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
A trans-Neptunian object written transneptunian object, is any minor planet in the Solar System that orbits the Sun at a greater average distance than Neptune, which has a semi-major axis of 30.1 astronomical units. TNOs are further divided into the classical and resonant objects of the Kuiper belt, the scattered disc and detached objects with the sednoids being the most distant ones; as of October 2018, the catalog of minor planets contains 528 numbered and more than 2,000 unnumbered TNOs. The first trans-Neptunian object to be discovered was Pluto in 1930, it took until 1992 to discover a second trans-Neptunian object orbiting the Sun directly, 15760 Albion. The most massive TNO known is Eris, followed by Pluto, 2007 Makemake and Haumea. More than 80 satellites have been discovered in orbit of trans-Neptunian objects. TNOs vary in color and are either grey-blue or red, they are thought to be composed of mixtures of rock, amorphous carbon and volatile ices such as water and methane, coated with tholins and other organic compounds.
Twelve minor planets with a semi-major axis greater than 150 AU and perihelion greater than 30 AU are known, which are called extreme trans-Neptunian objects. The orbit of each of the planets is affected by the gravitational influences of the other planets. Discrepancies in the early 1900s between the observed and expected orbits of Uranus and Neptune suggested that there were one or more additional planets beyond Neptune; the search for these led to the discovery of Pluto in February 1930, too small to explain the discrepancies. Revised estimates of Neptune's mass from the Voyager 2 flyby in 1989 showed that the problem was spurious. Pluto was easiest to find because it has the highest apparent magnitude of all known trans-Neptunian objects, it has a lower inclination to the ecliptic than most other large TNOs. After Pluto's discovery, American astronomer Clyde Tombaugh continued searching for some years for similar objects, but found none. For a long time, no one searched for other TNOs as it was believed that Pluto, which up to August 2006 was classified a planet, was the only major object beyond Neptune.
Only after the 1992 discovery of a second TNO, 15760 Albion, did systematic searches for further such objects begin. A broad strip of the sky around the ecliptic was photographed and digitally evaluated for moving objects. Hundreds of TNOs were found, with diameters in the range of 50 to 2,500 kilometers. Eris, the most massive TNO, was discovered in 2005, revisiting a long-running dispute within the scientific community over the classification of large TNOs, whether objects like Pluto can be considered planets. Pluto and Eris were classified as dwarf planets by the International Astronomical Union. On Monday, December 17, 2018 the discovery of 2018 VG18, nicknamed “Farout”, was announced. Farout is the most distant solar system object so-far observed and is about 120 AU away from the sun taking more than 1,000 years to complete one orbit. According to their distance from the Sun and their orbital parameters, TNOs are classified in two large groups: the Kuiper belt objects and the scattered disc objects.
The diagram to the right illustrates the distribution of known trans-Neptunian objects in relation to the orbits of the planets and the centaurs for reference. Different classes are represented in different colours. Resonant objects are plotted in classical Kuiper belt objects in blue; the scattered disc extends to the right, far beyond the diagram, with known objects at mean distances beyond 500 AU and aphelia beyond 1000 AU. The Edgeworth-Kuiper belt contains objects with an average distance to the Sun of 30 to about 55 AU having close-to-circular orbits with a small inclination from the ecliptic. Edgeworth-Kuiper belt objects are further classified into the resonant trans-Neptunian object, that are locked in an orbital resonance with Neptune, the classical Kuiper belt objects called "cubewanos", that have no such resonance, moving on circular orbits, unperturbed by Neptune. There are a large number of resonant subgroups, the largest being the twotinos and the plutinos, named after their most prominent member, Pluto.
Members of the classical Edgeworth-Kuiper belt include 50000 Quaoar and Makemake. The scattered disc contains objects farther from the Sun, with eccentric and inclined orbits; these orbits are non-planetary-orbit-crossing. A typical example is the most massive known Eris. Based on the Tisserand parameter relative to Neptune, the objects in the scattered disc can be further divided into the "typical" scattered disc objects with a TN of less than 3, into the detached objects with a TN greater than 3. In addition, detached objects have a time-averaged eccentricity greater than 0.2 The Sednoids are a further extreme sub-grouping of the detached objects with perihelia so distant that it is confirmed that their orbits cannot be explained by perturbations from the giant planets, nor by interaction with the galactic tides. Given the apparent magnitude of all but the biggest trans-Neptunian objects, the physical studies are limited to the following: thermal emissions for the largest objects colour indices, i.e. comparisons of the apparent magnitudes using different filters analysis of spectra and infraredStudying colours and spectra provides insight into the objects' origin and a potential correlation with other classes of objects, namely centaurs and some satellites of giant planets, suspected to originate in the Kuiper belt.
Nice is the seventh most populous urban area in France and the capital of the Alpes-Maritimes département. The metropolitan area of Nice extends beyond the administrative city limits, with a population of about 1 million on an area of 721 km2. Located in the French Riviera, on the south east coast of France on the Mediterranean Sea, at the foot of the Alps, Nice is the second-largest French city on the Mediterranean coast and the second-largest city in the Provence-Alpes-Côte d'Azur region after Marseille. Nice is 13 kilometres from the principality of Monaco and 30 kilometres from the French-Italian border. Nice's airport serves as a gateway to the region; the city is nicknamed Nice la Belle, which means Nice the Beautiful, the title of the unofficial anthem of Nice, written by Menica Rondelly in 1912. The area of today's Nice contains Terra Amata, an archaeological site which displays evidence of a early use of fire. Around 350 BC, Greeks of Marseille founded a permanent settlement and called it Nikaia, after Nike, the goddess of victory.
Through the ages, the town has changed hands many times. Its strategic location and port contributed to its maritime strength. For centuries it was a dominion of Savoy, was part of France between 1792 and 1815, when it was returned to the Kingdom of Piedmont-Sardinia until its re-annexation by France in 1860; the natural environment of the Nice area and its mild Mediterranean climate came to the attention of the English upper classes in the second half of the 18th century, when an increasing number of aristocratic families took to spending their winters there. The city's main seaside promenade, the Promenade des Anglais owes its name to visitors to the resort; the clear air and soft light have appealed to notable painters, such as Marc Chagall, Henri Matisse, Niki de Saint Phalle and Arman. Their work is commemorated in many of the city's museums, including Musée Marc Chagall, Musée Matisse and Musée des Beaux-Arts. Nice has the second largest hotel capacity in the country and it is one of its most visited cities, receiving 4 million tourists every year.
It has the third busiest airport in France, after the two main Parisian ones. It is the historical capital city of the County of Nice; the first known hominid settlements in the Nice area date back about 400,000 years. Nice was founded around 350 BC by the Greeks Phoceans of Massalia, was given the name of Nikaia in honour of a victory over the neighbouring Ligurians; the city soon became one of the busiest trading ports on the Ligurian coast. The ruins of Cemenelum are in Cimiez, now a district of Nice. In the 7th century, Nice joined. In 729 the city repulsed the Saracens. During the Middle Ages, Nice participated in the wars and history of Italy; as an ally of Pisa it was the enemy of Genoa, both the King of France and the Holy Roman Emperor endeavoured to subjugate it. During the 13th and 14th centuries the city fell more than once into the hands of the Counts of Provence, but it regained its independence though related to Genoa; the medieval city walls surrounded the Old Town. The landward side was protected by the River Paillon, covered over and is now the tram route towards the Acropolis.
The east side of the town was protected by fortifications on Castle Hill. Another river flowed into the port on the east side of Castle Hill. Engravings suggest that the port area was defended by walls. Under Monoprix in Place de Garibaldi are excavated remains of a well-defended city gate on the main road from Turin. In 1388 the commune placed itself under the protection of the Counts of Savoy. Nice participated – directly or indirectly – in the history of Savoy until 1860; the maritime strength of Nice now increased until it was able to cope with the Barbary pirates. In 1561 Emmanuel Philibert, Duke of Savoy abolished the use of Latin as an administrative language and established the Italian language as the official language of government affairs in Nice. During the struggle between Francis I and Charles V great damage was caused by the passage of the armies invading Provence. In 1538, in the nearby town of Villeneuve-Loubet, through the mediation of Pope Paul III, the two monarchs concluded a ten years' truce.
In 1543, Nice was attacked by the united Franco-Ottoman forces of Francis I and Barbarossa Hayreddin Pasha, in the Siege of Nice. Pestilence appeared again in 1550 and 1580. In 1600, Nice was taken by the Duke of Guise. By opening the ports of the county to all nations, proclaiming full freedom of trade, the commerce of the city was given great stimulu
The Kuiper belt called the Edgeworth–Kuiper belt, is a circumstellar disc in the outer Solar System, extending from the orbit of Neptune to 50 AU from the Sun. It is similar to the asteroid belt, but is far larger—20 times as wide and 20 to 200 times as massive. Like the asteroid belt, it consists of small bodies or remnants from when the Solar System formed. While many asteroids are composed of rock and metal, most Kuiper belt objects are composed of frozen volatiles, such as methane and water; the Kuiper belt is home to three recognized dwarf planets: Pluto and Makemake. Some of the Solar System's moons, such as Neptune's Triton and Saturn's Phoebe, may have originated in the region; the Kuiper belt was named after Dutch-American astronomer Gerard Kuiper, though he did not predict its existence. In 1992, Albion was discovered, the first Kuiper belt object since Charon. Since its discovery, the number of known KBOs has increased to over a thousand, more than 100,000 KBOs over 100 km in diameter are thought to exist.
The Kuiper belt was thought to be the main repository for periodic comets, those with orbits lasting less than 200 years. Studies since the mid-1990s have shown that the belt is dynamically stable and that comets' true place of origin is the scattered disc, a dynamically active zone created by the outward motion of Neptune 4.5 billion years ago. The Kuiper belt is distinct from the theoretical Oort cloud, a thousand times more distant and is spherical; the objects within the Kuiper belt, together with the members of the scattered disc and any potential Hills cloud or Oort cloud objects, are collectively referred to as trans-Neptunian objects. Pluto is the largest and most massive member of the Kuiper belt, the largest and the second-most-massive known TNO, surpassed only by Eris in the scattered disc. Considered a planet, Pluto's status as part of the Kuiper belt caused it to be reclassified as a dwarf planet in 2006, it is compositionally similar to many other objects of the Kuiper belt and its orbital period is characteristic of a class of KBOs, known as "plutinos", that share the same 2:3 resonance with Neptune.
After the discovery of Pluto in 1930, many speculated. The region now called, it was only in 1992. The number and variety of prior speculations on the nature of the Kuiper belt have led to continued uncertainty as to who deserves credit for first proposing it; the first astronomer to suggest the existence of a trans-Neptunian population was Frederick C. Leonard. Soon after Pluto's discovery by Clyde Tombaugh in 1930, Leonard pondered whether it was "not that in Pluto there has come to light the first of a series of ultra-Neptunian bodies, the remaining members of which still await discovery but which are destined to be detected"; that same year, astronomer Armin O. Leuschner suggested that Pluto "may be one of many long-period planetary objects yet to be discovered." In 1943, in the Journal of the British Astronomical Association, Kenneth Edgeworth hypothesized that, in the region beyond Neptune, the material within the primordial solar nebula was too spaced to condense into planets, so rather condensed into a myriad of smaller bodies.
From this he concluded that "the outer region of the solar system, beyond the orbits of the planets, is occupied by a large number of comparatively small bodies" and that, from time to time, one of their number "wanders from its own sphere and appears as an occasional visitor to the inner solar system", becoming a comet. In 1951, in a paper in Astrophysics: A Topical Symposium, Gerard Kuiper speculated on a similar disc having formed early in the Solar System's evolution, but he did not think that such a belt still existed today. Kuiper was operating on the assumption, common in his time, that Pluto was the size of Earth and had therefore scattered these bodies out toward the Oort cloud or out of the Solar System. Were Kuiper's hypothesis correct, there would not be a Kuiper belt today; the hypothesis took many other forms in the following decades. In 1962, physicist Al G. W. Cameron postulated the existence of "a tremendous mass of small material on the outskirts of the solar system". In 1964, Fred Whipple, who popularised the famous "dirty snowball" hypothesis for cometary structure, thought that a "comet belt" might be massive enough to cause the purported discrepancies in the orbit of Uranus that had sparked the search for Planet X, or, at the least, massive enough to affect the orbits of known comets.
Observation ruled out this hypothesis. In 1977, Charles Kowal discovered 2060 Chiron, an icy planetoid with an orbit between Saturn and Uranus, he used a blink comparator, the same device that had allowed Clyde Tombaugh to discover Pluto nearly 50 years before. In 1992, another object, 5145 Pholus, was discovered in a similar orbit. Today, an entire population of comet-like bodies, called the centaurs, is known to exist in the region between Jupiter and Neptune; the centaurs' orbits have dynamical lifetimes of a few million years. From the time of Chiron's discovery in 1977, astronomers have speculated that the centaurs therefore must be replenished by some outer reservoir. Further evidence for the existence of the Kuiper belt emerged from the study of comets; that comets have finite lifespans. As they approach the Sun, its heat causes their volatile surfaces to sublimate into space d
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
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