Mars Trojans Research Articles

Dynamics of 2023 FW14, the second L4 Mars trojan, and a physical characterization using the 10.4 m Gran Telescopio Canarias

Context. Known Mars trojans could be primordial small bodies that have remained in their present-day orbits for the age of the Solar System. Their orbital distribution is strongly asymmetric; there are over a dozen objects at the L5 point and just one at L4, (121514) 1999 UJ7. Most L5 trojans appear to form a collision-induced asteroid cluster, known as the Eureka family. Asteroid 2023 FW14 was recently discovered and it has a robust orbit determination that may be consistent with a Mars trojan status. Aims. Our aim is determine the nature and dynamical properties of 2023 FW14. Methods. We carried out an observational study of 2023 FW14 to derive its spectral class using the OSIRIS camera spectrograph at the 10.4 m Gran Telescopio Canarias. We investigated its possible trojan resonance with Mars using direct N-body simulations. Results. The reflectance spectrum of 2023 FW14 is not compatible with the olivine-rich composition of the Eureka family; it also does not resemble the composition of the Moon, although (101429) 1998 VF31 does. The Eureka family and 101429 are at the L5 point. The spectrum of 2023 FW14 is also different from two out of the three spectra in the literature of the other known L4 trojan, 121514, which are of C-type. The visible spectrum of 2023 FW14 is consistent with that of an X-type asteroid, as is the third spectrum of 121514. Our calculations confirm that 2023 FW14 is the second known L4 Mars trojan although it is unlikely to be primordial; it may remain in its present-day “tadpole” path for several million years before transferring to a Mars-crossing orbit. It might be a fragment of 121514, but a capture scenario seems more likely. Conclusions. The discovery of 2023 FW14 suggests that regular Mars-crossing asteroids can be captured as temporary Mars trojans.

Determination method of co-orbital objects in the solar system

ABSTRACT In this paper, based on two-dimensional maps from the semi-analytical Hamiltonian approach, we proposed an improved determination method to classify co-orbital objects in the solar system without numerical integration. Taking advantage of a simple pattern analysis, we present two certainty conditions to recognize co-orbital objects with uncertain orbital parameters. Then, our determination method is applied to classify potential co-orbital objects (PCOs) of Mars, Jupiter, Saturn, Uranus, and Neptune, and then their results are verified through numerical integration in the multiplanet model, respectively. Through our method, we identify 11 new co-orbital objects for the first time, including four Mars trojans i.e. tadpole (TP) objects, one short-term Mars quasi-satellite (QS), one Mars horseshoe (HS), one Jupiter QS, one short-term Uranus trojan, one Uranus PCO, and one Neptune PCO with short-term transitions between QS and HS, and one Neptune PCO with short-term transition between QS and TP. Numerical computation shows that except Saturn PCOs significantly perturbed by Jupiter, our determination method for co-orbital objects in the solar system is effective, but it cannot deal with the classification of PCOs near the boundary of different co-orbital regions. Since our method does not rely on time-consuming numerical integration, it is efficient and suitable for a large amount of screening for numerous co-orbital objects in the solar system.

Trajectory analysis for combined missions to mars and its Trojan Asteroids

While standalone missions to the Trojan Asteroids of Mars are costly, we analyze flyby scenarios of Mars Trojans, which can be achieved in combination with missions to Mars.

MEGASIM: Lifetimes and Resonances of Earth Trojan Asteroids—The Death of Primordial ETAs?

We present an analysis of lifetimes and resonances of Earth Trojan Asteroids (ETAs) in the MEGASIM data set. 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 (2010 TK7 and 2020 XL5), several Mars Trojans, and a Venus Trojan discovered. The estimated lifetimes of the known inner system Trojans are shorter than a million years, suggesting they are interlopers rather than members of a stable and long-lasting population. With the largest ETA n-body simulation to date, we are able to track their survival across a wide initialized parameter space. We find that the remaining fraction of ETAs over time is well fit with a stretched exponential function that, when extrapolated beyond our simulation run time, predicts zero ETAs by 2.33 Gyr. We also show correlations between ETA ejections and the periods of the Milankovitch cycles. Though Earth’s orbital dynamics dominate the instabilities of ETAs, we provide evidence that ETA ejections are linked to resonances found in the variation of the orbital elements of many if not all of the planets.

Using Mars co-orbitals to estimate the importance of rotation-induced YORP break-up events in Earth co-orbital space

ABSTRACT Both Earth and Mars host populations of co-orbital minor bodies. A large number of present-day Mars co-orbitals is probably associated with the fission of the parent body of Mars Trojan 5261 Eureka (1990 MB) during a rotation-induced Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) break-up event. Here, we use the statistical distributions of the Tisserand parameter and the relative mean longitude of Mars co-orbitals with eccentricity below 0.2 to estimate the importance of rotation-induced YORP break-up events in Martian co-orbital space. Machine-learning techniques (k-means++ and agglomerative hierarchical clustering algorithms) are applied to assess our findings. Our statistical analysis identified three new Mars Trojans: 2009 SE, 2018 EC4, and 2018 FC4. Two of them, 2018 EC4 and 2018 FC4, are probably linked to Eureka but we argue that 2009 SE may have been captured, so it is not related to Eureka. We also suggest that 2020 VT1, a recent discovery, is a transient Martian co-orbital of the horseshoe type. When applied to Earth co-orbital candidates with eccentricity below 0.2, our approach led us to identify some clustering, perhaps linked to fission events. The cluster with most members could be associated with Earth quasi-satellite 469219 Kamo‘oalewa (2016 HO3) that is a fast rotator. Our statistical analysis identified two new Earth co-orbitals: 2020 PN1, which follows a horseshoe path, and 2020 PP1, a quasi-satellite that is dynamically similar to Kamo‘oalewa. For both Mars and Earth co-orbitals, we found pairs of objects whose values of the Tisserand parameter differ by very small amounts, perhaps hinting at recent disruption events. Clustering algorithms and numerical simulations both suggest that 2020 KZ2 and Kamo‘oalewa could be related.

Population control of Mars Trojans by the Yarkovsky & YORP effects

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 121514, if they exist, are intrinsically more difficult to detect than Eureka's. Their non-discovery can be used as evidence of their non-existence only under the assumption that their brightness relative to the parent asteroid is similar to that in the Eureka family. To find out how efficiently Mars Trojans are lost from the Trojan clouds due to the Yarkovsky effect, we carry out dynamical simulations of test particles originating from these parent bodies. We find that objects originating from Eureka and 121514 begin escaping after ~1 Gyr, but that those from 101429 are already lost by that time, probably due to that asteroid's proximity to an eccentricity-type secular resonance within Mars's co-orbital region. This is the likely cause behind the absence of Trojans in the orbital vicinity of 101429. In contrast, the solitary status of 121514 points to an intrinsic inability of the asteroid to produce YORPlets during the most recent ~20% of the solar system's history, a finding potentially related to 121514’s present, low angular momentum rotational state, unless the Eureka family formed rapidly during a single fission event.

A Martian origin for the Mars Trojan asteroids

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 {\mu}m, 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 present new near-infrared observations of two Trojans (311999 2007 NS2 and 385250 2001 DH47) and find that both exhibit an olivine-rich reflectance spectrum similar to Eureka's. These measurements confirm that the progenitor of the cluster has an achondritic composition. Olivine-rich reflectance spectra are rare amongst asteroids but are seen around the largest basins on Mars. They are also consistent with some Martian meteorites (e.g. Chassigny), and with the material comprising much of the Martian mantle. Using numerical simulations, we show that the Mars Trojans are more likely to be impact ejecta from Mars than captured olivine-rich asteroids transported from the main belt. This result links directly specific asteroids to debris from the forming planets.

The olivine-dominated composition of the Eureka family of Mars Trojan asteroids

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-dominated A, or Sa, taxonomic class. As Eureka itself is also an olivine-dominated asteroid, it is likely that all family asteroids share a common origin and composition. We discuss the significance of these results in terms of the origin of the martian Trojan population.

Yarkovsky-driven spreading of the Eureka family of Mars Trojans

Out of nine known stable Mars Trojans, seven appear to be members of an orbital grouping including the largest Trojan, Eureka. In order to test if this could be a genetic family, we simulated the long term evolution of a tight orbital cluster centered on Eureka. We explored two cases: cluster dispersal through planetary gravity alone over 1Gyr, and a 1Gyr evolution due to both gravity and the Yarkovsky effect. We find that the dispersal of the cluster in eccentricity is primarily due to dynamical chaos, while the inclinations and libration amplitudes are primarily changed by the Yarkovsky effect. Current distribution of the cluster members orbits is indicative of an initially tight orbital grouping that was affected by a negative acceleration (i.e. one against the orbital motion) consistent with the thermal Yarkovsky effect. We conclude that the cluster is a genetic family formed either in a collision or through multiple rotational fissions. The cluster’s age is on the order of 1Gyr, and its long-term orbital evolution is likely dominated by the seasonal, rather than diurnal, Yarkovsky effect. If confirmed, Gyr-scale dominance of the seasonal Yarkovsky effect may indicate suppression of the diurnal Yarkovsky drift by the related YORP effect. Further study of Mars Trojans is essential for understanding the long-term orbital and rotational dynamics of small bodies in the absence of frequent collisions.

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.

Three new stable L5 Mars Trojans

Abstract Mars was second to Jupiter in being recognized as the host of a population of Trojan minor bodies. Since 1990, five asteroids – 5261 Eureka, (101429) 1998 VF31, (121514) 1999 UJ7, 2001 DH47 and (311999) 2007 NS2 – have been identified as Mars Trojans, one L4 and four L5. Dynamical and spectroscopic evidence suggests that some Mars Trojans may be remnants of the original planetesimal population that formed in the terrestrial planets region. Here, we revisit the long-term dynamical evolution of the previously known Mars Trojans and show that 2011 SC191, 2011 SL25 and 2011 UN63 are also trailing (L5) Mars Trojans. They appear to be as stable as Eureka and may have been Trojans over the age of the Solar system. The fact that five Trojans move in similar orbits and one of them is a binary may point to the disruption of a larger body early in the history of the Solar system. Such a catastrophic event may also explain the apparently strong asymmetry in terms of number of objects (one versus seven) between the L4 and L5 regions. Future spectroscopic observations should be able to reject or confirm a putative common chemical signature that may lend further support to a collisional scenario.

An optimal Mars Trojan asteroid search strategy

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 motion perpendicular to Gaia's CCD array is less than 0.40 arcsec per second.

An optimal Earth Trojan asteroid search strategy

Abstract 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 are four known Mars Trojans, and one Earth Trojan has been recently discovered. We present a new model that constrains optimal search areas, and imaging cadences for narrow and wide-field survey telescopes including the Gaia satellite for the most efficient use of telescope time to maximize the probability of detecting additional Earth Trojans.

Composition of the L5 Mars Trojans: Neighbors, not siblings

Mars is the only terrestrial planet known to have Trojan (co-orbiting) asteroids, with a confirmed population of at least 4 objects. The origin of these objects is not known; while several have orbits that are stable on Solar System timescales, work by Rivkin et al. [Rivkin, A.S., Binzel, R.P., Howell, E.S., Bus, S.J., Grier, J.A., 2003. Icarus 165, 349–354] showed they have compositions that suggest separate origins from one another. We have obtained infrared (0.8–2.5 μm) spectroscopy of the two largest L5 Mars Trojans, and confirm and extend the results of Rivkin et al. We suggest that the differentiated angrite meteorites are good spectral analogs for 5261 Eureka, the largest Mars Trojan. Meteorite analogs for 101429 1998 VF31 are more varied and include primitive achondrites and mesosiderites.

Albedos and diameters of three Mars Trojan asteroids

We observed the Mars Trojan Asteroids (5261) Eureka and (101429) 1998 VF 31 and the candidate Mars Trojan 2001 FR 127 at 11.2 and 18.1 microns using Michelle on the Gemini North telescope. We derive diameters of 1.28, 0.78, and <0.52 km, respectively, with corresponding geometric visible albedos of 0.39, 0.32, and >0.14. The albedos for Eureka and 1998 VF 31 are consistent with the taxonomic classes and compositions (S(I)/angritic and S(VII)/achondritic, respectively) and implied histories presented in a companion paper by Rivkin et al. Eureka's surface likely has a relatively high thermal inertia, implying a thin regolith that is consistent with predictions and the small size that we derive.

Dynamics of Mars Trojans

In this paper we explore the dynamical stability of the Mars Trojan region applying mainly Laskar's Frequency Map Analysis. This method yields the chaotic diffusion rate of orbits and allows to determine the most stable regions. It also gives the frequencies which are responsible for the instability of orbits. The most stable regions are found for inclinations between about 15° and 30°. For inclinations smaller than 15°, we confirm, by applying a synthetic secular theory, that the secular resonances ν 3 , ν 4 , ν 13 , ν 14 rapidly excite asteroid orbits within a few Myrs, or even faster. The asteroids are removed from the Trojan region after a close encounter with Mars. For large inclinations, the secular resonance ν 5 clears a small region around 30° while the Kozai resonance rapidly removes bodies for inclinations larger than 35°. The dynamical lifetimes of the three L5 Trojans, (5261) Eureka, 1998 VF31, 2001 DH47, and the only L4 Trojan 1999 UJ7 are determined by numerically integrating clouds of corresponding clones over the age of the Solar System. All four Trojans reside in the most stable region with smallest diffusion coefficients. Their dynamical half-lifetime is of the order of the age of the Solar System. The Yarkovsky force has little effect on the known Trojans but for bodies smaller than about 1–5 m the drag is strong enough to destabilize Trojans on a timescale shorter than 4.5 Gyr.

A survey of orbits of co-orbitals of Mars

Many asteroids with a semimajor axis close to that of Mars have been discovered in the last several years. Potentially some of these could be in 1:1 resonance with Mars, much as are the classic Trojan asteroids with Jupiter, and its lesser-known horseshoe companions with Earth. In the 1990s, two Trojan companions of Mars, 5261 Eureka and 1998 VF 31, were discovered, librating about the L 5 Lagrange point, 60° behind Mars in its orbit. Although several other potential Mars Trojans have been identified, our orbital calculations show only one other known asteroid, 1999 UJ 7, to be a Trojan, associated with the L 4 Lagrange point, 60° ahead of Mars in its orbit. We further find that asteroid 36017 (1999 ND 43) is a horseshoe librator, alternating with periods of Trojan motion. This asteroid makes repeated close approaches to Earth and has a chaotic orbit whose behavior can be confidently predicted for less than 3000 years. We identify two objects, 2001 HW 15 and 2000 TG 2, within the resonant region capable of undergoing what we designate “circulation transition”, in which objects can pass between circulation outside the orbit of Mars and circulation inside it, or vice versa. The eccentricity of the orbit of Mars appears to play an important role in circulation transition and in horseshoe motion. Based on the orbits and on spectroscopic data, the Trojan asteroids of Mars may be primordial bodies, while some co-orbital bodies may be in a temporary state of motion.

Spectroscopy and photometry of Mars Trojans

Mars is the only terrestrial planet known to have co-orbiting “Trojan” asteroids. We have obtained visible and near-IR reflectance spectra of three of these objects: 5261 Eureka and 1998 VF31 in the L5 region and 1999 UJ7 in the L4 region. We also obtained JHK spectrophotometry and a visible lightcurve for 5261 Eureka. The asteroid 5261 Eureka has a visible spectrum that is classified as Sr in the Bus taxonomy, and has infrared colors consistent with the A-class asteroids. The data for 1998 VF31 have a restricted wavelength range, but are most consistent with the Sr or Sa class, though we note a marginal consistency with the D class. We can rule out a C-class classification. 1999 UJ7 has an X-class or T-class spectrum, which is unlike that of the other two Mars Trojans. The photometric data for Eureka are limited, but we can constrain the period to longer than 5 hours (likely 5.5–6 hours) and lightcurve amplitude of at least 0.15 magnitude at this viewing geometry. The spectral differences among the Mars Trojans suggests that either they did not all form at their present solar distances or that they have not always been at their present sizes.

The role of secular resonances on trojans of the terrestrial planets

We investigate the role of secular resonances on the motion of terrestrial-planet trojans in tadpole motion for 5 Myr in the inclination range i ≤ 90°. We use a Fourier spectrum of the eccentricity vector, e, and angular momentum vector, L. When i > 40°, the trojans are in a Kozai resonance with Jupiter, which increases the eccentricity to planet-crossing values on a time-scale of 0.1 Myr; hence we found no stable trojan motion when i > 40°. Trojans of Mercury are unstable for a large range in inclination due to the resonances v 1 , v 1 2 and v 5 , and only those with low and high inclinations survived in our simulations. For Venus and Earth trojans, the v 3 and v 4 secular resonances with the Earth and Mars respectively increase the eccentricity to planet-crossing values for moderate inclinations. Venus trojans are also affected by the v 1 1 resonance with Mercury at high inclinations hence Venus and Earth trojans are stable only at low inclinations. Mars trojans are affected by the v 3 , v 4 , v 1 3 and v 1 4 resonances with the Earth and Mars for low inclinations which increase the eccentricity and suppress oscillations of the inclination. At i = 32°, the v 5 resonance destabilizes Mars trojans, although its width is less than a degree in inclination. The typical lifetime of inner-planet trojans trapped in a secular resonance is 1 Myr for Venus, Earth and Mars trojans, while it is 10 5 yr for Mercury trojans. Trojans in secular resonances are chaotic on time-scales of 10 3 -10 4 yr for all inner planets, while outside the resonances this becomes typically 10 6 yr.

The Dynamics of the Trojan Asteroids

The state of the art in the dynamics of the Trojan asteroids has progressed rapidly, since it has been possible to perform numerical integrations of many orbits for millions of years. Accurate proper elements are now computed by the synthetic method, that is from the output of a numerical integration; their stability, at least for time spans of a few million years, is good. This has allowed identification of Trojan families with an automated procedure closely mimicking the one used in the main belt. Although the families identified in a reliable way are only four, the occurrence of significant collisional evolution, not unlike that of the main belt, can be confirmed. The dynamical structure of the Trojan cloud, including the location of the main secular resonances, can be deduced from the proper elements and frequencies by a simple fit. However, many problems are not solved: the origin of a significant percentage of chaotic orbits showing no indications of instability; the location of the stability boundary of the Trojan cloud; the origin of the high inclination of most Trojans. We also do not know if there are “Trojans” for some other planets beside Jupiter: only one Mars Trojan has been found.