The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, greater than 1 is a hyperbola; the term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is used for the isolated two-body problem, but extensions exist for objects following a Klemperer rosette orbit through the galaxy. In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit; the eccentricity of this Kepler orbit is a non-negative number. The eccentricity may take the following values: circular orbit: e = 0 elliptic orbit: 0 < e < 1 parabolic trajectory: e = 1 hyperbolic trajectory: e > 1 The eccentricity e is given by e = 1 + 2 E L 2 m red α 2 where E is the total orbital energy, L is the angular momentum, mred is the reduced mass, α the coefficient of the inverse-square law central force such as gravity or electrostatics in classical physics: F = α r 2 or in the case of a gravitational force: e = 1 + 2 ε h 2 μ 2 where ε is the specific orbital energy, μ the standard gravitational parameter based on the total mass, h the specific relative angular momentum.
For values of e from 0 to 1 the orbit's shape is an elongated ellipse. The limit case between an ellipse and a hyperbola, when e equals 1, is parabola. Radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity. Radial orbits hence eccentricity equal to one. Keeping the energy constant and reducing the angular momentum, elliptic and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1. For a repulsive force only the hyperbolic trajectory, including the radial version, is applicable. For elliptical orbits, a simple proof shows that arcsin yields the projection angle of a perfect circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury, one must calculate the inverse sine to find the projection angle of 11.86 degrees. Next, tilt any circular object by that angle and the apparent ellipse projected to your eye will be of that same eccentricity; the word "eccentricity" comes from Medieval Latin eccentricus, derived from Greek ἔκκεντρος ekkentros "out of the center", from ἐκ- ek-, "out of" + κέντρον kentron "center".
"Eccentric" first appeared in English in 1551, with the definition "a circle in which the earth, sun. Etc. deviates from its center". By five years in 1556, an adjectival form of the word had developed; the eccentricity of an orbit can be calculated from the orbital state vectors as the magnitude of the eccentricity vector: e = | e | where: e is the eccentricity vector. For elliptical orbits it can be calculated from the periapsis and apoapsis since rp = a and ra = a, where a is the semimajor axis. E = r a − r p r a + r p = 1 − 2 r a r p + 1 where: ra is the radius at apoapsis. Rp is the radius at periapsis; the eccentricity of an elliptical orbit can be used to obtain the ratio of the periapsis to the apoapsis: r p r a = 1 − e 1 + e For Earth, orbital eccentricity ≈ 0.0167, apoapsis= aphelion and periapsis= perihelion relative to sun. For Earth's annual orbit path, ra/rp ratio = longest_radius / shortest_radius ≈ 1.034 relative to center point of path. The eccentricity of the Earth's orbit is about 0.0167.
A near-Earth object is any small Solar System body whose orbit brings it to proximity with Earth. By convention, a Solar System body is a NEO if its closest approach to the Sun is less than 1.3 astronomical units. If a NEO's orbit crosses the Earth's and the object is larger than 140 meters across, it is considered a hazardous object. Most known PHOs and NEOs are asteroids. There are over 19,000 known near-Earth asteroids, over a hundred short-period near-Earth comets, a number of solar-orbiting spacecraft and meteoroids large enough to be tracked in space before striking the Earth, it is now accepted that collisions in the past have had a significant role in shaping the geological and biological history of the Earth. NEOs have become of increased interest since the 1980s because of greater awareness of the potential danger some of the asteroids or comets pose; when impacting the Earth, asteroids as small as 20 m cause sufficiently strong shock waves and heat to damage the local environment and populations.
Larger asteroids penetrate the atmosphere to the surface of the Earth, producing craters if they hit ground and tsunamis if water bodies are hit. It is in principle possible to deflect asteroids, methods of mitigation are being researched. Based on the orbit calculations of identified NEOs, their risk of future impact is assessed on two scales, the Torino scale and the more complex Palermo scale, both of which rate a risk of any significance with values above 0; some NEOs have had temporarily positive Torino or Palermo scale ratings after their discovery, but as of March 2018, more precise calculations based on subsequent observations led to a reduction of the rating to or below 0 in all cases. Since 1998, the United States, the European Union, other nations are scanning for NEOs in an effort called Spaceguard; the initial US Congress mandate to NASA of cataloging at least 90% of NEOs that are at least 1 kilometre in diameter, which would cause a global catastrophe in case of an impact with Earth, had been met by 2011.
In years, the survey effort has been expanded to objects as small as about 140 m across, which still have the potential for large-scale, though not global, damage. NEOs have low surface gravity, many have Earth-like orbits making them easy targets for spacecraft; as of January 2019, five near-Earth comets and five near-Earth asteroids have been visited by spacecraft. Two near-Earth asteroids are being orbited by spacecraft that will return asteroid samples back to Earth. Plans for commercial asteroid mining have been drafted by private companies; the major technical astronomical definition for Near-Earth objects are small Solar System bodies with orbits around the Sun that by definition lie between 0.983 and 1.3 astronomical units away from the Sun. Thus, NEOs are not currently near the Earth, but they can approach the Earth closely. However, the term is used more flexibly sometimes, for example for objects in orbit around the Earth or for quasi-satellites, which have a more complex orbital relationship with the Earth.
When a NEO is detected, like all other small Solar System bodies, it is submitted to the International Astronomical Union's Minor Planet Center for cataloging. MPC maintains separate lists of potential NEOs; the orbits of some NEOs intersect that of the Earth, so they pose a collision danger. These are considered hazardous objects. For the asteroids among PHOs, the hazardous asteroids, MPC maintains a separate list. NEOs are catalogued by two separate units of the Jet Propulsion Laboratory of the National Aeronautics and Space Administration: the Center for Near Earth Object Studies and the Solar System Dynamics Group. PHAs are defined based on parameters relating to their potential to approach the Earth dangerously closely. Objects with an Earth minimum orbit intersection distance of 0.05 AU or less and an absolute magnitude of 22.0 or brighter are considered PHAs. Objects that cannot approach closer to the Earth than 0.05 AU, or are smaller than about 140 m in diameter, are not considered PHAs.
NASA's catalog of near-Earth objects includes the approach distances of asteroids and comets. The first near-Earth objects to be observed by humans were comets, their extraterrestrial nature was recognised and confirmed only after Tycho Brahe tried to measure the distance of a comet through its parallax in 1577. The 1758–1759 return of Halley's Comet was the first comet appearance predicted in advance; the first near-Earth asteroid to be discovered was 433 Eros in 1898. The asteroid was subject to several observation campaigns, because measurements of its orbit enabled a precise determination of the distance of the Earth from the Sun. In has been said. In 1937, asteroid 69230 Hermes was discovered when it passed the Earth at twice the distance of the Moon. Hermes was considered a threat. Hermes was re-discovered in 2003, is now known to be no threat for at least the next century. On June 14, 1968, the 1.4 km diameter asteroid 1566 Icarus passed Earth at a distance of 0.042482 AU (6,355,2
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
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 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
The scattered disc is a distant circumstellar disc in the Solar System, sparsely populated by icy small solar system bodies, which are a subset of the broader family of trans-Neptunian objects. The scattered-disc objects have orbital eccentricities ranging as high as 0.8, inclinations as high as 40°, perihelia greater than 30 astronomical units. These extreme orbits are thought to be the result of gravitational "scattering" by the gas giants, the objects continue to be subject to perturbation by the planet Neptune. Although the closest scattered-disc objects approach the Sun at about 30–35 AU, their orbits can extend well beyond 100 AU; this makes scattered objects among most distant objects in the Solar System. The innermost portion of the scattered disc overlaps with a torus-shaped region of orbiting objects traditionally called the Kuiper belt, but its outer limits reach much farther away from the Sun and farther above and below the ecliptic than the Kuiper belt proper; because of its unstable nature, astronomers now consider the scattered disc to be the place of origin for most periodic comets in the Solar System, with the centaurs, a population of icy bodies between Jupiter and Neptune, being the intermediate stage in an object's migration from the disc to the inner Solar System.
Perturbations from the giant planets send such objects towards the Sun, transforming them into periodic comets. Many objects of the proposed Oort cloud are thought to have originated in the scattered disc. Detached objects are not distinct from scattered disc objects, some such as Sedna have sometimes been considered to be included in this group. Traditionally, devices like a blink comparator were used in astronomy to detect objects in the Solar System, because these objects would move between two exposures—this involved time-consuming steps like exposing and developing photographic plates or films, people using a blink comparator to manually detect prospective objects. During the 1980s, the use of CCD-based cameras in telescopes made it possible to directly produce electronic images that could be digitized and transferred to digital images; because the CCD captured more light than film and the blinking could now be done at an adjustable computer screen, the surveys allowed for higher throughput.
A flood of new discoveries was the result: over a thousand trans-Neptunian objects were detected between 1992 and 2006. The first scattered-disc object to be recognised as such was 1996 TL66 identified in 1996 by astronomers based at Mauna Kea in Hawaii. Three more were identified by the same survey in 1999: 1999 CV118, 1999 CY118, 1999 CF119; the first object presently classified as an SDO to be discovered was 1995 TL8, found in 1995 by Spacewatch. As of 2011, over 200 SDOs have been identified, including Gǃkúnǁʼhòmdímà, 2002 TC302, Sedna and 2004 VN112. Although the numbers of objects in the Kuiper belt and the scattered disc are hypothesized to be equal, observational bias due to their greater distance means that far fewer SDOs have been observed to date. Known trans-Neptunian objects are divided into two subpopulations: the Kuiper belt and the scattered disc. A third reservoir of trans-Neptunian objects, the Oort cloud, has been hypothesized, although no confirmed direct observations of the Oort cloud have been made.
Some researchers further suggest a transitional space between the scattered disc and the inner Oort cloud, populated with "detached objects". The Kuiper belt is a thick torus of space, extending from about 30 to 50 AU comprising two main populations of Kuiper belt objects: the classical Kuiper-belt objects, which lie in orbits untouched by Neptune, the resonant Kuiper-belt objects; these ratios, called orbital resonances, allow KBOs to persist in regions which Neptune's gravitational influence would otherwise have cleared out over the age of the Solar System, since the objects are never close enough to Neptune to be scattered by its gravity. Those in 2:3 resonances are known as "plutinos", because Pluto is the largest member of their group, whereas those in 1:2 resonances are known as "twotinos". In contrast to the Kuiper belt, the scattered-disc population can be disturbed by Neptune. Scattered-disc objects come within gravitational range of Neptune at their closest approaches but their farthest distances reach many times that.
Ongoing research suggests that the centaurs, a class of icy planetoids that orbit between Jupiter and Neptune, may be SDOs thrown into the inner reaches of the Solar System by Neptune, making them "cis-Neptunian" rather than trans-Neptunian scattered objects. Some objects, like 1999 TD10, blur the distinction and the Minor Planet Center, which catalogues all trans-Neptunian objects, now lists centaurs and SDOs together; the MPC, makes a clear distinction between the Kuiper belt and the scattered disc, separating those objects in stable orbits from those in scattered orbits. However, the difference between the Kuiper belt and the scattered disc is not clear-cut, many astronomers see the scattered disc not as a separate population but as an outward region of the Kuiper belt. Another term used is "scattered Kuiper-belt object" for bodies of the scattered d
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