (ultraviolet-blue (UVB), visible (VIS) and near-infrared (NIR)) reflectance spectra of two members of the Eureka family of L5 Mars Trojans, in order to test a genetic relationship to Eureka. In addition to obtaining spectra, we also carried out VRI photometry of one of the VLT targets using the 2-m telescope at the Bulgarian National Astronomical Observatory - Rozhen and the two-channel focal reducer. We found that these asteroids belong to the olivine-domin…
On 2012 January 19, observers in the northeastern United States of America observed an occultation of 8.0-mag HIP 41337 star by the Jupiter-Trojan (911) Agamemnon, including one video recorded with a 36cm telescope that shows a deep brief secondary occultation that is likely due to a satellite, of about 5 km (most likely 3 to 10 km) across, at 278 km $\pm$ 5 km (0.0931 arcsec) from the asteroid's center as projected in the plane of the sky. A satellite this small and this close to the asteroid could not be resolved in the available VLT adaptive optics observations of Agamemnon recorded in 2003…
With a total mass similar to the main asteroid belt, the Jovian Trojan asteroids are a major feature in the solar system. Based upon the thermal infrared spectra of the largest Trojans obtained with the Spitzer space telescope, Emery et al. (2006) suggested that the surfaces of these Trojans may consist of fine-grained silicates suspended in a transparent matrix. To explore the transparent matrix hypothesis, we adopted a modified radiative transfer model to fit the Trojan spectra simultaneously both in the near and the thermal infrared regions. Our model shows that the Trojan spectra over a wi…
The long-standing co-orbital asteroids have been thought to be the possible source of zodiacal dust ring around the orbit of Venus, but inconsistent conclusions on the orbital stability thus existence of Venus Trojans are found in literature. We present in this paper a systematic survey of the orbital stability of Venus Trojans, taking into account the dynamical influences from the general relativity and the Yarkovsky effect. The orbits of thousands of fictitious Venus Trojans are numerically simulated. Using the method of frequency analysis, their orbital stabilities and the dynamical mechani…
The 2013 Planetary Science Decadal Survey identified a detailed investigation of the Trojan asteroids occupying Jupiter's L4 and L5 Lagrange points as a priority for future NASA missions. Observing these asteroids and measuring their physical characteristics and composition would aid in identification of their source and provide answers about their likely impact history and evolution, thus yielding information about the makeup and dynamics of the early Solar System. We present a conceptual design for a mission to the Jovian Trojan asteroids: the Trojan ASteroid Tour, Exploration, and Rendezvou…
We present fully covered phased light curves for 56 Jovian Trojan asteroids as acquired by the K2 mission of the Kepler space telescope. This set of objects has been monitored during Campaign 6 and represents a nearly unbiased subsample of the population of small Solar System bodies. We derived precise periods and amplitudes for all Trojans, and found their distributions to be compatible with the previous statistics. We point out, however, that ground-based rotation periods are often unreliable above 20h, and we find an overabundance of rotation periods above 60h compared with other minor plan…
We have searched Microvariability and Oscillations of STars (MOST) satellite photometry obtained in 2004, 2005, and 2007 of the solar-type star HD 209458 for Trojan asteroid swarms dynamically coupled with the system's transiting "hot Jupiter" HD 209458b. Observations of the presence and nature of asteroids around other stars would provide unique constraints on migration models of exoplanetary systems. Our results set an upper limit on the optical depth of Trojans in the HD 209458 system that can be used to guide current and future searches of similar systems by upcoming missions. Using cross-…
We present mid-infrared (8-33 micron) observations of the binary L5-Trojan system (617) Patroclus-Menoetius before, during, and after two shadowing events, using the Infrared Spectrograph (IRS) on board the Spitzer Space Telescope.F or the first time, we effectively observe changes in asteroid surface temperature in real time, allowing the thermal inertia to be determined very directly. A new detailed binary thermophysical model is presented which accounts for the system's known mutual orbit, arbitrary component shapes, and thermal conduction in the presence of eclipses. We obtain two local th…
We investigate the mineralogy of L5 Martian Trojan asteroids via reflectance spectroscopy, in particular (101429) 1998 $\mbox{VF}_{31}$, the only L5 Trojan that does not belong to the Eureka family (Christou, 2013). We find that this asteroid most likely belongs to the Bus-Demeo S-complex, in agreement with Rivkin et al. (2007) and obtain good spectral matches with Sq- or S-type asteroids, the lunar surface and of Martian and lunar meteorites. Mixture fitting to spectral endmembers suggests a surface abundance of Mg-rich orthopyroxene and iron metal or, alternatively, a mixture of plagioclase …
We describe the discovery of a satellite of the Trojan asteroid (3548) Eurybates in images obtained with the Hubble Space Telescope. The satellite was detected on three separate epochs, two in September 2018 and one in January 2020. The satellite has a brightness in all three epochs consistent with an effective diameter of d2 =1.2+/-0.4 km. The projected separation from Eurybates was s~1700-2300 km and varied in position, consistent with a large range of possible orbits. Eurybates is a target of the Lucy Discovery mission and the early detection of a satellite provides an opportunity for a sig…
The Trojan asteroids provide a unique perspective on the history of Solar System. As a large population of small bodies, they record important gravitational interactions and dynamical evolution of the Solar System. In the past decade, significant advances have been made in understanding physical properties, and there has been a revolution in thinking about the origin of Trojans. The ice and organics generally presumed to be a significant part of Trojan compositions have yet to be detected directly, though low density of the binary system Patroclus (and possibly low density of the binary/moonle…
Jupiter Trojan asteroids are located around L4 and L5 Lagrangian points on relatively stable orbits, in 1:1 MMR with Jupiter. However, not all of them lie in orbits that remain stable over the age of the Solar System. Unstable zones allow some Trojans to escape in time scales shorter than the Solar System age. This may contribute to populate other small body populations. In this paper, we study this process by performing long-term numerical simulations of the observed Trojans, focusing on the trajectories of those that leave the resonance. The orbits of current Trojans are taken as initial con…
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 Jupite…
We have observed well-sampled phase curves for nine Trojan asteroids in B-, V-, and I-bands. These were constructed from 778 magnitudes taken with the 1.3-m telescope on Cerro Tololo as operated by a service observer for the SMARTS consortium. Over our typical phase range of 0.2-10 deg, we find our phase curves to be adequately described by a linear model, for slopes of 0.04-0.09 mag/deg with average uncertainty less than 0.02 mag/deg. (The one exception, 51378 (2001 AT33), has a formally negative slope of -0.02 +- 0.01 mag/deg.) These slopes are too steep for the opposition surge mechanism to…
Recently the first Earth Trojan has been observed (Mainzer et al., ApJ 731) and found to be on an interesting orbit close to the Lagrange point L4 (Connors et al., Nature 475). In the present study we therefore perform a detailed investigation on the stability of its orbit and moreover extend the study to give an idea of the probability to find additional Earth-Trojans. Our results are derived using different approaches: a) we derive an analytical mapping in the spatial elliptic restricted three-body problem to find the phase space structure of the dynamical problem. We explore the stability o…
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 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 orbit…
Trojan asteroids orbit in the Lagrange points of the system Sun-planet-asteroid. Their dynamical stability make their physical properties important proxies for the early evolution of our solar system. To study their origin, we want to characterize the surfaces of Jupiter Trojan asteroids and check possible similarities with objects of the main belt and of the Kuiper Belt. We have obtained high-accuracy broad-band linear polarization measurements of six Jupiter Trojans of the L4 population and tried to estimate the main features of their polarimetric behaviour. We have compared the polarimetric…
Search for L4 Earth Trojan asteroids with the 2.5-meter Wide Field Survey Telescope
University of Science and Technology of China（中国科学技术大学）；Institute of Deep Space Sciences, Deep Space Exploration Laboratory（深空科学研究所，深空探测实验室）；College of Physics, Guizhou University（贵州大学物理学院）
Aims. We investigate the influence of the Yarkovsky force on the long-term orbital evolution of Jupiter Trojan asteroids. Methods. Clones of the observed population with different sizes and different thermal properties were numerically integrated for 1 Gyr with and without the Yarkovsky effect. The escape rate of these objects from the Trojan region as well as changes in the libration amplitude, eccentricity, and inclination were used as a metric of the strength of the Yarkovsky effect on the Trojan orbits. Results. Objects with radii $R\leq$1 km are significantly influenced by the Yarkovsky f…
In the outer Solar system, primordial Trojan asteroids may have remained dynamically stable for billions of years. Several thousands of them accompany Jupiter in its journey around the Sun and a similarly large population may be hosted by Neptune. In addition, recently captured or transient Jovian and Neptunian Trojans are not uncommon. In contrast, no Trojans of Saturn have been found yet and just one Uranian Trojan is known, 2011 QF99. Here, we discuss the identification of a second Trojan of Uranus: 2014 YX49. Like 2011 QF99, 2014 YX49 is a transient L4 Trojan although it orbits at higher i…
With the growing numbers of asteroids being discovered, identifying an observationally complete sample is essential for statistical analyses and for informing theoretical models of the dynamical evolution of the solar system. We present an easily implemented method of estimating the empirical observational completeness in absolute magnitude, H_lim, as a function of semi-major axis. Our method requires fewer assumptions and decisions to be made in its application, making results more transportable and reproducible amongst studies that implement it, as well as scalable to much larger datasets of…
The Hilda asteroids are primitive bodies in resonance with Jupiter whose origin and physical properties are not well understood. Current models posit that these asteroids formed in the outer Solar System and were scattered along with the Jupiter Trojans into their present-day positions during a chaotic episode of dynamical restructuring. In order to explore the surface composition of these enigmatic objects in comparison with an analogous study of Trojans (Emery et al. 2011), we present new near-infrared spectra (0.7-2.5 $μ$m) of 25 Hilda asteroids. No discernible absorption features are appar…
The paper is devoted to investigate the capture of asteroids by Venus, Earth and Mars into the 1:1 mean motion resonance especially into Trojan orbits. Current theoretical studies predict that Trojan asteroids are a frequent by-product of the planet formation. This is not only the case for the outer giant planets, but also for the terrestrial planets in the inner Solar System. By using numerical integrations, we investigated the capture efficiency and the stability of the captured objects. We found out that the capture efficiency is larger for the planets in the inner Solar System compared to …
We report near-infrared (0.7-2.5 micron) reflectance spectra for each of the six target asteroids of the forthcoming NASA Discovery-class mission Lucy. Five Jupiter Trojans (the binary (617) Patroclus system, (3548) Eurybates, (21900) Orus, (11351) Leucus, and (15094) Polymele) are well-characterized, with measurable spectral differences. We also report a survey-quality spectrum for main belt asteroid (52246) Donaldjohanson. We measured a continuum of spectral slopes including "red" (Orus, Leucus), "less red" (Eurybates, Patroclus-Menoetius) and intermediate (Polymele), indicating a range of c…
The term "jumping" Trojan was introduced by Tsiganis et al. (2000) in their studies of long-term dynamics exhibited by the asteroid (1868) Thersites, which had been observed to jump from librations around L4 to librations around L5. Another example of a "jumping" Trojan was found by Connors et al. (2011): librations of the asteroid 2010 TK7 around the Earth's libration point L4 preceded by its librations around L5. We explore the dynamics of "jumping" Trojans under the scope of the restricted planar elliptical three-body problem. Via double numerical averaging we construct evolutionary equatio…
Current models of Solar System evolution posit that the asteroid populations in resonance with Jupiter are comprised of objects scattered inward from the outer Solar System during a period of dynamical instability. In this paper, we present a new analysis of the absolute magnitude and optical color distribution of Hilda asteroids, which lie in the 3:2 mean motion resonance with Jupiter, with the goal of comparing the bulk properties with previously published results from an analogous study of Jupiter Trojans. We report an updated power law fit of the Hilda magnitude distribution through H=14. …
The population of Neptune Trojans is believed to be bigger than that of Jupiter Trojans and that of asteroids in the main belt, although only eight members of this far distant asteroid swarm have been observed up to now. Six leading Neptune Trojans around the Lagrange point L4 discovered earlier have been studied in detail, but two trailing ones found recently around the L5 point, 2004 KV18 and 2008 LC18, have not been investigated yet. In this paper, we report our investigations on the dynamical behaviors of these two new Neptune Trojans. Our calculations show that the asteroid 2004 KV18 is a…
We explore the hypothesis that the population of Martian Trojans is the result of a balance between the production of new asteroids ("YORPlets") through the YORP effect and their eventual escape from the Trojan clouds through Yarkovsky-driven orbital evolution. Our principal observables are: (5261) Eureka, its family of 8 asteroids and the family-less Trojans (101429) 1998 VF31 & (121514) 1999 UJ7. We model the population evolution as a birth-death random process and assume it is in a steady state. We then simulate the discovery of Trojans to-date and find that family members of 101429 and 121…
