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 $\sim$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 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.
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. 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…
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…
The Earth Trojans are co-orbitals 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 TK$_7$) has been discovered serendipitously. Here, we present a dynamical study of asteroid 2020 XL$_5$. With our meticulous followup astrometric observations of the object, we confirmed that it is a new Earth Trojan. However, its eccentric orb…
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…
We have carried out an extensive study of the possibility of the detection of Earth-mass and super-Earth Trojan planets using transit timing variation method with the Kepler space telescope. We have considered a system consisting of a transiting Jovian-type planet in a short period orbit, and determined the induced variations in its transit timing due to an Earth-mass/super-Earth Trojan planet. We mapped a large section of the phase space around the 1:1 mean-motion resonance and identified regions corresponding to several other mean-motion resonances where the orbit of the planet would be stab…
The only discovery of Earth Trojan 2010 TK$_7$ and the subsequent launch of OSIRIS-REx motive us to investigate the stability around the triangular Lagrange points $L_4$ and $L_5$ of the Earth. In this paper we present detailed dynamical maps on the $(a_0,i_0)$ plane with the spectral number (SN) indicating the stability. Two main stability regions, separated by a chaotic region arising from the $ν_3$ and $ν_4$ secular resonances, are found at low ($i_0\leq 15^\circ$) and moderate ($24^\circ\leq {i_0}\leq 37^\circ$) inclinations respectively. The most stable orbits reside below $i_0=10^\circ$ …
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…
Aim. We construct a new arc model to represent the global perturbation induced by the Jupiter Trojans for the development of the modern planetary ephemerides. Methods. The Jupiter Trojans are divided into two groups: (1) the 226 biggest ones with absolute magnitudes $H<11$, have well determined masses and are treated as individual bodies; (2) the remaining small ones with $H\geqslant11$, are modeled by two discrete arcs centered at Jupiter's L4 and L5 points, respectively. Then we derived the parameters characterizing the arcs, such as the total mass, the mass ratio, and the spatial distributi…
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.
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…
Trojans are circumstellar bodies that reside in characteristic 1:1 orbital resonances with planets. While all the trojans in our Solar System are small (< ~100 km), stable planet-size trojans may exist in extrasolar planetary systems, and the Kepler telescope constitutes a formidable tool to search for them. Here we report on a systematic search for extrasolar trojan companions to 2244 known Kepler Objects of Interest (KOIs), with epicyclic orbital characteristics similar to those of the Jovian trojan families. No convincing trojan candidates are found, despite a typical sensitivity down to Ea…
Venus has three known co-orbitals: (322756) 2001 CK32, 2002 VE68 and 2012 XE133. The first two have absolute magnitudes 18 < H < 21. The third one, significantly smaller at H = 23.4 mag, is a recent discovery that signals the probable presence of many other similar objects: small transient companions to Venus that are also potentially hazardous asteroids (PHAs). Here, we study the dynamical evolution of the recently discovered asteroid 2013 ND15. At H = 24.1 mag, this minor body is yet another small Venus co-orbital and PHA, currently close to the Lagrangian point L4 and following the most ecc…
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）
Constraining the presence of exotrojans in hot Jupiter systems using TTV observations from TESS
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）；CSST Science Center for the Guangdong-Hong Kong-Macau Great Bay Area, Sun Yat-sen University（中山大学粤港澳大湾区宇宙科学中心）；Instituto de Astrofísica de Canarias (IAC)（加那利群岛天文研究所）；Departamento de Astrofísica, Universidad de La Laguna (ULL)（拉帕拉斯大学天体物理学系）；Hainan University（海南大学）
Of the four giant planets in the Solar system, only Jupiter and Neptune are currently known to possess swarms of Trojan asteroids - small objects that experience a 1:1 mean motion resonance with their host planet. In Lykawka et al. (2009), we performed extensive dynamical simulations, including planetary migration, to investigate the origin of the Neptunian Trojan population. Utilising the vast amount of simulation data obtained for that work, together with fresh results from new simulations, we here investigate the dynamical capture of Trojans by all four giant planets from a primordial trans…
Most co-orbital objects in the Solar system are thought to follow tadpole-type orbits, behaving as Trojans. However, most of Earth's identified co-orbitals are moving along horseshoe-type orbits. The current tally of minor bodies considered to be Earth co-orbitals amounts to 18; of them, 12 are horseshoes, five are quasi-satellites, and one is a Trojan. The semimajor axis values of all these bodies librate between $0.983$ au and $1.017$ au. In this work, we have studied the dynamical behaviour of objects following orbits with semimajor axis within this range that may be in a 1:1 mean-motion re…
We present a short review of the impact regime experienced by the terrestrial planets within our own Solar system, describing the three populations of potentially hazardous objects which move on orbits that take them through the inner Solar system. Of these populations, the origins of two (the Near-Earth Asteroids and the Long-Period Comets) are well understood, with members originating in the Asteroid belt and Oort cloud, respectively. By contrast, the source of the third population, the Short-Period Comets, is still under debate. The proximate source of these objects is the Centaurs, a popul…
Determining the size and orbital distribution of the population of near-Earth asteroids (NEAs) is the focus of intense research, with the most recent models converging to a population of approximately $1000$ NEAs larger than 1 km and up to approximately $10^9$ NEAs with absolute magnitude $H<30$. We present an analysis of the combined observations of nine of the leading asteroid surveys over the past two decades, and show that for an absolute magnitude $H<17.75$, which is often taken as proxy for an average diameter larger than 1 km, the population of NEAs is $920\pm10$, lower than other recen…
We analyzed data from the first year of a survey for Near Earth Objects (NEOs) that we are carrying out with the Dark Energy Camera (DECam) on the 4-meter Blanco telescope at the Cerro Tololo Inter-American Observatory. We implanted synthetic NEOs into the data stream to derive our nightly detection efficiency as a function of magnitude and rate of motion. Using these measured efficiencies and the Solar System absolute magnitudes derived by the Minor Planet Center for the 1377 measurements of 235 unique NEOs detected, we directly derive, for the first time from a single observational data set,…
Co-orbital bodies are the byproduct of planet formation and evolution, as we know from the Solar System. Although planet-size co-orbitals do not exists in our planetary system, dynamical studies show that they can remain stable for long periods of time in the gravitational well of massive planets. Should they exist, their detection is feasible with the current instrumentation. In this paper, we present new ground-based observations searching for these bodies co-orbiting with nine close-in (P<5 days) planets, using different observing techniques. The combination of all of them allows us to rest…
We continue to investigate the binary system Kepler-16, consisting of a K-type main-sequence star, a red dwarf, and a circumbinary Saturnian planet. As part of our study, we describe the system's habitable zone based on different climate models. We also report on stability investigations for possible Earth-mass Trojans while expanding a previous study by B. L. Quarles and collaborators given in 2012. For the climate models we carefully consider the relevance of the system's parameters. Furthermore, we pursue new stability simulations for the Earth-mass objects starting along the orbit of Keple…
Massive data mining of image archives observed with large etendue facilities represents a great opportunity for orbital amelioration of poorly known virtual impactor asteroids (VIs). There are more than 1000 VIs known today; most of them have very short observed arcs and many are considered lost as they became extremely faint soon after discovery. We aim to improve the orbits of VIs and eliminate their status by data mining the existing image archives. Within the European Near Earth Asteroids Research (EURONEAR) project, we developed the Virtual Impactor search using Mega-Precovery (VIMP) soft…
The dynamical structure of the Earth co-orbital region and implications for the near-Earth asteroid population
ESA ESRIN（欧洲空间局地球观测中心）；Deimos Italia s.r.l.（德伊莫斯意大利有限公司）；Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）；Observatoire de Paris, Université PSL, Sorbonne Université, Université de Lille, LNE, CNRS（巴黎天文台、PSL大学、索邦大学、里尔大学、法国国家科学研究中心）
The distribution of solar system absolute magnitudes ($H$) for the near-Earth asteroids (NEAs) observable near opposition -- i.e. Amors, Apollos, and Atens ($A^3$) -- is derived from the set of ALL currently known NEAs. The result is based only on common sense assumptions of uniformly random distributions and that the orbital phase space and $H$-magnitude distribution of known NEAs is representative of the total population. There is no population or other modeling and no assumption on albedo except in interpreting the result as a size-frequency distribution (SFD). The analysis is based on the …
Arjuna-type orbits are characterized by being Earth-like, having both low-eccentricity and low-inclination. Objects following these trajectories experience repeated trappings in the 1:1 commensurability with the Earth and can become temporary Trojans, horseshoe librators, quasi-satellites, and even transient natural satellites. Here, we review what we know about this peculiar dynamical group and use a Monte Carlo simulation to characterize geometrically the Arjuna orbital domain, studying its visibility both from the ground and with the European Space Agency Gaia spacecraft. The visibility ana…
We have carried out a search for Main Belt Asteroids (MBAs) co-orbiting with the large MBA Vesta and the dwarf planet Ceres. Through improving the search criteria used in (Christou, 2000b) and numerical integrations of candidate coorbitals, we have identified approximately 51 (44) objects currently in co-orbital libration with Ceres (Vesta). We show that these form part of a larger population of transient coorbitals; 129 (94) MBAs undergo episodes of co-orbital libration with Ceres (Vesta) within a 2 Myr interval centred on the present. The lifetime in the resonance is typically a few times 10…
