The asteroid belt is the circumstellar disc in the Solar System located between the orbits of the planets Mars and Jupiter. It is occupied by numerous irregularly shaped bodies called minor planets; the asteroid belt is termed the main asteroid belt or main belt to distinguish it from other asteroid populations in the Solar System such as near-Earth asteroids and trojan asteroids. About half the mass of the belt is contained in the four largest asteroids: Ceres, Vesta and Hygiea; the total mass of the asteroid belt is 4% that of the Moon, or 22% that of Pluto, twice that of Pluto's moon Charon. Ceres, the asteroid belt's only dwarf planet, is about 950 km in diameter, whereas 4 Vesta, 2 Pallas, 10 Hygiea have mean diameters of less than 600 km; the remaining bodies range down to the size of a dust particle. The asteroid material is so thinly distributed that numerous unmanned spacecraft have traversed it without incident. Nonetheless, collisions between large asteroids do occur, these can produce an asteroid family whose members have similar orbital characteristics and compositions.
Individual asteroids within the asteroid belt are categorized by their spectra, with most falling into three basic groups: carbonaceous and metal-rich. The asteroid belt formed from the primordial solar nebula as a group of planetesimals. Planetesimals are the smaller precursors of the protoplanets. Between Mars and Jupiter, gravitational perturbations from Jupiter imbued the protoplanets with too much orbital energy for them to accrete into a planet. Collisions became too violent, instead of fusing together, the planetesimals and most of the protoplanets shattered; as a result, 99.9% of the asteroid belt's original mass was lost in the first 100 million years of the Solar System's history. Some fragments found their way into the inner Solar System, leading to meteorite impacts with the inner planets. Asteroid orbits continue to be appreciably perturbed whenever their period of revolution about the Sun forms an orbital resonance with Jupiter. At these orbital distances, a Kirkwood gap occurs. Classes of small Solar System bodies in other regions are the near-Earth objects, the centaurs, the Kuiper belt objects, the scattered disc objects, the sednoids, the Oort cloud objects.
On 22 January 2014, ESA scientists reported the detection, for the first definitive time, of water vapor on Ceres, the largest object in the asteroid belt. The detection was made by using the far-infrared abilities of the Herschel Space Observatory; the finding was unexpected because comets, not asteroids, are considered to "sprout jets and plumes". According to one of the scientists, "The lines are becoming more and more blurred between comets and asteroids." In 1596, Johannes Kepler predicted “Between Mars and Jupiter, I place a planet” in his Mysterium Cosmographicum. While analyzing Tycho Brahe's data, Kepler thought that there was too large a gap between the orbits of Mars and Jupiter. In an anonymous footnote to his 1766 translation of Charles Bonnet's Contemplation de la Nature, the astronomer Johann Daniel Titius of Wittenberg noted an apparent pattern in the layout of the planets. If one began a numerical sequence at 0 included 3, 6, 12, 24, 48, etc. doubling each time, added four to each number and divided by 10, this produced a remarkably close approximation to the radii of the orbits of the known planets as measured in astronomical units provided one allowed for a "missing planet" between the orbits of Mars and Jupiter.
In his footnote, Titius declared "But should the Lord Architect have left that space empty? Not at all."When William Herschel discovered Uranus in 1781, the planet's orbit matched the law perfectly, leading astronomers to conclude that there had to be a planet between the orbits of Mars and Jupiter. On January 1, 1801, Giuseppe Piazzi, chair of astronomy at the University of Palermo, found a tiny moving object in an orbit with the radius predicted by this pattern, he dubbed it "Ceres", after the Roman goddess of the patron of Sicily. Piazzi believed it to be a comet, but its lack of a coma suggested it was a planet. Thus, the aforementioned pattern, now known as the Titius–Bode law, predicted the semi-major axes of all eight planets of the time. Fifteen months Heinrich Olbers discovered a second object in the same region, Pallas. Unlike the other known planets and Pallas remained points of light under the highest telescope magnifications instead of resolving into discs. Apart from their rapid movement, they appeared indistinguishable from stars.
Accordingly, in 1802, William Herschel suggested they be placed into a separate category, named "asteroids", after the Greek asteroeides, meaning "star-like". Upon completing a series of observations of Ceres and Pallas, he concluded, Neither the appellation of planets nor that of comets, can with any propriety of language be given to these two stars... They resemble small stars so much. From this, their asteroidal appearance, if I take my name, call them Asteroids. By 1807, further investigation revealed two new objects in the region: Vesta; the burning of Lilienthal in the Napoleonic wars, where the main body of work had been done, brought this first period of discovery to a close. Despite Herschel's coinage, for several decades it remained common practice to refer to these objects as planets and to prefix t
The Sun is the star at the center of the Solar System. It is a nearly perfect sphere of hot plasma, with internal convective motion that generates a magnetic field via a dynamo process, it is by far the most important source of energy for life on Earth. Its diameter is about 1.39 million kilometers, or 109 times that of Earth, its mass is about 330,000 times that of Earth. It accounts for about 99.86% of the total mass of the Solar System. Three quarters of the Sun's mass consists of hydrogen; the Sun is a G-type main-sequence star based on its spectral class. As such, it is informally and not accurately referred to as a yellow dwarf, it formed 4.6 billion years ago from the gravitational collapse of matter within a region of a large molecular cloud. Most of this matter gathered in the center, whereas the rest flattened into an orbiting disk that became the Solar System; the central mass became so hot and dense that it initiated nuclear fusion in its core. It is thought that all stars form by this process.
The Sun is middle-aged. It fuses about 600 million tons of hydrogen into helium every second, converting 4 million tons of matter into energy every second as a result; this energy, which can take between 10,000 and 170,000 years to escape from its core, is the source of the Sun's light and heat. In about 5 billion years, when hydrogen fusion in its core has diminished to the point at which the Sun is no longer in hydrostatic equilibrium, its core will undergo a marked increase in density and temperature while its outer layers expand to become a red giant, it is calculated that the Sun will become sufficiently large to engulf the current orbits of Mercury and Venus, render Earth uninhabitable. After this, it will shed its outer layers and become a dense type of cooling star known as a white dwarf, no longer produce energy by fusion, but still glow and give off heat from its previous fusion; the enormous effect of the Sun on Earth has been recognized since prehistoric times, the Sun has been regarded by some cultures as a deity.
The synodic rotation of Earth and its orbit around the Sun are the basis of solar calendars, one of, the predominant calendar in use today. The English proper name Sun may be related to south. Cognates to English sun appear in other Germanic languages, including Old Frisian sunne, Old Saxon sunna, Middle Dutch sonne, modern Dutch zon, Old High German sunna, modern German Sonne, Old Norse sunna, Gothic sunnō. All Germanic terms for the Sun stem from Proto-Germanic *sunnōn; the Latin name for the Sun, Sol, is not used in everyday English. Sol is used by planetary astronomers to refer to the duration of a solar day on another planet, such as Mars; the related word solar is the usual adjectival term used for the Sun, in terms such as solar day, solar eclipse, Solar System. A mean Earth solar day is 24 hours, whereas a mean Martian'sol' is 24 hours, 39 minutes, 35.244 seconds. The English weekday name Sunday stems from Old English and is a result of a Germanic interpretation of Latin dies solis, itself a translation of the Greek ἡμέρα ἡλίου.
The Sun is a G-type main-sequence star. The Sun has an absolute magnitude of +4.83, estimated to be brighter than about 85% of the stars in the Milky Way, most of which are red dwarfs. The Sun is heavy-element-rich, star; the formation of the Sun may have been triggered by shockwaves from more nearby supernovae. This is suggested by a high abundance of heavy elements in the Solar System, such as gold and uranium, relative to the abundances of these elements in so-called Population II, heavy-element-poor, stars; the heavy elements could most plausibly have been produced by endothermic nuclear reactions during a supernova, or by transmutation through neutron absorption within a massive second-generation star. The Sun is by far the brightest object in the Earth's sky, with an apparent magnitude of −26.74. This is about 13 billion times brighter than the next brightest star, which has an apparent magnitude of −1.46. The mean distance of the Sun's center to Earth's center is 1 astronomical unit, though the distance varies as Earth moves from perihelion in January to aphelion in July.
At this average distance, light travels from the Sun's horizon to Earth's horizon in about 8 minutes and 19 seconds, while light from the closest points of the Sun and Earth takes about two seconds less. The energy of this sunlight supports all life on Earth by photosynthesis, drives Earth's climate and weather; the Sun does not have a definite boundary, but its density decreases exponentially with increasing height above the photosphere. For the purpose of measurement, the Sun's radius is considered to be the distance from its center to the edge of the photosphere, the apparent visible surface of the Sun. By this measure, the Sun is a near-perfect sphere with an oblateness estimated at about 9 millionths, which means that its polar diameter differs from its equatorial diameter by only 10 kilometres; the tidal effect of the planets is weak and does not affect the shape of the Sun. The Sun rotates faster at its equator than at its poles; this differential rotation is caused by convective motion
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 day is the period of time during which the Earth completes one rotation around its axis. A solar day is the length of time which elapses between the Sun reaching its highest point in the sky two consecutive times. In 1960, the second was redefined in terms of the orbital motion of the Earth in year 1900, was designated the SI base unit of time; the unit of measurement "day", was symbolized d. In 1967, the second and so the day were redefined by atomic electron transition. A civil day is 86,400 seconds, plus or minus a possible leap second in Coordinated Universal Time, plus or minus an hour in those locations that change from or to daylight saving time. Day can be defined as each of the twenty-four-hour periods, reckoned from one midnight to the next, into which a week, month, or year is divided, corresponding to a rotation of the earth on its axis; however its use depends on its context, for example when people say'day and night','day' will have a different meaning. It will mean the interval of light between two successive nights.
However, in order to be clear when using'day' in that sense, "daytime" should be used to distinguish it from "day" referring to a 24-hour period. The word day may refer to a day of the week or to a calendar date, as in answer to the question, "On which day?" The life patterns of humans and many other species are related to Earth's solar day and the day-night cycle. Several definitions of this universal human concept are used according to context and convenience. Besides the day of 24 hours, the word day is used for several different spans of time based on the rotation of the Earth around its axis. An important one is the solar day, defined as the time it takes for the Sun to return to its culmination point; because celestial orbits are not circular, thus objects travel at different speeds at various positions in their orbit, a solar day is not the same length of time throughout the orbital year. Because the Earth orbits the Sun elliptically as the Earth spins on an inclined axis, this period can be up to 7.9 seconds more than 24 hours.
In recent decades, the average length of a solar day on Earth has been about 86 400.002 seconds and there are about 365.2422 solar days in one mean tropical year. Ancient custom has a new day start at either the setting of the Sun on the local horizon; the exact moment of, the interval between, two sunrises or sunsets depends on the geographical position, the time of year. A more constant day can be defined by the Sun passing through the local meridian, which happens at local noon or midnight; the exact moment is dependent on the geographical longitude, to a lesser extent on the time of the year. The length of such a day is nearly constant; this is the time as indicated by modern sundials. A further improvement defines a fictitious mean Sun that moves with constant speed along the celestial equator. A day, understood as the span of time it takes for the Earth to make one entire rotation with respect to the celestial background or a distant star, is called a stellar day; this period of rotation is about 4 minutes less than 24 hours and there are about 366.2422 stellar days in one mean tropical year.
Other planets and moons have solar days of different lengths from Earth's. A day, in the sense of daytime, distinguished from night time, is defined as the period during which sunlight directly reaches the ground, assuming that there are no local obstacles; the length of daytime averages more than half of the 24-hour day. Two effects make daytime on average longer than nights; the Sun has an apparent size of about 32 minutes of arc. Additionally, the atmosphere refracts sunlight in such a way that some of it reaches the ground when the Sun is below the horizon by about 34 minutes of arc. So the first light reaches the ground when the centre of the Sun is still below the horizon by about 50 minutes of arc. Thus, daytime is on average around 7 minutes longer than 12 hours; the term comes from the Old English dæg, with its cognates such as dagur in Icelandic, Tag in German, dag in Norwegian, Danish and Dutch. All of them from the Indo-European root dyau which explains the similarity with Latin dies though the word is known to come from the Germanic branch.
As of October 17, 2015, day is the 205th most common word in US English, the 210th most common in UK English. A day, symbol d, defined as 86 400 seconds, is not an SI unit, but is accepted for use with SI; the Second is the base unit of time in SI units. In 1967–68, during the 13th CGPM, the International Bureau of Weights and Measures redefined a second as … the duration of 9 192 631 770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the caesium 133 atom; this makes the SI-based day last 794 243 384 928 000 of those periods. Due to tidal effects, the
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
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