In a previous paper, we have presented a global view of the stability of Neptune Trojan (NT hereafter) on inclined orbit. We discuss in this paper the dependence of stability of NT orbits on the eccentricity. High-resolution dynamical maps are constructed using the results of extensive numerical integrations of orbits initialized on the fine grids of initial semimajor axis (a0) versus eccentricity (e0). The extensions of regions of stable orbits on the (a0, e0) plane at different inclinations are shown. The maximum eccentricities of stable orbits in three most stable regions at low (0, 12deg.), medium (22,36deg.) and high (51, 59deg.) inclination, are found to be 0.10, 0.12 and 0.04, respectively. The fine structures in the dynamical maps are described. Via the frequency analysis method, the mechanisms that portray the dynamical maps are revealed. The secondary resonances, concerning the frequency of the librating resonant angle and the frequency of the quasi 2:1 mean motion resonance between Neptune and Uranus, are found deeply involved in the motion of NTs. Secular resonances are detected and they also contribute significantly to the triggering of chaos in the motion. Particularly, the effects of the secular resonance v8, v18 are clarified.
We also investigate the orbital stabilities of six observed NTs by checking the orbits of hundreds clones of them generated within the observing error bars. We conclude that four of them, except 2001 QR322 and 2005 TO74, are deeply inside the stable region. The 2001 QR322 is in the close vicinity of the most significant secondary resonance. The 2005 TO74 locates close to the boundary separating stable orbits from unstable ones, and it may be influenced by a secular resonance.
The present-day orbit distribution of the Neptune Trojans is a powerful probe of the dynamical environment of the outer solar system during the late stages of planet migration. In this work, I conservatively debias the inclination, eccentricity, and libration amplitude distributions of the Neptune Trojans by reducing a priori unknown discovery and follow-up survey properties to nuisance parameters and using a likelihood-free Bayesian rejection sampler for parameter estimation. Using this survey-agnostic approach, I confirm that the Neptune Trojans are a dynamically excited population: at $>$95…
In this work we report the detection of seven Neptune Trojans (NTs) in the Pan-STARRS 1 (PS1) survey. Five of these are new discoveries, consisting of four L4 Trojans and one L5 Trojan. Our orbital simulations show that the L5 Trojan stably librates for only several million years. This suggests that the L5 Trojan must be of recent capture origin. On the other hand, all four new L4 Trojans stably occupy the 1:1 resonance with Neptune for more than 1 Gyr. They can, therefore, be of primordial origin. Our survey simulation results show that the inclination width of the Neptune Trojan population s…
The fact that the Centaurs are the primary source of the Short Period Comets is well established. However, the origin of the Centaurs themselves is still under some debate, with a variety of different source reservoirs being proposed in the last decade. In this work, we suggest that the Neptune Trojans (together with the Jovian Trojans) could represent an additional significant source of Centaurs. Using dynamical simulations of the first Neptune Trojan discovered (2001 QR322), together with integrations following the evolution of clouds of theoretical Neptune Trojans obtained during simulation…
We present the results of detailed dynamical simulations of the effect of the migration of the four giant planets on both the transport of pre-formed Neptune Trojans, and the capture of new Trojans from a trans-Neptunian disk. We find that scenarios involving the slow migration of Neptune over a large distance (50Myr to migrate from 18.1AU to its current location) provide the best match to the properties of the known Trojans. Scenarios with faster migration (5Myr), and those in which Neptune migrates from 23.1AU to its current location, fail to adequately reproduce the current day Trojan popul…
We present the discovery of a long-term stable L5 (trailing) Neptune Trojan in data acquired to search for candidate Trans-Neptunian objects for the New Horizons spacecraft to fly by during an extended post-Pluto mission. This Neptune Trojan, 2011 HM102, has the highest inclination (29.4 degrees) of any known member of this population. It is intrinsically brighter than any single L5 Jupiter Trojan at H~8.18. We have determined its gri colors (a first for any L5 Neptune Trojan), which we find to be similar to the moderately red colors of the L4 Neptune Trojans, suggesting similar surface proper…
The Neptune Trojans are the most recently discovered population of small bodies in the Solar System. To date, only eight have been discovered, though it is thought likely that the total population at least rivals that of the asteroid belt. Their origin is still the subject of some debate. Here, we detail the results of dynamical studies of two Neptune Trojans, 2001 QR322 and 2008 LC18. We find that both objects lie very close to boundaries between dynamically stable and unstable regions, with a significant probability that either or both of the objects are actually unstable on timescales of a …
Neptune Trojans and Plutinos are two subpopulations of trans-Neptunian objects located in the 1:1 and the 3:2 mean motion resonances with Neptune, respectively, and therefore protected from close encounters with the planet. However, the orbits of these two kinds of objects may cross very often, allowing a higher collisional rate between them than with other kinds of trans-Neptunian objects, and a consequent size distribution modification of the two subpopulations. Observational colors and absolute magnitudes of Neptune Trojans and Plutinos show that i) there are no intrinsically bright (large)…
We explore planetary migration scenarios for formation of high inclination Neptune Trojans (NTs) and how they are affected by the planetary migration of Neptune and Uranus. If Neptune and Uranus's eccentricity and inclination were damped during planetary migration, then their eccentricities and inclinations were higher prior and during migration than their current values. Using test particle integrations we study the stability of primordial NTs, objects that were initially Trojans with Neptune prior to migration. We also study Trans-Neptunian objects captured into resonance with Neptune and be…
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…
In this work, we investigate the dynamical stability of pre-formed Neptune Trojans under the gravitational influence of the four giant planets in compact planetary architectures, over 10 Myr. In our modelling, the initial orbital locations of Uranus and Neptune (aN) were varied to produce systems in which those planets moved on non-resonant orbits, or in which they lay in their mutual 1:2, 2:3 and 3:4 mean-motion resonances (MMRs). In total, 420 simulations were carried out, examining 42 different architectures, with a total of 840000 particles across all runs. In the non-resonant cases, the T…
Close encounters (CEs) between celestial objects may exert significant influence on their orbits. The influence will be even enhanced when two groups of celestial objects are confined in stable orbital configurations, e.g. in adjacent mean motion resonances (MMRs). Plutinos and Neptune Trojans, trapped in the 2:3 and 1:1 MMRs with Neptune respectively, are such examples. %Meanwhile, many objects among these two groups have peculiar orbits, seemingly as the vestige of CEs. As the first part of our investigation, this paper provides a detailed description of CEs between Plutinos and Trojans and …
We present results examining the fate of the Trojan clouds produced in our previous work. We find that the stability of Neptunian Trojans seems to be strongly correlated to their initial post-migration orbital elements, with those objects that survive as Trojans for billions of years displaying negligible orbital evolution. The great majority of these survivors began the integrations with small eccentricities (e < 0.2) and small libration amplitudes (A < 30 - 40°). The survival rate of "pre-formed" Neptunian Trojans (which in general survived on dynamically cold orbits (e < 0.1, i < 5 - 10°)) …
Since early work on the stability of the first Neptunian Trojan, 2001 QR322, suggested that it was a dynamically stable, primordial body, it has been assumed this applies to both that object, and its more recently discovered brethren. However, it seems that things are no longer so clear cut. In this work, we present the results of detailed dynamical simulations of the orbital behaviour of 2001 QR322. Using an ephemeris for the object that has significantly improved since earlier works, we follow the evolution of 19683 test particles, placed on orbits within the observational error ellipse of 2…
The minor planets on orbits that are dynamically stable in Neptune's 1:1 resonance on Gyr timescales were likely emplaced by Neptune's outward migration. We explore the intrinsic libration amplitude, eccentricity, and inclination distribution of Neptune's stable Trojans, using the detections and survey efficiency of the Outer Solar System Origins Survey (OSSOS) and Pan-STARRS1. We find that the libration amplitude of the stable Neptunian Trojan population can be well modeled as a Rayleigh distribution with a libration amplitude width $σ_{A_phi}$ of 15$^\circ$. When taken as a whole, the Neptun…
In this work we present the results of a suite of dynamical simulations following the orbital evolution of 8,022 hypothetical Centaur objects. These Centaurs begin our integrations on orbits in the vicinity of the 2:1 mean motion resonance with Neptune, and we follow their dynamical evolution for a period of 3 Myr under the gravitational influence of a motionless Sun and the four Jovian planets. The great majority of the test particles studied rapidly escaped from the vicinity of the 2:1 mean motion resonance of Neptune and diffused throughout the Solar System. The average libration time of Ce…
The stability of Trojan type orbits around Neptune is studied. As the first part of our investigation, we present in this paper a global view of the stability of Trojans on inclined orbits. Using the frequency analysis method based on the FFT technique, we construct high resolution dynamical maps on the plane of initial semimajor axis $a_0$ versus inclination $i_0$. These maps show three most stable regions, with $i_0$ in the range of $(0^\circ,12^\circ), (22^\circ,36^\circ)$ and $(51^\circ,59^\circ)$ respectively, where the Trojans are most probably expected to be found. The similarity betwee…
The Neptune Trojans are the most recent addition to the panoply of Solar system small body populations. The orbit of the first discovered member, 2001 QR$_{322}$, was investigated shortly after its discovery, based on early observations of the object, and it was found to be dynamically stable on timescales comparable to the age of the Solar system. As further observations were obtained of the object over the following years, the best-fit solution for its orbit changed. We therefore carried out a new study of 2001 QR$_{322}$'s orbit in 2010, finding that it lay on the boundary between dynamical…
We present an ultra-deep survey for Neptune Trojans using the Subaru 8.2-m and Magellan 6.5-m telescopes. The survey reached a 50% detection efficiency in the R-band at 25.7 magnitudes and covered 49 square degrees of sky. This depth corresponds to Neptune Trojans that are about 16 km in radius (assuming an albedo of 0.05). A paucity of smaller Neptune Trojans (radii < 45 km) compared to larger ones was found. The brightest Neptune Trojans appear to follow a steep power-law slope (q = 5+-1) similar to the brightest objects in the other known stable reservoirs such as the Kuiper Belt, Jupiter T…
The recent discovery of the first Neptune Trojan at the planet's trailing (L5) Lagrange point, 2008 LC18, offers an opportunity to confirm the formation mechanism of a member of this important tracer population for the Solar system's dynamical history. We tested the stability of 2008 LC18's orbit through a detailed dynamical study, using test particles spread across the orbital uncertainties in a, e, i and Ω. This showed that the wide uncertainties of the published orbit span regions of both extreme dynamical instability, with lifetimes < 100 Myr, and with significant stability (> 1 Gyr lifeti…
We report the discovery of the eighth and ninth known Trojans in stable orbits around Neptune's leading Lagrange point, L4. The objects 2014 QO$_{441}$ and 2014 QP$_{441}$ were detected in data obtained during the 2013-14 and 2014-15 observing seasons by the Dark Energy Survey, using the Dark Energy Camera (DECam) on the 4-meter Blanco telescope at Cerro Tololo Inter-American Observatory. Both are in high-inclination orbits (18.8$^{\circ}$ and 19.4$^{\circ}$ respectively). With an eccentricity of 0.104, 2014 QO$_{441}$ has the most eccentric orbit of the eleven known stable Neptune Trojans. He…
The Trojan asteroids of Jupiter and Neptune are likely to have been captured from original heliocentric orbits in the dynamically excited ("hot") population of the Kuiper belt. However, it has long been known that the optical color distributions of the Jovian Trojans and the hot population are not alike. This difference has been reconciled with the capture hypothesis by assuming that the Trojans were resurfaced (for example, by sublimation of near-surface volatiles) upon inward migration from the Kuiper belt (where blackbody temperatures are $\sim$40 K) to Jupiter's orbit ($\sim$125 K). Here, …
We have performed a detailed dynamical study of the recently identified Neptunian Trojan 2004 KV18, only the second object to be discovered librating around Neptune's trailing Lagrange point, L5. We find that 2004 KV18 is moving on a highly unstable orbit, and was most likely captured from the Centaur population at some point in the last ~1 Myr, having originated in the Scattered Disk, beyond the orbit of Neptune. The instability of 2004 KV18 is so great that many of the test particles studied leave the Neptunian Trojan cloud within just ~0.1 - 0.3 Myr, and it takes just 37 million years for h…
Early migration damped Neptune's eccentricity. Here, we assume that the damped value was much smaller than the value observed today, and show that the closest flyby of $\sim 0.1 \; \mathrm{M_{\odot}}$ star over $\sim 4.5 \mathrm{\; Gyr}$ in the field, at a distance of $\sim 10^3 \mathrm{\; AU}$ would explain the value of Neptune's eccentricity observed today.
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…
Neptune's dynamical history shaped the current orbits of Kuiper belt objects (KBOs), leaving clues to the planet's orbital evolution. In the "classical" region, a population of dynamically "hot" high-inclination KBOs overlies a flat "cold" population with distinct physical properties. Simulations of qualitatively different histories for Neptune -including smooth migration on a circular orbit or scattering by other planets to a high eccentricity - have not simultaneously produced both populations. We explore a general Kuiper belt assembly model that forms hot classical KBOs interior to Neptune …
The orbital distribution of trans-Neptunian objects provides strong evidence for the radial migration of Neptune. The outer planets' orbits are thought to have become unstable during the early stages with Jupiter having scattering encounters with a Neptune-class planet. As a consequence, Jupiter jumped inward by a fraction of an au, as required from inner solar system constraints, and obtained its current orbital eccentricity. The timing of these events is often linked to the lunar Late Heavy Bombardment that ended ~700 Myr after the dispersal of the protosolar nebula (t_0). Here we show inste…
The link between the dynamical evolution of the giant planets and the Kuiper Belt orbital structure can provide clues and insight about the dynamical history of the Solar System. The classical region of the Kuiper Belt has two populations (the cold and hot populations) with completely different physical and dynamical properties. These properties have been explained in the framework of a subset of the simulations of the Nice Model, in which Neptune remained on a low-eccentricity orbit (Neptune's eccentricity is never larger than 0.1) throughout the giant planet instability. However, recent simu…
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…
The dynamical structure of the Kuiper belt can be used as a clue to the formation and evolution of the Solar System, planetary systems in general, and Neptune's early orbital history in particular. The problem is best addressed by forward modeling where different initial conditions and Neptune's orbital evolutions are tested, and the model predictions are compared to orbits of known Kuiper belt objects (KBOs). It has previously been established that Neptune radially migrated, by gravitationally interacting with an outer disk of planetesimals, from the original radial distance r < 25 au to its …
The current dynamical structure of the Kuiper belt was shaped by the orbital evolution of the giant planets, especially Neptune, during the era following planet formation, when the giant planets may have undergone planet-planet scattering and/or planetesimal-driven migration. Numerical simulations of this process, while reproducing many properties of the belt, fail to generate the high inclinations and eccentricities observed for some objects while maintaining the observed dynamically "cold" population. We present the first of a three-part parameter study of how different dynamical histories o…
We use numerical integrations to investigate the dynamical evolution of resonant Trojan and quasi-satellite companions during the late stages of migration of the giant planets Jupiter, Saturn, Uranus, and Neptune. Our migration simulations begin with Jupiter and Saturn on orbits already well separated from their mutual 2:1 mean-motion resonance. Neptune and Uranus are decoupled from each other and have orbital eccentricities damped to near their current values. From this point we adopt a planet migration model in which the migration speed decreases exponentially with a characteristic timescale…
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…
We report the discovery of an eccentric hot Neptune and a non-transiting outer planet around TOI-1272. We identified the eccentricity of the inner planet, with an orbital period of 3.3 d and $R_{\rm p,b} = 4.1 \pm 0.2$ $R_\oplus$, based on a mismatch between the observed transit duration and the expected duration for a circular orbit. Using ground-based radial velocity measurements from the HIRES instrument at the Keck Observatory, we measured the mass of TOI-1272b to be $M_{\rm p,b} = 25 \pm 2$ $M_\oplus$. We also confirmed a high eccentricity of $e_b = 0.34 \pm 0.06$, placing TOI-1272b among…
Observations of Kuiper belt objects (KBOs) in Neptune's 5:2 resonance present two puzzles: this third order resonance hosts a surprisingly large population, comparable to the prominent populations of Plutinos and Twotinos in the first order 3:2 and 2:1 resonances, respectively; secondly, their eccentricities are concentrated near $0.4$. To shed light on these puzzles, we investigate the phase space near this resonance with use of Poincaré sections of the circular planar restricted three body model. We find several transitions in the phase space structure with increasing eccentricity, which we …
We report the discovery of HIP-97166b (TOI-1255b), a transiting sub-Neptune on a 10.3-day orbit around a K0 dwarf 68 pc from Earth. This planet was identified in a systematic search of TESS Objects of Interest for planets with eccentric orbits, based on a mismatch between the observed transit duration and the expected duration for a circular orbit. We confirmed the planetary nature of HIP-97166b with ground-based radial velocity measurements and measured a mass of $M_{b} =$ 20 $\pm$ 2 $M_\bigoplus$ along with a radius of $R_{b} =$ 2.7 $\pm$ 0.1 $R_\bigoplus$ from photometry. We detected an add…
The Scattered Disk Objects (SDOs) are thought to be a small fraction of the ancient population of leftover planetesimals in the outer solar system that were gravitationally scattered by the giant planets and have managed to survive primarily by capture and sticking in Neptune's exterior mean motion resonances (MMRs). In order to advance understanding of the role of MMRs in the dynamics of the SDOs, we investigate the phase space structure of a large number of Neptune's MMRs in the semi-major axis range 33--140~au by use of Poincaré sections of the circular planar restricted three body model fo…
Most Neptune-mass planets in close-in orbits (orbital periods less than a few days) present nonzero eccentricity, typically around 0.15. This is somehow unexpected, as these planets undergo strong tidal dissipation that should circularize their orbits in a time-scale shorter than the age of the system. In this paper we discuss some mechanisms that can oppose to bodily tides, namely, thermal atmospheric tides, evaporation of the atmosphere, and excitation from a distant companion. In the first two cases, the eccentricity can increase consistently, while in the last one, the eccentricity can onl…
GJ436b is a unique member of the transiting extrasolar planet population being one of the smallest and least irradiated and possessing an eccentric orbit. Because of its size, mass and density, GJ436b could plausibly have an atmospheric metallicity similar to Neptune (20-60 times solar abundances), which makes it an ideal target to study the effects of atmospheric metallicity on dynamics and radiative transfer in an extrasolar planetary atmosphere. We present three-dimensional atmospheric circulation models that include realistic non-gray radiative transfer for 1, 3, 10, 30, and 50 times solar…
We present the confirmation of a new sub-Neptune close to the transition between super-Earths and sub-Neptunes transiting the M2 dwarf TOI- 269 (TIC 220479565, V = 14.4 mag, J = 10.9 mag, Rstar = 0.40 Rsun, Mstar = 0.39 Msun, d = 57 pc). The exoplanet candidate has been identified in multiple TESS sectors, and validated with high-precision spectroscopy from HARPS and ground-based photometric follow-up from ExTrA and LCO-CTIO. We determined mass, radius, and bulk density of the exoplanet by jointly modeling both photometry and radial velocities with juliet. The transiting exoplanet has an orbit…
TOI-216 hosts a pair of warm, large exoplanets discovered by the TESS Mission. These planets were found to be in or near the 2:1 resonance, and both of them exhibit transit timing variations (TTVs). Precise characterization of the planets' masses and radii, orbital properties, and resonant behavior can test theories for the origins of planets orbiting close to their stars. Previous characterization of the system using the first six sectors of TESS data suffered from a degeneracy between planet mass and orbital eccentricity. Radial velocity measurements using HARPS, FEROS, and PFS break that de…
There are excesses of sub-Neptunes just wide of period commensurabilities like the 3:2 and 2:1, and corresponding deficits narrow of them. Any theory that explains this period ratio structure must also explain the strong transit timing variations (TTVs) observed near resonance. Besides an amplitude and a period, a sinusoidal TTV has a phase. Often overlooked, TTV phases are effectively integration constants, encoding information about initial conditions or the environment. Many TTVs near resonance exhibit non-zero phases. This observation is surprising because dissipative processes that captur…
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…
We report the detection of the Rossiter-McLaughlin effect for the eccentric, super-Neptune exoplanet HAT-P-11b, based on radial velocity measurements taken with HDS mounted on the Subaru 8.2m telescope, and simultaneous photometry with the FTN 2.0m telescope, both located in Hawai'i. The observed radial velocities during a planetary transit of HAT-P-11b show a persistent blue-shift, suggesting a spin-orbit misalignment in the system. The best-fit value for the projected spin-orbit misalignment angle is $λ= 103_{-19}^{+23}$ deg. Our result supports the notion that eccentric exoplanetary systems…
The stability of eight nominal fictitious Uranus Trojan orbits over the age of the Solar system has been measured. The initial inclinations, i0, were 0 deg., 5 deg., 15 deg., and 30 deg. relative to the ecliptic plane. Initial eccentricities ranged from 0 to 0.1 for i0 = 0 deg., 5 deg., and 0 to 0.2 for i0 = 15 deg., 30 deg. Half of the orbits were in the L4 swarm, and half were in the L5 swarm. Orbits in the L4 swarm had mean longitudes 8.8 deg. from the nominal L4 Lagrange point, and orbits in the L5 swarm had mean longitudes 18.2 deg. from the nominal L5 point. I integrated 10,000 massless …
Approximately 10-20% of all Kuiper belt objects (KBOs) occupy mean-motion resonances with Neptune. This dynamical configuration likely resulted from resonance capture as Neptune migrated outward during the late stages of planet formation. The details of Neptune's planetesimal-driven migration, including its radial extent and the concurrent eccentricity evolution of the planet, are the subject of considerable debate. Two qualitatively different proposals for resonance capture have been proposed--migration-induced capture driven by smooth outward evolution of Neptune's orbit and chaotic capture …
With the growth of comparative exoplanetology, it is increasingly clear that investigating the relationships between inner and outer planets plays a key role in discriminating between competing formation and evolution models. To do so, it is important to probe the inner region of systems hosting long-period giants in search for undetected lower-mass planetary companions. In this work we present our results on the K-dwarf star BD-11~4672, already known to host a long-period giant planet, as the first output of a subsample of the GAPS programme specifically aimed at assessing the impact of ineff…
We report observations of the Jupiter Trojan asteroid (3548) Eurybates and its satellite Queta with the Hubble Space Telescope and use these observations to perform an orbital fit to the system. Queta orbits Eurybates with a semimajor axis of $2350\pm11$ km at a period of $82.46\pm0.06$ days and an eccentricity of $0.125\pm0.009$. From this orbit we derive a mass of Eurybates of $1.51\pm0.03 \times 10^{17}$ kg, corresponding to an estimated density of $1.1\pm0.3$ g cm$^{-3}$, broadly consistent with densities measured for other Trojans, C-type asteroids in the outer main asteroid belt, and sma…
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…
The area of stable motion for fictitious Trojan asteroids around Uranus' equilateral equilibrium points is investigated with respect to the inclination of the asteroid's orbit to determine the size of the regions and their shape. For this task we used the results of extensive numerical integrations of orbits for a grid of initial conditions around the points L4 and L5, and analyzed the stability of the individual orbits. Our basic dynamical model was the Outer Solar System (Jupiter, Saturn, Uranus and Neptune). We integrated the equations of motion of fictitious Trojans in the vicinity of the …
We study the phase space of eccentric coplanar co-orbitals in the non-restricted case. Departing from the quasi-circular case, we describe the evolution of the phase space as the eccentricities increase. We find that over a given value of the eccentricity, around $0.5$ for equal mass co-orbitals, important topological changes occur in the phase space. These changes lead to the emergence of new co-orbital configurations and open a continuous path between the previously distinct trojan domains near the $L_4$ and $L_5$ eccentric Lagrangian equilibria. These topological changes are shown to be lin…
The angle between the spin of a star and its planets' orbital planes traces the history of the planetary system. Exoplanets orbiting close to cool stars are expected to be on circular, aligned orbits because of strong tidal interactions with the stellar convective envelope. Spin-orbit alignment can be measured when the planet transits its star, but such ground-based spectroscopic measurements are challenging for cool, slowly-rotating stars. Here we report the characterization of a planet three-dimensional trajectory around an M dwarf star, derived by mapping the spectrum of the stellar photosp…
