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

asteroid An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. ...

s that share the planet

Jupiter Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but slightly less than one-thousand ...

's orbit around the Sun. Relative to Jupiter, each trojan librates around one of Jupiter's stable Lagrange points: 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 lon ...

of about 5.2 AU. The first Jupiter trojan discovered,

588 Achilles Achilles (minor planet designation: 588 Achilles) is a large Jupiter trojan asteroid of the Greek camp. Achilles was the first Jupiter trojan to be discovered, and was discovered by Max Wolf at the Heidelberg Observatory in 1906. Wolf named the m ...

, 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 A major branch of classical mythology, Greek mythology is the body of myths originally told by the ancient Greeks, and a genre of Ancient Greek folklore. These stories concern the origin and nature of the world, the lives and activities o ...

after a figure of the

Trojan War In Greek mythology, the Trojan War was waged against the city of Troy by the Achaeans ( Greeks) after Paris of Troy took Helen from her husband Menelaus, king of Sparta. The war is one of the most important events in Greek mythology and ...

, 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. Like main-belt asteroids, Jupiter trojans form families. , 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 fil ...

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 of giant planets. The term "Trojan Asteroid" specifically refers to the asteroids co-orbital with Jupiter, but the general term " trojan" is sometimes more generally applied to other small Solar System bodies with similar relationships to larger bodies: Mars trojans, Neptune trojans, Uranus trojans and

Earth trojan An Earth trojan is an asteroid that orbits the Sun in the vicinity of the Earth–Sun Lagrangian 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 ...

s are known to exist. 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 is the larval stage in the biological life cycle of an amphibian. Most tadpoles are fully aquatic, though some species of amphibians have tadpoles that are terrestrial. Tadpoles have some fish-like features that may not be found ...

or horseshoe orbit. These leading and trailing points are called the and Lagrange points. 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 Edward Emerson Barnard (December 16, 1857 – February 6, 1923) was an American astronomer. He was commonly known as E. E. Barnard, and was recognized as a gifted observational astronomer. He is best known for his discovery of the high proper mo ...

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

Heidelberg-Königstuhl State Observatory Heidelberg-Königstuhl State Observatory (german: Landessternwarte Heidelberg-Königstuhl) is a historic astronomical observatory located near the summit of the Königstuhl hill in the city of Heidelberg in Germany. The predecessor of the curr ...

discovered an

at the

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

of the Sun–

system, later named

. In 1906–1907 two more Jupiter trojans were found by fellow German astronomer August Kopff ( 624 Hektor and

617 Patroclus 617 Patroclus ( ) is a large binary Jupiter trojan asteroid. It is a dark D-type asteroid and a slow rotator, due to the 103-hour orbital period of its two components. It is one of five Jovian asteroids targeted by the '' Lucy'' space probe, an ...

). 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 Johann Palisa (6 December 1848 – 2 May 1925) was an Austrian astronomer, born in Troppau, Austrian Silesia, now Czech Republic. He was a prolific discoverer of asteroids, discovering 122 in all, from 136 Austria in 1874 to 1073 G ...

Vienna en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...

, who was the first to accurately calculate their orbits. Asteroids in the leading () orbit are named after Greek heroes (the "Greek node or camp" or "

Achilles In Greek mythology, Achilles ( ) or Achilleus ( grc-gre, Ἀχιλλεύς) was a hero of the Trojan War, the greatest of all the Greek warriors, and the central character of Homer's '' Iliad''. He was the son of the Nereid Thetis and Pe ...

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

Troy Troy ( el, Τροία and Latin: Troia, Hittite: 𒋫𒊒𒄿𒊭 ''Truwiša'') or Ilion ( el, Ίλιον and Latin: Ilium, Hittite: 𒃾𒇻𒊭 ''Wiluša'') was an ancient city located at Hisarlik in present-day Turkey, south-west of Ç ...

(the "Trojan node or camp"). The asteroids

and 624 Hektor were named before the Greece/Troy rule was devised, resulting in a "Greek spy",

Patroclus In Greek mythology, as recorded in Homer's ''Iliad'', Patroclus (pronunciation variable but generally ; grc, Πάτροκλος, Pátroklos, glory of the father) was a childhood friend, close wartime companion, and the presumed (by some later a ...

, in the Trojan node and a "Trojan spy", Hector, in the Greek node.

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 Absolute magnitude () is a measure of the luminosity of a celestial object on an inverse logarithmic astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent magnitude that the object would have if it ...

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 measure of the diffuse reflection of solar radiation out of the total solar radiation and measured on a scale from 0, corresponding to a black body that absorbs all incident radiation, to 1, corresponding to a body that refle ...

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 624 Hektor, 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 Ea ...

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 representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1. I ...

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,

was the first Jupiter trojan to be identified as a binary asteroid. The binary's orbit is extremely close, at 650 km, compared to 35,000 km for the primary's Hill sphere. The largest Jupiter trojan— 624 Hektor— is probably a

contact binary In astronomy, a contact binary is a binary star system whose component stars are so close that they touch each other or have merged to share their gaseous envelopes. A binary system whose stars share an envelope may also be called an overcontac ...

with a moonlet. (Satellite Discovery)

Physical properties

Jupiter trojans are dark bodies of irregular shape. Their geometric albedos 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 curves 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 Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...

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. Founded in 1876, Calvin University is an educational institution of the Christian Reformed Church and stands in the Reformed (Calvinist) ...

examined the light curves of a debiased sample of ten Jupiter trojans, and found a

median In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value. The basic f ...

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 tim ...

(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 asteroids. 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 911 Agamemnon, provisional designation ', is a large Jupiter trojan and a suspected binary asteroid from the Greek camp, approximately in diameter. It was discovered on 19 March 1919, by German astronomer Karl Reinmuth at the Heidelberg Observat ...

and

, 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, 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, ...

), and possibly

magnesium Magnesium is a chemical element with the 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 of the periodic ...

-rich

silicate In chemistry, 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 a ...

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 The W. M. Keck Observatory is an astronomical observatory with two telescopes at an elevation of 4,145 meters (13,600 ft) near the summit of Mauna Kea in the U.S. state of Hawaii. Both telescopes have aperture primary mirrors, and when ...

in Hawaii announced in 2006 that it had measured the density of the binary Jupiter trojan

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, when passing close to the Sun, warms and begins to release gases, a process that is called outgassing. This produces a visible atmosphere or coma, and sometimes also a tail. These phenomena ...

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 System Capitalization 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 "Solar ...

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 the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...

and

helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic ta ...

from the protoplanetary disk; 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. Per the Chamberlin–Moulton planetesimal hypothesis, they are believed to form out of cosmic dust grains. Believed to have formed in the Solar System ...

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, 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

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 nine and a half times that of Earth. It has only one-eighth the average density of Earth; h ...

, 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 describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscil ...

. Encounters between planets resulted in

Uranus Uranus is the seventh planet from the Sun. Its name is a reference to the Greek god of the sky, Uranus ( Caelus), who, according to Greek mythology, was the great-grandfather of Ares (Mars), grandfather of Zeus (Jupiter) and father of ...

and

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

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 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 was selected as one of their next two Discovery Program missions. Lucy is set to explore seven Jupiter trojans. It 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. The Japanese space agency has proposed the OKEANOS

solar sail Solar sails (also known as light sails and photon sails) are a method of spacecraft propulsion using radiation pressure exerted by sunlight on large mirrors. A number of spaceflight missions to test solar propulsion and navigation have been ...

for the late 2020s to either analyse a Trojan asteroid ''in situ'' or to perform a sample-return mission.

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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