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
Heidelberg is a university town in Baden-Württemberg situated on the river Neckar in south-west Germany. In the 2016 census, its population was 159,914, with a quarter of its population being students. Located about 78 km south of Frankfurt, Heidelberg is the fifth-largest city in the German state of Baden-Württemberg. Heidelberg is part of the densely populated Rhine-Neckar Metropolitan Region. Founded in 1386, Heidelberg University is Germany's oldest and one of Europe's most reputable universities. A scientific hub in Germany, the city of Heidelberg is home to several internationally renowned research facilities adjacent to its university, including four Max Planck Institutes. A former residence of the Electorate of the Palatinate, Heidelberg is a popular tourist destination due to its romantic cityscape, including Heidelberg Castle, the Philosophers' Walk, the baroque style Old Town. Heidelberg is in the Rhine Rift Valley, on the left bank of the lower part of the Neckar in a steep valley in the Odenwald.
It is bordered by the Gaisberg mountains. The Neckar here flows in an east-west direction. On the right bank of the river, the Heiligenberg mountain rises to a height of 445 meters; the Neckar flows into the Rhine 22 kilometres north-west in Mannheim. Villages incorporated during the 20th century stretch from the Neckar Valley along the Bergstraße, a road running along the Odenwald hills. Heidelberg is on European walking route E1. Since Heidelberg is among the warmest regions of Germany, plants atypical of the central-European climate flourish there, including almond and fig trees. Alongside the Philosophenweg on the opposite side of the Old Town, winegrowing was restarted in 2000. There is a wild population of African rose-ringed parakeets, a wild population of Siberian swan geese, which can be seen on the islands in the Neckar near the district of Bergheim. Heidelberg is a unitary authority within the Regierungsbezirk Karlsruhe; the Rhein-Neckar-Kreis rural district surrounds it and has its seat in the town, although the town is not a part of the district.
Heidelberg is a part of the Rhine-Neckar Metropolitan Region referred to as the Rhein-Neckar Triangle. This region consists of the southern part of the State of Hessen, the southern part of the State of Rhineland-Palatinate, the administrative districts of Mannheim and Heidelberg, the southern municipalities of the Rhein-Neckar-Kreis; the Rhein-Neckar Triangle became a European metropolitan area in 2005. Heidelberg consists of 15 districts distributed in six sectors of the town. In the central area are Altstadt and Weststadt; the new district will have 5,000–6,000 residents and employment for 7,000. Further new residential space for 10,000-15,000 residents was made available in Patrick Henry Village following the departure of the US Armed Forces; the following towns and communes border the city of Heidelberg, beginning in the west and in a clockwise direction: Edingen-Neckarhausen, Schriesheim, Schönau, Neckargemünd, Gaiberg, Sandhausen, Plankstadt and Mannheim. Heidelberg has an oceanic climate, defined by the protected valley between the Pfälzerwald and the Odenwald.
Year-round, the mild temperatures are determined by maritime air masses coming from the west. In contrast to the nearby Upper Rhine Plain, Heidelberg's position in the valley leads to more frequent easterly winds than average; the hillsides of the Odenwald favour precipitation. The warmest month is July, the coldest is January. Temperatures rise beyond 30 °C in midsummer. According to the German Meteorological Service, Heidelberg was the warmest place in Germany in 2009. Between 600,000 and 200,000 years ago, "Heidelberg Man" died at nearby Mauer, his jaw bone was discovered in 1907. Scientific dating determined his remains as the earliest evidence of human life in Europe. In the 5th century BC, a Celtic fortress of refuge and place of worship were built on the Heiligenberg, or "Mountain of Saints". Both places can still be identified. In 40 AD, a fort occupied by the 24th Roman cohort and the 2nd Cyrenaican cohort; the early Byzantine/late Roman Emperor Valentinian I, in 369 AD, built new and maintained older castra and a signal tower on the bank of the Neckar.
They built a wooden bridge based on stone pillars across it. The camp protected the first civilian settlements; the Romans remained until 260 AD. The local administrative center in Roman times was the nearby city of Lopodunum. Modern Heidelberg can trace its beginnings to the fifth century; the village Bergheim is first mentioned for that period in documents dated to 769 AD. Bergheim now lies in the middle of modern Heidelberg; the people converted to Christianity. In 863 AD, the monastery of St. Michael was founded on the Heiligenberg inside the double rampart of the Celtic fortress. Around 1130, the Neuburg Monastery was founded in the Neckar valley. At the same time, the bishopric of Worms extended its influence into the valley, founding Schönau Abbey in 1142. Modern He
Kundry is an S-type asteroid belonging to the Flora family in the Main Belt. Its rotation period is 12.605 hours. Like a number of asteroids discovered by Max Wolf around this time, it is named after a female character in opera, in this case from Richard Wagner's Parsifal. 553 Kundry at AstDyS-2, Asteroids—Dynamic Site Ephemeris · Observation prediction · Orbital info · Proper elements · Observational info 553 Kundry at the JPL Small-Body Database Close approach · Discovery · Ephemeris · Orbit diagram · Orbital elements · Physical parameters
Die Walküre, WWV 86B is the second of the four music dramas that constitute Richard Wagner's Der Ring des Nibelungen. It was performed, as a single opera, at the National Theatre Munich on 26 June 1870, received its first performance as part of the Ring cycle at the Bayreuth Festspielhaus on 14 August 1876; as the Ring cycle was conceived by Wagner in reverse order of performance, Die Walküre was the penultimate of the four texts to be written, although Wagner composed the music in the proper sequence. The text was completed by July 1852, the music by March 1856. In his composition Wagner followed the principles related to the form of musical drama which he had set out in his 1851 essay Opera and Drama under which the music would interpret the text reflecting the feelings and moods behind the work, by using a system of recurring leitmotifs to represent people and situations rather than the conventional operatic units of arias and choruses. Wagner showed greater flexibility in the application of these principles in Act 3 when the Valkyrie maidens engage in regular ensemble singing.
As with Das Rheingold, Wagner wished to defer any performance of the new work until it could be shown in the context of the completed cycle, but the 1870 Munich premiere was arranged at the insistence of his patron, King Ludwig II of Bavaria. More so than the other Ring dramas, Die Walküre has achieved some popularity as a stand-alone work, continues to be performed independently from its role in the tetralogy; the story of Die Walküre is based on the Norse mythology told in the Volsunga Saga and the Poetic Edda. In this version the Volsung twins Sieglinde and Siegmund, separated in childhood and fall in love; this union angers the gods. Sieglinde and the couple's unborn child are saved by the defiant actions of Wotan's Valkyrie daughter Brünnhilde, who as a result faces the gods' retribution. Wagner began work on what became his Ring project in October 1848 when he prepared a prose outline for Siegfried's Death, based on the legendary hero of Germanic myth. During the following months he developed the outline into libretto.
After his flight to Switzerland in May 1849, Wagner continued to expand his project, having decided that a single work would not suffice for his purposes. He would therefore create a series of music dramas, each telling a stage of the story, basing the narrative on a combination of myth and imagination. In 1851 he outlined his purposes in his essay "A Communication to My Friends": "I propose to produce my myth in three complete dramas, preceded by a lengthy Prelude"; each of these dramas would, he said, constitute an independent whole, but would not be performed separately. "At a specially-appointed Festival, I propose, some future time, to produce those three Dramas with their Prelude, in the course of three days and a fore-evening". In accordance with this scheme Wagner preceded Siegfried's Death (later Götterdämmerung with the story of Siegfried's youth, Young Siegfried renamed Siegfried; this was in turn preceded by Die Walküre, dealing with Siegfried's origins, the whole tetralogy being fronted by a prologue, Das Rheingold.
Because Wagner prepared his texts in reverse chronological sequence, Die Walküre was the third of the dramas to be conceived and written, but appears second in the tetralogy. During the lengthy time that has passed since the gods entered Valhalla at the end of Das Rheingold, Fafner has used the Tarnhelm to assume the form of a dragon, guards the gold and the ring in the depths of the forest. Wotan has visited Erda seeking wisdom, by her has fathered a daughter, Brünnhilde. These, with Brünnhilde, form the Valkyries, whose task is to recover heroes fallen in battle and bring them to Valhalla, where they will protect the fortress from Alberich's assault should the dwarf recover the ring. Wotan has wandered the earth, with a woman of the Völsung race has fathered the twins Siegmund and Sieglinde, who have grown up separately and unaware of each other. From the Volsungs Wotan hopes for a hero who, unencumbered by the gods' treaties, will obtain the ring from Fafner; as a storm rages, Siegmund finds shelter from his enemies in a large dwelling built around a massive ash-tree.
Unarmed and wounded, he collapses with exhaustion. Sieglinde enters; as they talk, they look at each other with growing emotion. Siegmund gets ready to leave, telling Sieglinde that misfortune follows him and he does not want to bring it on her. Hunding returns, questions Siegmund's presence. Calling himself Wehwalt, Siegmund explains that he grew up in the forest with his parents and twin sister. One day he found their home burned down, his mother killed and his sister gone, he fought with the relatives of a girl being forced into marriage. His weapons were destroyed, the bride was killed, he was forced to flee. Hunding reveals. Before leaving, Sieglinde gives a meaningful glance to a particular spot on the tree in which, the firelight reveals, a sword is buried to the hilt. Sieglinde returns, she reveals that she was forced into the marriage and that during their wedding feast, an old man appeared and plunged a sword into the trunk of the ash tree which neither Hunding nor any of his companions have been a
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
Maximilian Franz Joseph Cornelius "Max" Wolf was a German astronomer and a pioneer in the field of astrophotography. He was chairman of astronomy at the University of Heidelberg and director of the Heidelberg-Königstuhl State Observatory from 1902 until his death. Max Wolf was born in Germany on June 21, 1863, the son of medical doctor Franz Wolf, his father encouraged an interest in science and built an observatory for his son in the garden of the family home. It is from here that Wolf was credited with his first astronomical discovery, comet 14P/Wolf, in 1884. Wolf attended his local university and, in 1888, at the age of 25, was awarded a Ph. D. by the University of Heidelberg. He spent one year of post-graduate study in Stockholm, the only significant time he would spend outside of Heidelberg in his life, he returned to the University of Heidelberg and accepted the position of privat-docent in 1890. A popular lecturer in astronomy, he declined offers of positions from other institutions. In 1902 he was appointed Chair of Astronomy and Director of the new Landessternwarte Heidelberg-Königstuhl observatory, positions he would hold until his death in 1932.
While the new observatory was being built Wolf was appointed to supervise the construction and outfitting of the astrophysics half of the observatory. He proved to be not only a capable supervisor but a successful fundraiser; when sent to America to study the construction of the large new telescopes being built there he returned not only with telescope plans but with a grant of $10,000 from the American philanthropist Catherine Wolfe Bruce. Wolf designed and ordered a double refractor telescope from American astronomer and instrument builder John Brashear; this instrument, known as the Bruce double-astrograph, with parallel 16 in lenses and a fast f/5 focal ratio, became the observatory's primary research telescope. Wolf raised money for a 28 in reflector telescope, the first for the observatory, used for spectroscopy. In 1910 Wolf proposed to the Carl Zeiss optics firm the creation of a new instrument which would become known as the planetarium. World War I intervened before the invention could be developed, but the Carl Zeiss company resumed this project after peace was restored.
The first official public showing was at the Deutsches Museum in Munich, Germany on October 21, 1923. During his trip to America Wolf was interested in learning more about the new field of astrophotography, he met the American astronomer and astrophotographer E. E. Barnard, the two became lifelong correspondents, competitors and friends. Wolf wrote a long obituary for Barnard upon his death in 1923. Heidelberg University became well known for astronomy under Wolf's leadership. Wolf himself was an active researcher, contributing numerous papers in many areas of astronomy up to the end of his life, he died in Heidelberg on October 3, 1932, at the age of 69. He was survived by three sons. Wolf continued to discover them throughout his life, he co-discovered several comets, including 14P/Wolf and 43P/Wolf-Harrington. Wolf won a competition with E. E. Barnard on who would be the first to observe the return of Halley's Comet in April 1910, he discovered or co-discovered four supernovae: SN 1895A, SN 1909A, SN 1920A, with Reinmuth, SN 1926A.
One of the many significant contributions Wolf made was in the determination of the nature of dark nebulae. These areas of the sky, thought since William Herschel's time to be "holes in the sky", were a puzzle to astronomers of the time. In collaboration with E. E. Barnard, Wolf proved, by careful photographic analysis, that dark nebulae were huge clouds of fine opaque dust. Along with E. E. Barnard, Wolf applied astrophotography to the observation of stars; the Bruce double-astrograph was designed to hunt dim asteroids but it was found to be ideally suited for the study of the proper motion of low-luminosity stars using much the same technique. In 1919 Wolf published a catalog of the locations of over one thousand stars along with their measured proper motion; these stars are still identified by his name and catalog number. Among the stars he discovered is Wolf 359, a dim red dwarf, found to be one of the nearest stars to our solar system, he continued to add proper motion star discoveries to this catalog throughout his life, with the catalog totaling over 1500 stars, many more than all of his competitors combined.
These stars are significant because stars with low luminosity and high proper motion, such as Barnard's Star and Wolf 359, are relatively close to the Earth and thus the stars in Wolf's catalog remain popular subjects for astronomical research. The methods used by E. E. Barnard and Wolf were continued by Frank Elmore Ross and George Van Biesbroeck through the mid-20th century. Since that time photographic plates have been replaced with more sensitive electronic photodetectors for astronomical surveys. In 1891, Wolf discovered his first asteroid, 323 Brucia, named it after Catherine Wolfe Bruce, he pioneered the use of astrophotographic techniques to automate the discovery of asteroids, as opposed to older visual methods, as a result of which asteroid discovery rates increased. In time-exposure photographs, asteroids appear as short streaks due to their planetary motion with respect to fixed stars. Wolf discovered more than 200 asteroids in his lifetime. Among his many discoveries was 588 Achilles in 1906, as well as two other Trojans: 659 Nestor and 884 Priamus.
He discovered 887 Alinda in 1918, now recognized as an Earth-crossing Amor asteroid (or sometimes classified as
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