Earth Trojan Research Articles

MEGASIM: Distribution and Detection of Earth Trojan Asteroids

Using N-body simulation results from the MEGASIM data set, we present spatial distributions of Earth Trojan Asteroids and assess the detectability of the population in current and next-generation ground-based astronomical surveys. Our high-fidelity Earth Trojan Asteroid (ETA) distribution maps show never-before-seen high-resolution spatial features that evolve over timescales up to 1 Gyr. The simulation was synchronized to start times and timelines of two observational astronomy surveys: (1) the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST) and (2) the Zwicky Transient Facility (ZTF). We calculate upper limits for the number of ETAs potentially observable with both the ZTF and LSST surveys. Due to the Yarkovsky Effect, we find no stable ETAs on billion-year timescales likely to be detected by any ETA survey, as no C-type or S-type ETAs (with H < 22 and H < 24, respectively) are likely to be stable on billion-year timescales, and ETAs large enough to remain stable on billion-year timescales are very rare relative to the rest of the ETA population. We find that a twilight ETA survey will not drastically increase the likelihood of individual ETA detection, but it would provide orders of magnitude more observations of select ETA populations. The null detection to date from ZTF restricts the potential ETA population to hundreds of objects larger than 100 m (at H ≈ 22), while a null detection by LSST will further restrict the ETA population to tens of objects larger than 100 m.

A Rendezvous Mission to the Second Earth Trojan Asteroid 2020 XL5 with Low-Thrust Multi-Gravity Assist Techniques

As the second of Earth’s Trojan asteroids, 2020 XL5 is worthy of rendezvous and even sample return missions in many aspects. In this paper, a rendezvous mission to Earth’s second Trojan asteroid 2020 XL5 is proposed. However, due to its high inclination and large eccentricity, direct impulsive transfer requires large amounts of fuel consumption. To address this challenge, we explore the benefits of electric propulsion and multi-gravity assist techniques for interplanetary missions. These two techniques are integrated in this mission design. The design of a low-thrust gravity-assist (LTGA) trajectory in multi-body dynamics is thoroughly investigated, which is a complex process. A comprehensive framework including three steps is presented here for optimization of LTGA trajectories in multi-body dynamics. The rendezvous mission to 2020 XL5 is designed with this three-step approach. The most effective transfer sequence among the outcomes involves Earth–Venus–Earth–Venus-2020 XL5. Numerical results indicate that the combination of electric propulsion and multi-gravity assists can greatly reduce the fuel consumption, with fuel consumption of 9.03%, making it a highly favorable choice for this rendezvous mission.

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.

A Collision Mechanism for the Removal of Earth's Trojan Asteroids

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 (ETs). Dynamical simulations show that the parameter space for stable ETs is substantial, so their apparent absence poses a mystery. This work uses a large ensemble of N-body simulations to explore how the Trojan population dynamically responds if Earth suffers large collisions, such as those thought to have occurred to form the Moon and/or to have given Earth its late veneer. We show that such collisions can be highly disruptive to the primordial Trojan population, and could have eliminated it altogether. More specifically, if Earth acquired the final 1% of its mass through collisions, then only ∼1% of the previously bound Trojan population would remain.

Introducing MEGASIM: Multitudinous Earth Greek/Trojan Asteroid SIMulation*

Abstract We announce the completion of two new Earth Trojan Asteroid (ETA) simulations. ETAs co-orbit the Sun with Earth and remain loosely bound to the fourth or fifth Lagrange points. To date, two ETAs have been detected (2010 TK7 and 2020 XL5); however, based on their orbits, these are likely temporary captures rather than members of a primordial population. The motivation for our simulations is multi-faceted: (1) the lack of a detected population despite literature claims of stability over the age of the solar system, (2) ETAs are important for both solar system science and planetary defense, and (3) the proximity of ETAs makes them prime candidates for space exploration missions. These simulations are of extremely high fidelity, large in number and long in simulation time. We will be releasing a series of papers based upon these simulations.

Orbital stability analysis and photometric characterization of the second Earth Trojan asteroid 2020 XL5

Trojan asteroids are small bodies orbiting around the L4 or L5 Lagrangian points of a Sun-planet system. Due to their peculiar orbits, they provide key constraints to the Solar System evolution models. Despite numerous dedicated observational efforts in the last decade, asteroid 2010 TK7 has been the only known Earth Trojan thus far. Here we confirm that the recently discovered 2020 XL5 is the second transient Earth Trojan known. To study its orbit, we used archival data from 2012 to 2019 and observed the object in 2021 from three ground-based observatories. Our study of its orbital stability shows that 2020 XL5 will remain in L4 for at least 4 000 years. With a photometric analysis we estimate its absolute magnitude to be {H}_{r}=18.5{8}_{-0.15}^{+0.16}, and color indices suggestive of a C-complex taxonomy. Assuming an albedo of 0.06 ± 0.03, we obtain a diameter of 1.18 ± 0.08 km, larger than the first known Earth Trojan asteroid.

A new entry for the elusive Earth Trojans

A new entry for the elusive Earth Trojans

The Second Earth Trojan 2020 XL5

Abstract The Earth Trojans are coorbitals librating around the Lagrange points L 4 or L 5 of the Sun–Earth system. Although many numerical studies suggest that they can maintain their dynamical status and be stable on timescales up to a few tens of thousands of years or even longer, they remain an elusive population. Thus far only one transient member (2010 TK7) has been discovered serendipitously. Here, we present a dynamical study of asteroid 2020 XL5. With our meticulous follow-up astrometric observations of the object, we confirmed that it is a new Earth Trojan. However, its eccentric orbit brings it close encounters with Venus on a frequent basis. Based on our N-body integration, we found that the asteroid was captured into the current Earth Trojan status in the fifteenth century, and then it has a likelihood of 99.5% to leave the L 4 region within the next ∼10 kyr. Therefore, it is most likely that 2020 XL5 is dynamically unstable over this timescale.

A Search for L4 Earth Trojan Asteroids Using a Novel Track-before-detect Multiepoch Pipeline

Abstract 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 2 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 less sky coverage. Additionally, we elaborate on previous upper-limit calculations using current asteroid population statistics and an extensive asteroid simulation to provide the most up-to-date population constraints. We find an L4 Earth Trojan population of for H = 13.93, for H = 16, and for H = 22.

A Drake Equation for Alien Artifacts

I propose a version of the Drake equation to include searching for alien artifacts, which may be located on the Moon, Earth Trojans, and Earth co-orbital objects. The virtue of searching for artifacts is their lingering endurance in space, long after they go dead. I compare a search for extraterrestrial artifacts (SETA) strategy with the existing listening to stars search for extraterrestrial intelligence (SETI) strategy. I construct a ratio of a SETA Drake equation for artifacts to the conventional Drake equation so that most terms cancel out. This ratio is a good way to debate the efficacy of SETI versus SETA. The ratio is the product of two terms: one is the ratio of the length of time that probes from extraterrestrial (ET) civilizations could be present in the near-Earth region to the length of time that ET civilizations transmit signals to the Solar System. The second term is the ratio of the respective origin volumes: the volume from which probes can come, which is affected by the long-term passage of stars near the Sun, to the volume of transmitting civilizations. Scenarios are quantified that suggest that looking for alien artifacts near Earth is a credible alternative approach relative to listening to stars. This argues for emphasis on artifact searches, ET archeology. I suggest study of existing high-resolution images of the Moon, imaging of the Earth Trojans and Earth co-orbitals, and probe missions to the latter two. Close inspection in these near-Earth regions, which also may hold primordial remnants of the early Solar System, yields concrete astronomical research.

Transient Terrestrial Trojans: Comparative Short-term Dynamical Evolution of 2010 TK7 and 2020 XL5

Abstract The Trojan asteroids of Mars and Jupiter are long-term stable, those of Earth are expected to be just transient companions. The first Trojan of our planet, 2010 TK7, was discovered in 2010 and its resonant state was found to be transient. Here, we provide a preliminary assessment of the current dynamical status and short-term orbital evolution of 2020 XL5, a recently discovered near-Earth asteroid that might be the second known representative of this elusive population. Our calculations show that the current orbit determination of 2010 TK7 is consistent with that of a robust, present-day, yet transient, L4 Earth Trojan. In sharp contrast, the current orbit determination of 2020 XL5 is still too uncertain and its orbital evolution too chaotic to confirm a current Trojan engagement with Earth, although the nominal orbit shows such a behavior. More observations are required to provide a conclusive answer.

An Earth Trojans search mission with asteroid flybys and rendezvous to 2010TK7

In this paper, a mission about Earth’s Trojan asteroids is proposed, which is a rendezvous mission to 2010TK7 with two flybys to Near Earth asteroids (NEAs), and then cruise around L4 point with a survey for potential Earth’s Trojan asteroids around L4. The flyby targets are searched in NEAs first. Flyby sequence 1949 ​MA-2003LC5 is chosen among the search results. The low-thrust transfer trajectories are designed with two parts using indirect method. One part is the transfer trajectory corresponding to the Earth-1949MA-2003LC5-2010TK7 flyby sequence, and the other is the transfer trajectory from 2010TK7 to the cruise orbit. Intermediate orbit is designed to observe asteroid 2010TK7. The cruise orbit is a quasi-periodic orbit restricted in the stable region of Earth’s Trojan asteroids so as to search more Earth’s Trojan asteroids. For a spacecraft with initial mass of 300 ​kg, the total fuel consumption of this mission is 42.184%.

Search for L5 Earth Trojans with DECam.

Most of the major planets in the Solar System support populations of co-orbiting bodies, known as Trojans, at their L4 and L5 Lagrange points. In contrast, Earth has only one known co-orbiting companion. This paper presents the results from a search for Earth Trojans using the DECam instrument on the Blanco Telescope at CTIO. This search found no additional Trojans in spite of greater coverage compared to previous surveys of the L5 point. Therefore, the main result of this work is to place the most stringent constraints to date on the population of Earth Trojans. These constraints depend on assumptions regarding the underlying population properties, especially the slope of the magnitude distribution (which in turn depends on the size and albedo distributions of the objects). For standard assumptions, we calculate upper limits to a 90% confidence limit on the L5 population of N ET < 1 for magnitude H < 15.5, N ET =60-85 for H < 19.7, and N ET = 97 for H=20.4. This latter magnitude limit corresponds to Trojans ∼300 m in size for albedo 0.15. At H=19.7, these upper limits are consistent with previous L4 Earth Trojan constraints and significantly improve L5 constraints.

The case for a deep search for Earth’s Trojan asteroids

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.

Solar Sail Transfers and Trajectory Design to Sun-Earth L4, L5: Solar Observations and Potential Earth Trojan Exploration

The Sun-Earth triangular Lagrange point, L5, offers an ideal location to monitor the space weather. Furthermore, L4, L5 may harbor Earth ‘Trojan’ asteroids and space dust that are of significant interest to the scientific community. No spacecraft has, thus far, entered an orbit in the vicinity of Sun-Earth triangular points in part because of high propellant costs. By incorporating solar sail dynamics in the model representing CR3BP, the concept of a mission to L4, L5 can be re-evaluated and the total ΔV can be reconsidered. A solar sail is employed to increase the energy of the spacecraft and deliver the spacecraft to an orbit about an artificial Lagrange point by leveraging solar radiation pressure and, potentially, without any insertion ΔV.

Orbital stability of Earth Trojans

The only discovery of Earth Trojan 2010 TK7 and the subsequent launch of OSIRIS-REx have motived us to investigate the stability around the triangular Lagrange points of the Earth, L4 and L5. In this paper we present detailed dynamical maps on the (a0, i0) plane with the spectral number (SN) indicating the stability. Two main stability regions, separated by a chaotic region arising from the ν3 and ν4 secular resonances, are found at low (i0 ≤ 15°) and moderate (24 ° ≤i0 ≤ 37°) inclinations, respectively. The most stable orbits reside below i0 = 10° and they can survive the age of the solar system. The nodal secular resonance ν13 could vary the inclinations from 0° to ∼10° according to their initial values, while ν14 could pump up the inclinations to ∼20° and upwards. The fine structures in the dynamical maps are related to higher degree secular resonances, of which different types dominate different areas. The dynamical behaviour of the tadpole and horseshoe orbits, reflected in their secular precession, show great differences in the frequency space. The secular resonances involving the tadpole orbits are more sensitive to the frequency drift of the inner planets, thus the instabilities could sweep across the phase space, leading to the clearance of tadpole orbits. We are more likely to find terrestrial companions on horseshoe orbits. The Yarkovsky effect could destabilize Earth Trojans in varying degrees. We numerically obtain the formula describing the stabilities affected by the Yarkovsky effect and find the asymmetry between the prograde and retrograde rotating Earth Trojans. The existence of small primordial Earth Trojans that avoid being detected but survive the Yarkovsky effect for 4.5 Gyr is substantially ruled out.

OSIRIS-REx low-velocity particles during outbound cruise

We analyzed high-angular rate streaks first recorded by OSIRIS-REx’s MapCam during a 2017 search for Earth Trojan asteroids. We interpret them as water-ice particles that translated across the imager’s field of view, originating from the spacecraft itself. Their translation velocities approximated 0.1–1 m/s based on reasonable conclusions about their range. Pursuing several lines of investigation to seek a coherent hypothesis, we conclude that the episodic releases of the water ice particles are associated with spacecraft attitudes that resulted in solar illumination of previously shadowed regions. This correlation suggests that the OSIRIS-REx spacecraft itself possesses micro-climatic zones consisting of hot regions and cold traps that may temporarily potentially pass volatiles back and forth before losing most of them.

Solar system science with the Wide-Field Infrared Survey Telescope

We present a community-led assessment of the solar system investigations achievable with NASA’s next-generation space telescope, the Wide Field Infrared Survey Telescope (WFIRST). WFIRST will provide imaging, spectroscopic, and coronagraphic capabilities from 0.43 to 2.0 μm and will be a potential contemporary and eventual successor to the James Webb Space Telescope (JWST). Surveys of irregular satellites and minor bodies are where WFIRST will excel with its 0.28 deg2 field-of-view Wide Field Instrument. Potential ground-breaking discoveries from WFIRST could include detection of the first minor bodies orbiting in the inner Oort Cloud, identification of additional Earth Trojan asteroids, and the discovery and characterization of asteroid binary systems similar to Ida/Dactyl. Additional investigations into asteroids, giant planet satellites, Trojan asteroids, Centaurs, Kuiper belt objects, and comets are presented. Previous use of astrophysics assets for solar system science and synergies between WFIRST, Large Synoptic Survey Telescope, JWST, and the proposed Near-Earth Object Camera mission is discussed. We also present the case for implementation of moving target tracking, a feature that will benefit from the heritage of JWST and enable a broader range of solar system observations.

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.

Long term stability of Earth Trojans

We explore the long-term stability of Earth Trojans by using a chaos indicator, the Frequency Map Analysis. We find that there is an extended stability region at low eccentricity and for inclinations lower than about $$50^{\circ }$$ even if the most stable orbits are found at $$i \le 40^{\circ }$$ . This region is not limited in libration amplitude, contrary to what found for Trojan orbits around outer planets. We also investigate how the stability properties are affected by the tidal force of the Earth–Moon system and by the Yarkovsky force. The tidal field of the Earth–Moon system reduces the stability of the Earth Trojans at high inclinations while the Yarkovsky force, at least for bodies larger than 10 m in diameter, does not seem to strongly influence the long-term stability. Earth Trojan orbits with the lowest diffusion rate survive on timescales of the order of $$10^9$$ years but their evolution is chaotic. Their behaviour is similar to that of Mars Trojans even if Earth Trojans appear to have shorter lifetimes.