Achilles (

minor planet designation A formal minor-planet designation is, in its final form, a number–name combination given to a minor planet (asteroid, centaur, trans-Neptunian object and dwarf planet but not comet). Such designation always features a leading number (catalog or ...

: 588 Achilles) is a large Jupiter trojan asteroid of the

Greek camp This is a list of Jupiter trojans that lie in the Greek camp, an elongated curved region around the leading Lagrangian point (), 60 ° ahead of Jupiter in its orbit. All the asteroids at Jupiter's point have names corresponding to participants ...

. Achilles was the first Jupiter trojan to be discovered, and was discovered by

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� ...

at the Heidelberg Observatory in 1906. Wolf named the minor planet after the legendary hero Achilles from Greek mythology. The dark D-type asteroid measures approximately in diameter which makes it one of the 10 largest Jupiter trojans. It has a

rotation period The rotation period of a celestial object (e.g., star, gas giant, planet, moon, asteroid) may refer to its sidereal rotation period, i.e. the time that the object takes to complete a single revolution around its axis of rotation relative to the ...

of 7.3 hours and possibly a spherical shape.

Discovery

''Achilles'' was discovered on 22 February 1906, by the German astronomer

at the Heidelberg-Königstuhl State Observatory in southern Germany. It was the first discovery of a Jupiter trojan, although had been observed as ' two years previously. This body, however, remained unconfirmed as the observation period was not long enough to calculate an orbit. August Kopff, a colleague of Wolf at Heidelberg, then discovered

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, and ...

eight months after ''Achilles'', and, in early 1907, he discovered the largest of all Jupiter trojans, 624 Hektor.

Orbit and classification

''Achilles'' orbits the Sun at a distance of 4.4–6.0 AU in 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 th ...

of the Sun– Jupiter System once every 11 years and 11 months (4,343 days;

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 long ...

of 5.21 AU). Its orbit shows an eccentricity of 0.15 and an inclination of 10 degrees from the plane of the ecliptic. ''Achilles'' is the first known example of the stable solution of the three-body problem worked out by French mathematician Joseph Lagrange in 1772, after whom the minor planet

1006 Lagrangea Lagrangea (minor planet designation: 1006 Lagrangea), provisional designation , is a carbonaceous background asteroid from the outer region of the asteroid belt, approximately 30 kilometers in diameter. It was discovered on 12 September 1923, by ...

is named. After the discovery of other asteroids with similar orbital characteristics, which were also named after heroes from the Trojan War ''(see below)'', the term "Trojan asteroids" or "Jupiter trojans" became commonly used. In addition, a rule was established that the point was the "

", whereas the point was the " Trojan camp", though not before each camp had acquired a "spy" (''Hektor'' in the Greek camp and ''Patroclus'' in the Trojan camp).

Physical characteristics

Spectral type

In the Tholen taxonomic scheme, ''Achilles'' is classified as a D-type asteroid with an unusual spectrum (DU). Its V–I color index of 0.94 is typical for most larger Jupiter trojans ''(see table below)''.

Photometry

''Achilles''

of 7.3 hours is somewhat shorter than that of most other large Jupiter trojans but close to that of 911 Agamemnon, 3451 Mentor and 3317 Paris, which are similar in size ''(see table below)''. Its low brightness amplitude is indicative of a rather spherical shape. From July 2007 until September 2008, coordinated photometric observations were carried out by astronomers at

Simeiz Simeiz ( uk, Сімеїз, russian: Симеи́з, crh, Simeiz) is a resort town, an urban-type settlement in Yalta Municipality in the Autonomous Republic of Crimea, a territory recognized by a majority of countries as part of Ukraine and incorp ...

(Crimea), Rozhen (Bulgaria), Maidanak (Uzbekistan) and Kharkiv (Ukraine) observatories. Analysis of the obtained lightcurves determined a period of hours with a brightness amplitude of 0.02–0.11 magnitude (). Alternative period determinations by Cláudia Angeli (7.0 h), Robert Stephens (7.312 h),

Stefano Mottola This is a list of minor-planet discoverers credited by the Minor Planet Center with the discovery of one or several minor planets (such as near-Earth and main-belt asteroids, Jupiter trojans and distant objects). , the discovery of 612,011 numb ...

(7.32 h) and Vincenzo Zappalà (12 h) are mostly in good agreement ().

Diameter and albedo

According to the surveys carried out by the Infrared Astronomical Satellite, IRAS, the Japanese Akari satellite, and the NEOWISE mission of NASA's Wide-field Infrared Survey Explorer, the body's surface has a very low albedo in the range of 0.0328 to 0.043, making its absolute magnitude of approximately 8.57 correspond to a diameter of 130.1 to 135.5 kilometers. ''Achilles'' is the 6th largest Jupiter trojan according to IRAS and Akari, and the 4th largest based on NEOWISE data:

Naming

This minor planet's name was suggested by Austrian astronomer

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 Gel ...

. It was named after Achilles, the legendary hero from Greek mythology and central figure in Homer's '' Iliad'' which tells the accounts of the Trojan War ''(also see 5700 Homerus and 6604 Ilias)''. As an infant, Achilles was plunged in the River Styx by his mother Thetis ''(also see 17 Thetis)'', thus rendering his body invulnerable excepting the heel by which he was held. He slew Hector (''see also 624 Hektor''), the greatest Trojan warrior. He was eventually killed by an arrow in the heel by Paris (''see 3317 Paris'').