The Jupiter trojans, commonly called trojan asteroids or simply trojans, are a large group of

asteroid An asteroid is a minor planet—an object larger than a meteoroid that is neither a planet nor an identified comet—that orbits within the Solar System#Inner Solar System, inner Solar System or is co-orbital with Jupiter (Trojan asteroids). As ...

s that share the planet

Jupiter Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a Jupiter mass, mass more than 2.5 times that of all the other planets in the Solar System combined a ...

's orbit around the

Sun The Sun is the star at the centre of the Solar System. It is a massive, nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy from its surface mainly as visible light a ...

. Relative to Jupiter, each

trojan Trojan or Trojans may refer to: * Of or from the ancient city of Troy * Trojan language, the language of the historical Trojans Arts and entertainment Music * '' Les Troyens'' ('The Trojans'), an opera by Berlioz, premiered part 1863, part 18 ...

librates around one of Jupiter's stable

Lagrange points In celestial mechanics, the Lagrange points (; also Lagrangian points or libration points) are points of equilibrium for small-mass objects under the gravitational influence of two massive orbiting bodies. Mathematically, this involves t ...

: either ', existing 60° ahead of the planet in its orbit, or ', 60° behind. Jupiter trojans are distributed in two elongated, curved regions around these Lagrangian points with an average

semi-major axis In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the longe ...

of about 5.2 AU. The first Jupiter trojan discovered, 588 Achilles, was spotted in 1906 by German astronomer

Max Wolf Maximilian Franz Joseph Cornelius Wolf (21 June 1863 – 3 October 1932) was a German astronomer and a pioneer in the field of astrophotography. He was the chairman of astronomy at the University of Heidelberg and director of the Heidelberg-K� ...

. More than 9,800 Jupiter trojans have been found . By convention, they are each named from

Greek mythology Greek mythology is the body of myths originally told by the Ancient Greece, ancient Greeks, and a genre of ancient Greek folklore, today absorbed alongside Roman mythology into the broader designation of classical mythology. These stories conc ...

after a figure of the

Trojan War The Trojan War was a legendary conflict in Greek mythology that took place around the twelfth or thirteenth century BC. The war was waged by the Achaeans (Homer), Achaeans (Ancient Greece, Greeks) against the city of Troy after Paris (mytho ...

, hence the name "trojan". The total number of Jupiter trojans larger than 1 km in diameter is believed to be about , approximately equal to the number of asteroids larger than 1 km in the

asteroid belt The asteroid belt is a torus-shaped region in the Solar System, centered on the Sun and roughly spanning the space between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies called asteroids ...

. Like main-belt asteroids, Jupiter trojans form

families Family (from ) is a group of people related either by consanguinity (by recognized birth) or affinity (by marriage or other relationship). It forms the basis for social order. Ideally, families offer predictability, structure, and safety as ...

. , many Jupiter trojans showed to observational instruments as dark bodies with reddish, featureless spectra. No firm evidence of the presence of water, or any other specific compound on their surface has been obtained, but it is thought that they are coated in tholins, organic polymers formed by the Sun's radiation. The Jupiter trojans' densities (as measured by studying

binaries A binary file is a computer file that is not a text file. The term "binary file" is often used as a term meaning "non-text file". Many binary file formats contain parts that can be interpreted as text; for example, some computer document files ...

or rotational lightcurves) vary from 0.8 to 2.5 g·cm⁻³. Jupiter trojans are thought to have been captured into their orbits during the early stages of the Solar System's formation or slightly later, during the

migration Migration, migratory, or migrate may refer to: Human migration * Human migration, physical movement by humans from one region to another ** International migration, when peoples cross state boundaries and stay in the host state for some minimum le ...

of giant planets. The term "Trojan Asteroid" specifically refers to the asteroids co-orbital with Jupiter, but the general term "

" is sometimes more generally applied to other

small Solar System bodies A small Solar System body (SSSB) is an object in the Solar System that is neither a planet, a dwarf planet, nor a natural satellite. The term was first IAU definition of planet, defined in 2006 by the International Astronomical Union (IAU) as fo ...

with similar relationships to larger bodies:

Mars trojan The Mars trojans are a group of trojan objects that share the orbit of the planet Mars around the Sun. They can be found around the two Lagrangian points 60° ahead of and behind Mars. The origin of the Mars trojans is not well understood. One t ...

Neptune trojan Neptune trojans are bodies that orbit the Sun near one of the stable Lagrangian points of Neptune, similar to the trojans of other planets. They therefore have approximately the same orbital period as Neptune and follow roughly the same orbita ...

Uranus trojan A Uranus trojan is an asteroid that shares an orbit with Uranus Uranus is the seventh planet from the Sun. It is a gaseous cyan-coloured ice giant. Most of the planet is made of water, ammonia, and methane in a Supercritical fluid, supercr ...

s and

Earth trojan An Earth trojan is an asteroid that orbits the Sun in the vicinity of the Earth–Sun Lagrange points (leading 60°) or (trailing 60°), thus having an orbit similar to Earth's. Only two Earth trojans have so far been discovered. The name "tr ...

s are known to exist. Temporary

Venus Venus is the second planet from the Sun. It is often called Earth's "twin" or "sister" planet for having almost the same size and mass, and the closest orbit to Earth's. While both are rocky planets, Venus has an atmosphere much thicker ...

trojans and

Saturn Saturn is the sixth planet from the Sun and the second largest in the Solar System, after Jupiter. It is a gas giant, with an average radius of about 9 times that of Earth. It has an eighth the average density of Earth, but is over 95 tim ...

trojans exist, as well as for

1 Ceres Ceres ( minor-planet designation: 1 Ceres) is a dwarf planet in the middle main asteroid belt between the orbits of Mars and Jupiter. It was the first known asteroid, discovered on 1 January 1801 by Giuseppe Piazzi at Palermo Astronomical O ...

and

4 Vesta Vesta (minor-planet designation: 4 Vesta) is one of the largest objects in the asteroid belt, with a mean diameter of . It was discovered by the German astronomer Heinrich Wilhelm Matthias Olbers on 29 March 1807 and is named after Vesta (mytho ...

. The term "Trojan asteroid" is normally understood to specifically mean the Jupiter trojans because the first Trojans were discovered near Jupiter's orbit and Jupiter currently has by far the most known Trojans.

Observational history

In 1772, Italian-born mathematician

Joseph-Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangiarestricted three-body problem, predicted that a small body sharing an orbit with a planet but lying 60° ahead or behind it will be trapped near these points. The trapped body will librate slowly around the point of equilibrium in a

tadpole A tadpole or polliwog (also spelled pollywog) is the Larva, larval stage in the biological life cycle of an amphibian. Most tadpoles are fully Aquatic animal, aquatic, though some species of amphibians have tadpoles that are terrestrial animal, ...

or horseshoe orbit. These leading and trailing points are called the and

Lagrange point In celestial mechanics, the Lagrange points (; also Lagrangian points or libration points) are points of equilibrium for small-mass objects under the gravitational influence of two massive orbiting bodies. Mathematically, this involves t ...

s. The first asteroids trapped in Lagrange points were observed more than a century after Lagrange's hypothesis. Those associated with Jupiter were the first to be discovered. E. E. Barnard made the first recorded observation of a trojan, (identified as A904 RD at the time), in 1904, but neither he nor others appreciated its significance at the time. Barnard believed he had seen the recently discovered Saturnian satellite Phoebe, which was only two arc-minutes away in the sky at the time, or possibly an asteroid. The object's identity was not understood until its orbit was calculated in 1999. The first accepted discovery of a trojan occurred in February 1906, when astronomer

of Heidelberg-Königstuhl State Observatory discovered an

at the

Lagrangian point In celestial mechanics, the Lagrange points (; also Lagrangian points or libration points) are points of equilibrium (mechanics), equilibrium for small-mass objects under the gravity, gravitational influence of two massive orbit, orbiting b ...

of the

–

system, later named 588 Achilles. In 1906–1907 two more Jupiter trojans were found by fellow German astronomer

August Kopff August Kopff (February 5, 1882 – April 25, 1960) was a German astronomer and discoverer of several comets and asteroids. Kopff studied and worked in Heidelberg, getting his PhD there in 1906 and he then joined the Humboldt University of Berli ...

(

624 Hektor 624 Hektor is the largest Jupiter trojan and the namesake of the Hektor family, with a highly elongated shape equivalent in volume to a sphere of approximately 225 to 250 kilometers diameter. It was discovered on 10 February 1907, by astronom ...

and 617 Patroclus). Hektor, like Achilles, belonged to the swarm ("ahead" of the planet in its orbit), whereas Patroclus was the first asteroid known to reside at the Lagrangian point ("behind" the planet). By 1938, 11 Jupiter trojans had been detected. This number increased to 14 only in 1961. As instruments improved, the rate of discovery grew rapidly: by January 2000, a total of 257 had been discovered; by May 2003, the number had grown to 1,600. there are 4,601 known Jupiter trojans at and 2,439 at .

Nomenclature

The custom of naming all asteroids in Jupiter's and points after famous heroes of the

was suggested by Johann Palisa of

Vienna Vienna ( ; ; ) is the capital city, capital, List of largest cities in Austria, most populous city, and one of Federal states of Austria, nine federal states of Austria. It is Austria's primate city, with just over two million inhabitants. ...

, who was the first to accurately calculate their orbits. Asteroids in the leading () orbit are named after

Greek Greek may refer to: Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group *Greek language, a branch of the Indo-European language family **Proto-Greek language, the assumed last common ancestor of all kno ...

heroes (the "Greek node or camp" or "

Achilles In Greek mythology, Achilles ( ) or Achilleus () was a hero of the Trojan War who was known as being the greatest of all the Greek warriors. The central character in Homer's ''Iliad'', he was the son of the Nereids, Nereid Thetis and Peleus, ...

group"), and those at the trailing () orbit are named after the heroes of

Troy Troy (/; ; ) or Ilion (; ) was an ancient city located in present-day Hisarlik, Turkey. It is best known as the setting for the Greek mythology, Greek myth of the Trojan War. The archaeological site is open to the public as a tourist destina ...

(the "Trojan node or camp"). The asteroids 617 Patroclus and

were named before the Greece/Troy rule was devised, resulting in a "Greek spy",

Patroclus In Greek mythology, Patroclus (generally pronounced ; ) was a Greek hero of the Trojan War and an important character in Homer's ''Iliad''. Born in Opus, Patroclus was the son of the Argonaut Menoetius. When he was a child, he was exiled from ...

, in the Trojan node and a "Trojan spy",

Hector In Greek mythology, Hector (; , ) was a Trojan prince, a hero and the greatest warrior for Troy during the Trojan War. He is a major character in Homer's ''Iliad'', where he leads the Trojans and their allies in the defense of Troy, killing c ...

, in the Greek node. In 2018, at its 30th General Assembly in Vienna, the

International Astronomical Union The International Astronomical Union (IAU; , UAI) is an international non-governmental organization (INGO) with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach, education, and developmen ...

amended the naming convention for Jupiter trojans, allowing for asteroids with '' H'' larger than 12 (that is, a mean diameter smaller than approximately 22 kilometers, for an assumed albedo of 0.057) to be named after Olympic athletes, because there are now far more known Jupiter trojans than available names of Greek and Trojan warriors that fought in the Trojan war.

Numbers and mass

Estimates of the total number of Jupiter trojans are based on deep surveys of limited areas of the sky. The swarm is believed to hold between 160,000 and 240,000 asteroids with diameters larger than 2 km and about 600,000 with diameters larger than 1 km. If the swarm contains a comparable number of objects, there are more than Jupiter trojans 1 km in size or larger. For the objects brighter than absolute magnitude 9.0 the population is probably complete. These numbers are similar to that of comparable asteroids in the asteroid belt. The total mass of the Jupiter trojans is estimated at 0.0001 of the mass of Earth or one-fifth of the mass of the asteroid belt. Two more recent studies indicate that the above numbers may overestimate the number of Jupiter trojans by several-fold. This overestimate is caused by (1) the assumption that all Jupiter trojans have a low

albedo Albedo ( ; ) is the fraction of sunlight that is Diffuse reflection, diffusely reflected by a body. It is measured on a scale from 0 (corresponding to a black body that absorbs all incident radiation) to 1 (corresponding to a body that reflects ...

of about 0.04, whereas small bodies may have an average albedo as high as 0.12; (2) an incorrect assumption about the distribution of Jupiter trojans in the sky. According to the new estimates, the total number of Jupiter trojans with a diameter larger than 2 km is and in the L₄ and L₅ swarms, respectively. These numbers would be reduced by a factor of 2 if small Jupiter trojans are more reflective than large ones. The number of Jupiter trojans observed in the swarm is slightly larger than that observed in . Because the brightest Jupiter trojans show little variation in numbers between the two populations, this disparity is probably due to observational bias. Some models indicate that the swarm may be slightly more stable than the swarm. The largest Jupiter trojan is

, which has a mean diameter of 203 ± 3.6 km. There are few large Jupiter trojans in comparison to the overall population. With decreasing size, the number of Jupiter trojans grows very quickly down to 84 km, much more so than in the asteroid belt. A diameter of 84 km corresponds to an absolute magnitude of 9.5, assuming an

of 0.04. Within the 4.4–40 km range the Jupiter trojans' size distribution resembles that of the main-belt asteroids. Nothing is known about the masses of the smaller Jupiter trojans. The size distribution suggests that the smaller Trojans may be the products of collisions by larger Jupiter trojans.

Orbits

Jupiter trojans have orbits with radii between 5.05 and 5.35 AU (the mean semi-major axis is 5.2 ± 0.15 AU), and are distributed throughout elongated, curved regions around the two Lagrangian points; each swarm stretches for about 26° along the orbit of Jupiter, amounting to a total distance of about 2.5 AU. The width of the swarms approximately equals two Hill's radii, which in the case of Jupiter amounts to about 0.6 AU. Many of Jupiter trojans have large

orbital inclination Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object. For a satellite orbiting the Earth ...

s relative to Jupiter's orbital plane—up to 40°. Jupiter trojans do not maintain a fixed separation from Jupiter. They slowly librate around their respective equilibrium points, periodically moving closer to Jupiter or farther from it. Jupiter trojans generally follow paths called tadpole orbits around the Lagrangian points; the average period of their libration is about 150 years. The amplitude of the libration (along the Jovian orbit) varies from 0.6° to 88°, with the average being about 33°. Simulations show that Jupiter trojans can follow even more complicated trajectories when moving from one Lagrangian point to another—these are called horseshoe orbits (currently no Jupiter Trojan with such an orbit is known, though

one 1 (one, unit, unity) is a number, numeral, and glyph. It is the first and smallest positive integer of the infinite sequence of natural numbers. This fundamental property has led to its unique uses in other fields, ranging from science to sp ...

is known for Neptune).

Dynamical families and binaries

Discerning dynamical families within the Jupiter trojan population is more difficult than it is in the asteroid belt, because the Jupiter trojans are locked within a far narrower range of possible positions. This means that clusters tend to overlap and merge with the overall swarm. By 2003 roughly a dozen dynamical families were identified. Jupiter-trojan families are much smaller in size than families in the asteroid belt; the largest identified family, the Menelaus group, consists of only eight members. In 2001, 617 Patroclus was the first Jupiter trojan to be identified as a

binary asteroid A binary asteroid is a system of two asteroids orbiting their common barycenter. The binary nature of 243 Ida was discovered when the Galileo spacecraft flew by the asteroid in 1993. Since then numerous binary asteroids and several triple a ...

. The binary's orbit is extremely close, at 650 km, compared to 35,000 km for the primary's

Hill sphere The Hill sphere is a common model for the calculation of a Sphere of influence (astrodynamics), gravitational sphere of influence. It is the most commonly used model to calculate the spatial extent of gravitational influence of an astronomical ...

. The largest Jupiter trojan—

— is probably a contact binary with a moonlet. (Satellite Discovery)

Physical properties

Jupiter trojans are dark bodies of irregular shape. Their

geometric albedo In astronomy, the geometric albedo of a celestial body is the ratio of its actual brightness as seen from the light source (i.e. at zero phase angle (astronomy), phase angle) to that of an ''idealized'' flat, fully reflecting, diffuse reflection, d ...

s generally vary between 3 and 10%. The average value is 0.056 ± 0.003 for the objects larger than 57 km, and 0.121 ± 0.003 (R-band) for those smaller than 25 km. The asteroid 4709 Ennomos has the highest albedo (0.18) of all known Jupiter trojans. Little is known about the masses, chemical composition, rotation or other physical properties of the Jupiter trojans.

Rotation

The rotational properties of Jupiter trojans are not well known. Analysis of the rotational

light curve In astronomy, a light curve is a graph (discrete mathematics), graph of the Radiance, light intensity of a celestial object or region as a function of time, typically with the magnitude (astronomy), magnitude of light received on the ''y''-axis ...

s of 72 Jupiter trojans gave an average rotational period of about 11.2 hours, whereas the average period of the control sample of asteroids in the asteroid belt was 10.6 hours. The distribution of the rotational periods of Jupiter trojans appeared to be well approximated by a Maxwellian function,The Maxwellian function is

F=\begin\fracP^2\exp(-(P-P_0)^2/\sigma^2)\end

, where

P_0

is the average rotational period,

\sigma

is the dispersion of periods. whereas the distribution for main-belt asteroids was found to be non-Maxwellian, with a deficit of periods in the range 8–10 hours. The Maxwellian distribution of the rotational periods of Jupiter trojans may indicate that they have undergone a stronger collisional evolution compared to the asteroid belt. In 2008 a team from

Calvin College Calvin University, formerly Calvin College, is a private Christian university in Grand Rapids, Michigan, United States. Founded in 1876, Calvin University is an educational institution of the Christian Reformed Church and stands in the Reforme ...

examined the

s of a debiased sample of ten Jupiter trojans, and found a

median The median of a set of numbers is the value separating the higher half from the lower half of a Sample (statistics), data sample, a statistical population, population, or a probability distribution. For a data set, it may be thought of as the “ ...

spin period of 18.9 hours. This value was significantly higher than that for main-belt asteroids of similar size (11.5 hours). The difference could mean that the Jupiter trojans possess a lower average density, which may imply that they formed in the

Kuiper belt The Kuiper belt ( ) is a circumstellar disc in the outer Solar System, extending from the orbit of Neptune at 30 astronomical units (AU) to approximately 50 AU from the Sun. It is similar to the asteroid belt, but is far larger—20 times ...

(see below).

Composition

Spectroscopically, the Jupiter trojans mostly are

D-type asteroid D-type asteroids have a very low albedo and a featureless reddish spectrum. It has been suggested that they have a composition of organic-rich silicates, carbon and anhydrous silicates, possibly with water ice in their interiors. D-type asteroids ...

s, which predominate in the outer regions of the asteroid belt. A small number are classified as P or

C-type asteroid C-type (carbonaceous ) asteroids are the most common variety, forming around 75% of known asteroids. They are volatile-rich and distinguished by a very low albedo because their composition includes a large amount of carbon, in addition to rocks ...

s. Their spectra are red (meaning that they reflect more light at longer wavelengths) or neutral and featureless. No firm evidence of water, organics or other chemical compounds has been obtained . 4709 Ennomos has an albedo slightly higher than the Jupiter-trojan average, which may indicate the presence of water ice. Some other Jupiter Trojans, such as 911 Agamemnon and 617 Patroclus, have shown very weak absorptions at 1.7 and 2.3 μm, which might indicate the presence of organics. The Jupiter trojans' spectra are similar to those of the irregular moons of Jupiter and, to a certain extent,

comet nuclei The nucleus is the solid, central part of a comet, formerly termed a ''dirty snowball'' or an ''icy dirtball''. A cometary nucleus is composed of Rock (geology), rock, dust, and frozen gases. When heated by the Sun, the gases Sublimation (physi ...

, though Jupiter trojans are spectrally very different from the redder Kuiper belt objects. A Jupiter trojan's spectrum can be matched to a mixture of water ice, a large amount of carbon-rich material (

charcoal Charcoal is a lightweight black carbon residue produced by strongly heating wood (or other animal and plant materials) in minimal oxygen to remove all water and volatile constituents. In the traditional version of this pyrolysis process, ca ...

), and possibly

magnesium Magnesium is a chemical element; it has Symbol (chemistry), symbol Mg and atomic number 12. It is a shiny gray metal having a low density, low melting point and high chemical reactivity. Like the other alkaline earth metals (group 2 ...

-rich

silicate A silicate is any member of a family of polyatomic anions consisting of silicon and oxygen, usually with the general formula , where . The family includes orthosilicate (), metasilicate (), and pyrosilicate (, ). The name is also used ...

s. The composition of the Jupiter trojan population appears to be markedly uniform, with little or no differentiation between the two swarms. A team from the Keck Observatory in Hawaii announced in 2006 that it had measured the density of the binary Jupiter trojan 617 Patroclus as being less than that of water ice (0.8 g/cm³), suggesting that the pair, and possibly many other Trojan objects, more closely resemble

comet A comet is an icy, small Solar System body that warms and begins to release gases when passing close to the Sun, a process called outgassing. This produces an extended, gravitationally unbound atmosphere or Coma (cometary), coma surrounding ...

s or Kuiper belt objects in composition—water ice with a layer of dust—than they do the main-belt asteroids. Countering this argument, the density of Hektor as determined from its rotational lightcurve (2.480 g/cm³) is significantly higher than that of 617 Patroclus. Such a difference in densities suggests that density may not be a good indicator of asteroid origin.

Origin and evolution

Two main theories have emerged to explain the formation and evolution of the Jupiter trojans. The first suggests that the Jupiter trojans formed in the same part of the

Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Sola ...

as Jupiter and entered their orbits while it was forming. The last stage of Jupiter's formation involved runaway growth of its mass through the accretion of large amounts of

hydrogen Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter ...

and

helium Helium (from ) is a chemical element; it has chemical symbol, symbol He and atomic number 2. It is a colorless, odorless, non-toxic, inert gas, inert, monatomic gas and the first in the noble gas group in the periodic table. Its boiling point is ...

from the

protoplanetary disk A protoplanetary disk is a rotating circumstellar disc of dense gas and dust surrounding a young newly formed star, a T Tauri star, or Herbig Ae/Be star. The protoplanetary disk may not be considered an accretion disk; while the two are sim ...

; during this growth, which lasted for only about 10,000 years, the mass of Jupiter increased by a factor of ten. The

planetesimal Planetesimals () are solid objects thought to exist in protoplanetary disks and debris disks. Believed to have formed in the Solar System about 4.6 billion years ago, they aid study of its formation. Formation A widely accepted theory of pla ...

s that had approximately the same orbits as Jupiter were caught by the increased gravity of the planet. The capture mechanism was very efficient—about 50% of all remaining planetesimals were trapped. This hypothesis has two major problems: the number of trapped bodies exceeds the observed population of Jupiter trojans by four

orders of magnitude In a ratio scale based on powers of ten, the order of magnitude is a measure of the nearness of two figures. Two numbers are "within an order of magnitude" of each other if their ratio is between 1/10 and 10. In other words, the two numbers are wi ...

, and the present Jupiter trojan asteroids have larger orbital inclinations than are predicted by the capture model. Simulations of this scenario show that such a mode of formation also would inhibit the creation of similar trojans for

, and this has been borne out by observation: to date no trojans have been found near Saturn. In a variation of this theory Jupiter captures trojans during its initial growth then migrates as it continues to grow. During Jupiter's migration the orbits of objects in horseshoe orbits are distorted causing the L4 side of these orbits to be over occupied. As a result, an excess of trojans is trapped on the L4 side when the horseshoe orbits shift to tadpole orbits as Jupiter grows. This model also leaves the Jupiter trojan population 3–4 orders of magnitude too large. The second theory proposes that the Jupiter trojans were captured during the migration of the giant planets described in the Nice model. In the Nice model the orbits of the giant planets became unstable years after the Solar System's formation when Jupiter and Saturn crossed their 1:2 mean-motion

resonance Resonance is a phenomenon that occurs when an object or system is subjected to an external force or vibration whose frequency matches a resonant frequency (or resonance frequency) of the system, defined as a frequency that generates a maximu ...

. Encounters between planets resulted in

Uranus Uranus is the seventh planet from the Sun. It is a gaseous cyan-coloured ice giant. Most of the planet is made of water, ammonia, and methane in a Supercritical fluid, supercritical phase of matter, which astronomy calls "ice" or Volatile ( ...

and

Neptune Neptune is the eighth and farthest known planet from the Sun. It is the List of Solar System objects by size, fourth-largest planet in the Solar System by diameter, the third-most-massive planet, and the densest giant planet. It is 17 t ...

being scattered outward into the primordial

, disrupting it and throwing millions of objects inward. When Jupiter and Saturn were near their 1:2 resonance the orbits of pre-existing Jupiter trojans became unstable during a secondary resonance with Jupiter and Saturn. This occurred when the period of the trojans' libration about their Lagrangian point had a 3:1 ratio to the period at which the position where Jupiter passes Saturn circulated relative to its perihelion. This process was also reversible allowing a fraction of the numerous objects scattered inward by Uranus and Neptune to enter this region and be captured as Jupiter's and Saturn's orbits separated. These new trojans had a wide range of inclinations, the result of multiple encounters with the giant planets before being captured. This process can also occur later when Jupiter and Saturn cross weaker resonances. In a

revised version The Revised Version (RV) or English Revised Version (ERV) of the Bible is a late-19th-century British revision of the King James Version. It was the first (and remains the only) officially authorised and recognised revision of the King James Vers ...

of the Nice model Jupiter trojans are captured when Jupiter encounters an ice giant during the instability. In this version of the Nice model one of the ice giants (Uranus, Neptune, or a lost fifth planet) is scattered inward onto a Jupiter-crossing orbit and is scattered outward by Jupiter causing the orbits of Jupiter and Saturn to quickly separate. When Jupiter's semi-major axis jumps during these encounters existing Jupiter trojans can escape and new objects with semi-major axes similar to Jupiter's new semi-major axis are captured. Following its last encounter the ice giant can pass through one of the libration points and perturb their orbits leaving this libration point depleted relative to the other. After the encounters end some of these Jupiter trojans are lost and others captured when Jupiter and Saturn are near weak mean motion resonances such as the 3:7 resonance via the mechanism of the original Nice model. The long-term future of the Jupiter trojans is open to question, because multiple weak resonances with Jupiter and Saturn cause them to behave chaotically over time. Collisional shattering slowly depletes the Jupiter trojan population as fragments are ejected. Ejected Jupiter trojans could become temporary satellites of Jupiter or Jupiter-family comets. Simulations show that the orbits of up to 17% of Jupiter trojans are unstable over the age of the Solar System. Levison et al. believe that roughly 200 ejected Jupiter trojans greater than 1 km in diameter might be travelling the Solar System, with a few possibly on Earth-crossing orbits. Some of the escaped Jupiter trojans may become Jupiter-family comets as they approach the Sun and their surface ice begins evaporating.

Exploration

On 4 January 2017 NASA announced that ''

Lucy Lucy is an English language, English feminine given name derived from the Latin masculine given name Lucius with the meaning ''as of light'' (''born at dawn or daylight'', maybe also ''shiny'', or ''of light complexion''). Alternative spellings ar ...

'' was selected as one of their next two Discovery Program missions. ''Lucy'' is set to explore seven Jupiter trojans. It was launched on October 16, 2021, and will arrive at the Trojan cloud in 2027 after two Earth gravity assists and a fly-by of a main-belt asteroid. It will then return to the vicinity of Earth for another gravity assist to take it to Jupiter's Trojan cloud where it will visit 617 Patroclus.

Notes

References

External links

* * *
NASA's WISE Colors in Unknowns on Jupiter Asteroids
(NASA 2012-322 : 15 October 2012) *
3D Gravity Simulation of the Ten Largest Jupiter Trojan Asteroids
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