The kilometre, or kilometer is a unit of length in the metric system, equal to one thousand metres. It is now the measurement unit used for expressing distances between geographical places on land in most of the world. K is used in some English-speaking countries as an alternative for the word kilometre in colloquial writing and speech. A slang term for the kilometre in the US and UK military is klick. There are two common pronunciations for the word; the former follows a pattern in English whereby metric units are pronounced with the stress on the first syllable and the pronunciation of the actual base unit does not change irrespective of the prefix. It is preferred by the British Broadcasting Corporation and the Australian Broadcasting Corporation. Many scientists and other users in countries where the metric system is not used, use the pronunciation with stress on the second syllable; the latter pronunciation follows the stress pattern used for the names of measuring instruments. The problem with this reasoning, however, is that the word meter in those usages refers to a measuring device, not a unit of length.
The contrast is more obvious in countries using the British rather than American spelling of the word metre. When Australia introduced the metric system in 1975, the first pronunciation was declared official by the government's Metric Conversion Board. However, the Australian prime minister at the time, Gough Whitlam, insisted that the second pronunciation was the correct one because of the Greek origins of the two parts of the word. By the 8 May 1790 decree, the Constituent assembly ordered the French Academy of Sciences to develop a new measurement system. In August 1793, the French National Convention decreed the metre as the sole length measurement system in the French Republic; the first name of the kilometre was "Millaire". Although the metre was formally defined in 1799, the myriametre was preferred to the "kilometre" for everyday use; the term "myriamètre" appeared a number of times in the text of Develey's book Physique d'Emile: ou, Principes de la science de la nature, while the term kilometre only appeared in an appendix.
French maps published in 1835 had scales showing myriametres and "lieues de Poste". The Dutch gave it the local name of the mijl, it was only in 1867 that the term "kilometer" became the only official unit of measure in the Netherlands to represent 1000 metres. Two German textbooks dated 1842 and 1848 give a snapshot of the use of the kilometre across Europe - the kilometre was in use in the Netherlands and in Italy and the myriametre was in use in France. In 1935, the International Committee for Weights and Measures abolished the prefix "myria-" and with it the "myriametre", leaving the kilometre as the recognised unit of length for measurements of that magnitude. In the United Kingdom, road signs show distances in miles and location marker posts that are used for reference purposes by road engineers and emergency services show distance references in unspecified units which are kilometre-based; the advent of the mobile phone has been instrumental in the British Department for Transport authorising the use of driver location signs to convey the distance reference information of location marker posts to road users should they need to contact the emergency services.
In the US, the National Highway System Designation Act of 1995 prohibits the use of federal-aid highway funds to convert existing signs or purchase new signs with metric units. The Executive Director of the US Federal Highway Administration, Jeffrey Paniati, wrote in a 2008 memo: "Section 205 of the National Highway System Designation Act of 1995 prohibited us from requiring any State DOT to use the metric system during project development activities. Although the State DOT's had the option of using metric measurements or dual units, all of them abandoned metric measurements and reverted to sole use of inch-pound values." The Manual on Uniform Traffic Control Devices since 2000 is published in both metric and American Customary Units. Some sporting disciplines feature 1000 m races in major events, but in other disciplines though world records are catalogued, the one kilometre event remains a minority event; the world records for various sporting disciplines are: Conversion of units, for comparison with other units of length Cubic metre Metric prefix Mileage Odometer Orders of magnitude Square kilometre Media related to Distance indicators at Wikimedia Commons
An hour is a unit of time conventionally reckoned as 1⁄24 of a day and scientifically reckoned as 3,599–3,601 seconds, depending on conditions. The hour was established in the ancient Near East as a variable measure of 1⁄12 of the night or daytime; such seasonal, temporal, or unequal hours varied by latitude. The hour was subsequently divided into each of 60 seconds. Equal or equinoctial hours were taken as 1⁄24 of the day. Since this unit was not constant due to long term variations in the Earth's rotation, the hour was separated from the Earth's rotation and defined in terms of the atomic or physical second. In the modern metric system, hours are an accepted unit of time defined as 3,600 atomic seconds. However, on rare occasions an hour may incorporate a positive or negative leap second, making it last 3,599 or 3,601 seconds, in order to keep it within 0.9 seconds of UT1, based on measurements of the mean solar day. The modern English word hour is a development of the Anglo-Norman houre and Middle English ure, first attested in the 13th century.
It displaced the Old English "tide" and "stound". The Anglo-Norman term was a borrowing of Old French ure, a variant of ore, which derived from Latin hōra and Greek hṓrā. Like Old English tīd and stund, hṓrā was a vaguer word for any span of time, including seasons and years, its Proto-Indo-European root has been reconstructed as *yeh₁-, making hour distantly cognate with year. The time of day is expressed in English in terms of hours. Whole hours on a 12-hour clock are expressed using the contracted phrase o'clock, from the older of clock. Hours on a 24-hour clock are expressed as "hundred" or "hundred hours". Fifteen and thirty minutes past the hour is expressed as "a quarter past" or "after" and "half past" from their fraction of the hour. Fifteen minutes before the hour may be expressed as "a quarter to", "of", "till", or "before" the hour; the ancient Egyptians began dividing the night into wnwt at some time before the compilation of the Dynasty V Pyramid Texts in the 24th century BC. By 2150 BC, diagrams of stars inside Egyptian coffin lids—variously known as "diagonal calendars" or "star clocks"—attest that there were 12 of these.
Clagett writes that it is "certain" this duodecimal division of the night followed the adoption of the Egyptian civil calendar placed c. 2800 BC on the basis of analyses of the Sothic cycle, but a lunar calendar long predated this and would have had twelve months in each of its years. The coffin diagrams show that the Egyptians took note of the heliacal risings of 36 stars or constellations, one for each of the ten-day "weeks" of their civil calendar; each night, the rising of eleven of these decans were noted, separating the night into twelve divisions whose middle terms would have lasted about 40 minutes each. The original decans used by the Egyptians would have fallen noticeably out of their proper places over a span of several centuries. By the time of Amenhotep III, the priests at Karnak were using water clocks to determine the hours; these were filled to the brim at sunset and the hour determined by comparing the water level against one of its twelve gauges, one for each month of the year.
During the New Kingdom, another system of decans was used, made up of 24 stars over the course of the year and 12 within any one night. The division of the day into 12 hours was accomplished by sundials marked with ten equal divisions; the morning and evening periods when the sundials failed to note time were observed as the first and last hours. The Egyptian hours were connected both with the priesthood of the gods and with their divine services. By the New Kingdom, each hour was conceived as a specific region of the sky or underworld through which Ra's solar barge travelled. Protective deities were used as the names of the hours; as the protectors and resurrectors of the sun, the goddesses of the night hours were considered to hold power over all lifespans and thus became part of Egyptian funerary rituals. Two fire-spitting cobras were said to guard the gates of each hour of the underworld, Wadjet and the rearing cobra were sometimes referenced as wnwt from their role protecting the dead through these gates.
The Egyptian for astronomer, used as a synonym for priest, was wnwty, "One of the Hours" or "Hour-Watcher". The earliest forms of wnwt include one or three stars, with the solar hours including the determinative hieroglyph for "sun". Ancient China divided its day into 100 "marks" running from midnight to midnight; the system is said to have been used since remote antiquity, credited to the legendary Yellow Emperor, but is first attested in Han-era water clocks and in the 2nd-century history of that dynasty. It was measured with sundials and water clocks. Into the Eastern Han, the Chinese measured their day schematically, adding the 20-ke difference between the solstices evenly throughout the year, one every nine days. During the night, time was more commonly
Jet Propulsion Laboratory
The Jet Propulsion Laboratory is a federally funded research and development center and NASA field center in La Cañada Flintridge, United States, though it is referred to as residing in Pasadena, because it has a Pasadena ZIP Code. Founded in the 1930s, the JPL is owned by NASA and managed by the nearby California Institute of Technology for NASA; the laboratory's primary function is the construction and operation of planetary robotic spacecraft, though it conducts Earth-orbit and astronomy missions. It is responsible for operating NASA's Deep Space Network. Among the laboratory's major active projects are the Mars Science Laboratory mission, the Mars Reconnaissance Orbiter, the Juno spacecraft orbiting Jupiter, the NuSTAR X-ray telescope, the SMAP satellite for earth surface soil moisture monitoring, the Spitzer Space Telescope, it is responsible for managing the JPL Small-Body Database, provides physical data and lists of publications for all known small Solar System bodies. The JPL's Space Flight Operations Facility and Twenty-Five-Foot Space Simulator are designated National Historic Landmarks.
JPL traces its beginnings to 1936 in the Guggenheim Aeronautical Laboratory at the California Institute of Technology when the first set of rocket experiments were carried out in the Arroyo Seco. Caltech graduate students Frank Malina, Qian Xuesen, Weld Arnold, Apollo M. O. Smith, along with Jack Parsons and Edward S. Forman, tested a small, alcohol-fueled motor to gather data for Malina's graduate thesis. Malina's thesis advisor was engineer/aerodynamicist Theodore von Kármán, who arranged for U. S. Army financial support for this "GALCIT Rocket Project" in 1939. In 1941, Parsons, Martin Summerfield, pilot Homer Bushey demonstrated the first jet-assisted takeoff rockets to the Army. In 1943, von Kármán, Malina and Forman established the Aerojet Corporation to manufacture JATO rockets; the project took on the name Jet Propulsion Laboratory in November 1943, formally becoming an Army facility operated under contract by the university. During JPL's Army years, the laboratory developed two deployed weapon systems, the MGM-5 Corporal and MGM-29 Sergeant intermediate-range ballistic missiles.
These missiles were the first US ballistic missiles developed at JPL. It developed a number of other weapons system prototypes, such as the Loki anti-aircraft missile system, the forerunner of the Aerobee sounding rocket. At various times, it carried out rocket testing at the White Sands Proving Ground, Edwards Air Force Base, Goldstone, California. In 1954, JPL teamed up with Wernher von Braun's engineers at the Army Ballistic Missile Agency's Redstone Arsenal in Huntsville, Alabama, to propose orbiting a satellite during the International Geophysical Year; the team lost that proposal to Project Vanguard, instead embarked on a classified project to demonstrate ablative re-entry technology using a Jupiter-C rocket. They carried out three successful sub-orbital flights in 1956 and 1957. Using a spare Juno I, the two organizations launched the United States' first satellite, Explorer 1, on January 31, 1958. JPL was transferred to NASA in December 1958, becoming the agency's primary planetary spacecraft center.
JPL engineers designed and operated Ranger and Surveyor missions to the Moon that prepared the way for Apollo. JPL led the way in interplanetary exploration with the Mariner missions to Venus and Mercury. In 1998, JPL opened the Near-Earth Object Program Office for NASA; as of 2013, it has found 95% of asteroids that are a kilometer or more in diameter that cross Earth's orbit. JPL was early to employ female mathematicians. In the 1940s and 1950s, using mechanical calculators, women in an all-female computations group performed trajectory calculations. In 1961, JPL hired Dana Ulery as the first female engineer to work alongside male engineers as part of the Ranger and Mariner mission tracking teams. JPL has been recognized four times by the Space Foundation: with the Douglas S. Morrow Public Outreach Award, given annually to an individual or organization that has made significant contributions to public awareness of space programs, in 1998; when it was founded, JPL's site was west of a rocky flood-plain – the Arroyo Seco riverbed – above the Devil's Gate dam in the northwestern panhandle of the city of Pasadena.
While the first few buildings were constructed in land bought from the city of Pasadena, subsequent buildings were constructed in neighboring unincorporated land that became part of La Cañada Flintridge. Nowadays, most of the 177 acres of the U. S. federal government-owned NASA property that makes up the JPL campus is located in La Cañada Flintridge. Despite this, JPL still uses a Pasadena address as its official mailing address; the city of La Cañada Flintridge was incorporated in 1976, well after JPL attained international recognition as a Pasadena institution. There has been occasional rivalry between the two cities over the issue of which one should be mentioned in the media as the home of the laboratory. There are 6,000 full-time Caltech employees, a few thousand additional contractors working on any given day. NASA has a resident office at the facility staffed by federal managers who oversee JPL's activities and work for NASA. There are some Caltech graduate students, college student interns and co-op students.
The JPL Education Office serves educators and students by providi
Orders of magnitude (length)
The following are examples of orders of magnitude for different lengths. To help compare different orders of magnitude, the following list describes various lengths between 1.6 × 10 − 35 metres and 10 10 10 122 metres. To help compare different orders of magnitude, this section lists lengths shorter than 10−23 m. 1.6 × 10−11 yoctometres – the Planck length. 1 ym – 1 yoctometre, the smallest named subdivision of the metre in the SI base unit of length, one septillionth of a metre 1 ym – length of a neutrino. 2 ym – the effective cross-section radius of 1 MeV neutrinos as measured by Clyde Cowan and Frederick Reines To help compare different orders of magnitude, this section lists lengths between 10−23 metres and 10−22 metres. To help compare different orders of magnitude, this section lists lengths between 10−22 m and 10−21 m. 100 ym – length of a top quark, one of the smallest known quarks To help compare different orders of magnitude, this section lists lengths between 10−21 m and 10−20 m. 2 zm – length of a preon, hypothetical particles proposed as subcomponents of quarks and leptons.
2 zm – radius of effective cross section for a 20 GeV neutrino scattering off a nucleon 7 zm – radius of effective cross section for a 250 GeV neutrino scattering off a nucleon To help compare different orders of magnitude, this section lists lengths between 10−20 m and 10−19 m. 15 zm – length of a high energy neutrino 30 zm – length of a bottom quark To help compare different orders of magnitude, this section lists lengths between 10−19 m and 10−18 m. 177 zm – de Broglie wavelength of protons at the Large Hadron Collider To help compare different orders of magnitude, this section lists lengths between 10−18 m and 10−17 m. 1 am – sensitivity of the LIGO detector for gravitational waves 1 am – upper limit for the size of quarks and electrons 1 am – upper bound of the typical size range for "fundamental strings" 1 am – length of an electron 1 am – length of an up quark 1 am – length of a down quark To help compare different orders of magnitude, this section lists lengths between 10−17 m and 10−16 m. 10 am – range of the weak force To help compare different orders of magnitude, this section lists lengths between 10−16 m and 10−15 m. 100 am – all lengths shorter than this distance are not confirmed in terms of size 850 am – approximate proton radius The femtometre is a unit of length in the metric system, equal to 10−15 metres.
In particle physics, this unit is more called a fermi with abbreviation "fm". To help compare different orders of magnitude, this section lists lengths between 10−15 metres and 10−14 metres. 1 fm – length of a neutron 1.5 fm – diameter of the scattering cross section of an 11 MeV proton with a target proton 1.75 fm – the effective charge diameter of a proton 2.81794 fm – classical electron radius 7 fm – the radius of the effective scattering cross section for a gold nucleus scattering a 6 MeV alpha particle over 140 degrees To help compare different orders of magnitude, this section lists lengths between 10−14 m and 10−13 m. 1.75 to 15 fm – Diameter range of the atomic nucleus To help compare different orders of magnitude, this section lists lengths between 10−13 m and 10−12 m. 570 fm – typical distance from the atomic nucleus of the two innermost electrons in the uranium atom, the heaviest naturally-occurring atom To help compare different orders of magnitude this section lists lengths between 10−12 and 10−11 m. 1 pm – distance between atomic nuclei in a white dwarf 2.4 pm – The Compton wavelength of the electron 5 pm – shorter X-ray wavelengths To help compare different orders of magnitude this section lists lengths between 10−11 and 10−10 m. 25 pm – approximate radius of a helium atom, the smallest neutral atom 50 pm – radius of a hydrogen atom 50 pm – bohr radius: approximate radius of a hydrogen atom ~50 pm – best resolution of a high-resolution transmission electron microscope 60 pm – radius of a carbon atom 93 pm – length of a diatomic carbon molecule To help compare different orders of magnitude this section lists lengths between 10−10 and 10−9 m. 100 pm – 1 ångström 100 pm – covalent radius of sulfur atom 120 pm – van der Waals radius of a neutral hydrogen atom 120 pm – radius of a gold atom 126 pm – covalent radius of ruthenium atom 135 pm – covalent radius of technetium atom 150 pm – Length of a typical covalent bond 153 pm – covalent radius of silver atom 155 pm – covalent radius of zirconium atom 175 pm – covalent radius of thulium atom 200 pm – highest resolution of a typical electron microscope 225 pm – covalent radius of caesium atom 280 pm – Average size of the water molecule 298 pm – radius of a caesium atom, calculated to be the largest atomic radius 340 pm – thickness of single layer graphene 356.68 pm – width of diamond unit cell 403 pm – width of lithium fluoride unit cell 500 pm – Width of protein α helix 543 pm – silicon lattice spacing 560 pm – width of sodium chloride unit cell 700 pm – width of glucose molecule 780 pm – mean width of quartz unit cell 820 pm – mean width of ice unit cell 900 pm – mean width of coesite unit cell To help compare different orders
An asteroid family is a population of asteroids that share similar proper orbital elements, such as semimajor axis and orbital inclination. The members of the families are thought to be fragments of past asteroid collisions. An asteroid family is a more specific term than asteroid group whose members, while sharing some broad orbital characteristics, may be otherwise unrelated to each other. Large prominent families contain several hundred recognized asteroids. Small, compact families may have only about ten identified members. About 33% to 35% of asteroids in the main belt are family members. There are about 20 to 30 reliably recognized families, with several tens of less certain groupings. Most asteroid families are found in the main asteroid belt, although several family-like groups such as the Pallas family, Hungaria family, the Phocaea family lie at smaller semi-major axis or larger inclination than the main belt. One family has been identified associated with the dwarf planet Haumea; some studies have tried to find evidence of collisional families among the trojan asteroids, but at present the evidence is inconclusive.
The families are thought to form as a result of collisions between asteroids. In many or most cases the parent body was shattered, but there are several families which resulted from a large cratering event which did not disrupt the parent body; such cratering families consist of a single large body and a swarm of asteroids that are much smaller. Some families have complex internal structures which are not satisfactorily explained at the moment, but may be due to several collisions in the same region at different times. Due to the method of origin, all the members have matching compositions for most families. Notable exceptions are those families. Asteroid families are thought to have lifetimes of the order of a billion years, depending on various factors; this is shorter than the Solar System's age, so few if any are relics of the early Solar System. Decay of families occurs both because of slow dissipation of the orbits due to perturbations from Jupiter or other large bodies, because of collisions between asteroids which grind them down to small bodies.
Such small asteroids become subject to perturbations such as the Yarkovsky effect that can push them towards orbital resonances with Jupiter over time. Once there, they are rapidly ejected from the asteroid belt. Tentative age estimates have been obtained for some families, ranging from hundreds of millions of years to less than several million years as for the compact Karin family. Old families are thought to contain few small members, this is the basis of the age determinations, it is supposed that many old families have lost all the smaller and medium-sized members, leaving only a few of the largest intact. A suggested example of such old family remains are 113 Amalthea pair. Further evidence for a large number of past families comes from analysis of chemical ratios in iron meteorites; these show that there must have once been at least 50 to 100 parent bodies large enough to be differentiated, that have since been shattered to expose their cores and produce the actual meteorites. When the orbital elements of main belt asteroids are plotted, a number of distinct concentrations are seen against the rather uniform distribution of non-family background asteroids.
These concentrations are the asteroid families. Interlopers are asteroids classified as family members based on their so-called proper orbital elements but having spectroscopic properties distinct from the bulk of the family, suggesting that they, contrary to the true family members, did not originate from the same parent body that once fragmented upon a collisional impact. Speaking and their membership are identified by analysing the proper orbital elements rather than the current osculating orbital elements, which fluctuate on timescales of tens of thousands of years; the proper elements are related constants of motion that remain constant for times of at least tens of millions of years, longer. The Japanese astronomer Kiyotsugu Hirayama pioneered the estimation of proper elements for asteroids, first identified several of the most prominent families in 1918. In his honor, asteroid families are sometimes called Hirayama families; this applies to the five prominent groupings discovered by him.
Present day computer-assisted searches have identified more than a hundred asteroid families. The most prominent algorithms have been the hierarchical clustering method, which looks for groupings with small nearest-neighbour distances in orbital element space, wavelet analysis, which builds a density-of-asteroids map in orbital element space, looks for density peaks; the boundaries of the families are somewhat vague because at the edges they blend into the background density of asteroids in the main belt. For this reason the number of members among discovered asteroids is only known and membership is uncertain for asteroids near the edges. Additionally, some interlopers from the heterogeneous background asteroid population are expected in the central regions of a family. Since the true family members caused by the collision are expected to have similar compositions, most such interlopers can in principle be recognised by spectral properties which do not matc
The National Aeronautics and Space Administration is an independent agency of the United States Federal Government responsible for the civilian space program, as well as aeronautics and aerospace research. NASA was established in 1958; the new agency was to have a distinctly civilian orientation, encouraging peaceful applications in space science. Since its establishment, most US space exploration efforts have been led by NASA, including the Apollo Moon landing missions, the Skylab space station, the Space Shuttle. NASA is supporting the International Space Station and is overseeing the development of the Orion Multi-Purpose Crew Vehicle, the Space Launch System and Commercial Crew vehicles; the agency is responsible for the Launch Services Program which provides oversight of launch operations and countdown management for unmanned NASA launches. NASA science is focused on better understanding Earth through the Earth Observing System. From 1946, the National Advisory Committee for Aeronautics had been experimenting with rocket planes such as the supersonic Bell X-1.
In the early 1950s, there was challenge to launch an artificial satellite for the International Geophysical Year. An effort for this was the American Project Vanguard. After the Soviet launch of the world's first artificial satellite on October 4, 1957, the attention of the United States turned toward its own fledgling space efforts; the US Congress, alarmed by the perceived threat to national security and technological leadership, urged immediate and swift action. On January 12, 1958, NACA organized a "Special Committee on Space Technology", headed by Guyford Stever. On January 14, 1958, NACA Director Hugh Dryden published "A National Research Program for Space Technology" stating: It is of great urgency and importance to our country both from consideration of our prestige as a nation as well as military necessity that this challenge be met by an energetic program of research and development for the conquest of space... It is accordingly proposed that the scientific research be the responsibility of a national civilian agency...
NACA is capable, by rapid extension and expansion of its effort, of providing leadership in space technology. While this new federal agency would conduct all non-military space activity, the Advanced Research Projects Agency was created in February 1958 to develop space technology for military application. On July 29, 1958, Eisenhower signed the National Aeronautics and Space Act, establishing NASA; when it began operations on October 1, 1958, NASA absorbed the 43-year-old NACA intact. A NASA seal was approved by President Eisenhower in 1959. Elements of the Army Ballistic Missile Agency and the United States Naval Research Laboratory were incorporated into NASA. A significant contributor to NASA's entry into the Space Race with the Soviet Union was the technology from the German rocket program led by Wernher von Braun, now working for the Army Ballistic Missile Agency, which in turn incorporated the technology of American scientist Robert Goddard's earlier works. Earlier research efforts within the US Air Force and many of ARPA's early space programs were transferred to NASA.
In December 1958, NASA gained control of the Jet Propulsion Laboratory, a contractor facility operated by the California Institute of Technology. The agency's leader, NASA's administrator, is nominated by the President of the United States subject to approval of the US Senate, reports to him or her and serves as senior space science advisor. Though space exploration is ostensibly non-partisan, the appointee is associated with the President's political party, a new administrator is chosen when the Presidency changes parties; the only exceptions to this have been: Democrat Thomas O. Paine, acting administrator under Democrat Lyndon B. Johnson, stayed on while Republican Richard Nixon tried but failed to get one of his own choices to accept the job. Paine was confirmed by the Senate in March 1969 and served through September 1970. Republican James C. Fletcher, appointed by Nixon and confirmed in April 1971, stayed through May 1977 into the term of Democrat Jimmy Carter. Daniel Goldin was appointed by Republican George H. W. Bush and stayed through the entire administration of Democrat Bill Clinton.
Robert M. Lightfoot, Jr. associate administrator under Democrat Barack Obama, was kept on as acting administrator by Republican Donald Trump until Trump's own choice Jim Bridenstine, was confirmed in April 2018. Though the agency is independent, the survival or discontinuation of projects can depend directly on the will of the President; the first administrator was Dr. T. Keith Glennan appointed by Republican President Dwight D. Eisenhower. During his term he brought together the disparate projects in American space development research; the second administrator, James E. Webb, appointed by President John F. Kennedy, was a Democrat who first publicly served under President Harry S. Truman. In order to implement the Apollo program to achieve Kennedy's Moon la
The Jupiter trojans called Trojan asteroids or Trojans, are a large group of asteroids that share the planet Jupiter's orbit around the Sun. Relative to Jupiter, each Trojan librates around one of Jupiter's two stable Lagrange points: L4, lying 60° ahead of the planet in its orbit, L5, 60° behind. Jupiter trojans are distributed in two elongated, curved regions around these Lagrangian points with an average semi-major axis of about 5.2 AU. The first Jupiter trojan discovered, 588 Achilles, was spotted in 1906 by German astronomer Max Wolf. A total of 7,040 Jupiter trojans have been found as of October 2018. By convention, they are each named from Greek mythology after a figure of the Trojan War, hence the name "Trojan"; the total number of Jupiter trojans larger than 1 km in diameter is believed to be about 1 million equal to the number of asteroids larger than 1 km in the asteroid belt. Like main-belt asteroids, Jupiter trojans form families. Jupiter trojans are dark bodies with 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 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 later, during the migration of giant planets; the term "Trojan Asteroid" refers to the asteroids co-orbital with Jupiter, but the general term "trojan" is sometimes more applied to other small Solar System bodies with similar relationships to larger bodies: for example, there are both Mars trojans and Neptune trojans, as well as a recently-discovered Earth trojan. The term "Trojan asteroid" is understood to mean the Jupiter trojans because the first Trojans were discovered near Jupiter's orbit and Jupiter has by far the most known Trojans. In 1772, Italian-born mathematician Joseph-Louis Lagrange, in studying the restricted 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 around the point of equilibrium in a tadpole or horseshoe orbit. These leading and trailing points are called the L5 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 made the first recorded observation of a trojan, 1999 RM11, in 1904, but neither he nor others appreciated its significance at the time. Barnard believed he had seen the discovered Saturnian satellite Phoebe, only two arc-minutes away in the sky at the time, or 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 Max Wolf of Heidelberg-Königstuhl State Observatory discovered an asteroid at the L4 Lagrangian point of the Sun–Jupiter system named 588 Achilles. In 1906–1907 two more Jupiter trojans were found by fellow German astronomer August Kopff.
Hektor, like Achilles, belonged to the L4 swarm, whereas Patroclus was the first asteroid known to reside at the L5 Lagrangian point. 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; as of October 2018 there are 4,601 known Jupiter trojans at L4 and 2,439 at L5. The custom of naming all asteroids in Jupiter's L4 and L5 points after famous heroes of the Trojan War was suggested by Johann Palisa of Vienna, the first to calculate their orbits. Asteroids in the leading orbit are named after Greek heroes, those at the trailing orbit are named after the heroes of Troy; the asteroids 617 Patroclus and 624 Hektor were named before the Greece/Troy rule was devised, resulting in a Greek spy in the Trojan node and a Trojan spy in the Greek node. Estimates of the total number of Jupiter trojans are based on deep surveys of limited areas of the sky; the L4 swarm is believed to hold between 160–240,000 asteroids with diameters larger than 2 km and about 600,000 with diameters larger than 1 km.
If the L5 swarm contains a comparable number of objects, there are more than 1 million Jupiter trojans 1 km in size or larger. For the objects brighter than absolute magnitude 9.0 the population is 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 the assumption that all Jupiter trojans have a low albedo of about 0.04, whereas small bodies may have an average albedo as high as 0.12. According to the new estimates, the total number of Jupiter trojans with a diameter larger than 2 km is 6,300 ± 1,000 and 3,400 ± 500 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 L4