text:
Oort cloud
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
This article is about the outer Oort cloud. For the inner Oort cloud, see Hills cloud.
This graphic shows the distance from the Oort cloud to the rest of the Solar System and two of the nearest stars measured in astronomical units. The scale is logarithmic, with each specified distance ten times further out than the previous one. Red arrow indicates location of Voyager 1, a space probe that will reach the Oort cloud in about 300 years.
An artist's impression of the Oort cloud and the Kuiper belt (inset). Sizes of individual objects have been exaggerated for visibility.
Types of distant minor planets
Cis-Neptunian objects
Centaurs
Neptune trojans
Trans-Neptunian objects (TNOs)‡
Kuiper belt objects (KBOs)
Classical KBOs (cubewanos)
Resonant KBOs
Plutinos (2:3 resonance)
Scattered disc objects (SDOs)
Resonant SDOs
Detached objects
Sednoids
Oort cloud objects (ICO/OCOs)
‡ Trans-Neptunian dwarf planets are
called "plutoids"
v
t
e
The Oort cloud (/ɔːrt, ʊərt/),[1] named after the Dutch astronomer Jan Oort, sometimes called the Öpik–Oort cloud,[2] is a theoretical cloud of predominantly icy planetesimals proposed to surround the Sun at distances ranging from 50,000 to 200,000 AU (0.8 to 3.2 ly).[note 1][3] It is divided into two regions: a disc-shaped inner Oort cloud (or Hills cloud) and a spherical outer Oort cloud. Both regions lie beyond the heliosphere and in interstellar space.[3][4] The Kuiper belt and the scattered disc, the other two reservoirs of trans-Neptunian objects, are less than one thousandth as far from the Sun as the Oort cloud.
The outer limit of the Oort cloud defines the cosmographical boundary of the Solar System and the extent of the Sun's Hill sphere.[5] The outer Oort cloud is only loosely bound to the Solar System, and thus is easily affected by the gravitational pull both of passing stars and of the Milky Way itself. These forces occasionally dislodge comets from their orbits within the cloud and send them toward the inner Solar System.[3] Based on their orbits, most of the short-period comets may come from the scattered disc, but some may still have originated from the Oort cloud.[3][6]
Astronomers conjecture that the matter composing the Oort cloud formed closer to the Sun and was scattered far into space by the gravitational effects of the giant planets early in the Solar System's evolution.[3] Although no confirmed direct observations of the Oort cloud have been made, it may be the source of all long-period and Halley-type comets entering the inner Solar System, and many of the centaurs and Jupiter-family comets as well.[6]
The existence of the Oort cloud was first postulated by Estonian astronomer Ernst Öpik in 1932.[7]
Contents
1 Hypothesis
2 Structure and composition
3 Origin
4 Comets
5 Tidal effects
6 Stellar perturbations and stellar companion hypotheses
7 Future exploration
8 See also
9 References
10 Notes
11 External links
Hypothesis[edit]
There are two main classes of comet: short-period comets (also called ecliptic comets) and long-period comets (also called nearly isotropic comets). Ecliptic comets have relatively small orbits, below 10 AU, and follow the ecliptic plane, the same plane in which the planets lie. All long-period comets have very large orbits, on the order of thousands of AU, and appear from every direction in the sky.[8]
A. O. Leuschner in 1907 suggested that many comets believed to have parabolic orbits, and thus making single visits to the solar system, actually had elliptical orbits and would return after very long periods.[9] In 1932 Estonian astronomer Ernst Öpik postulated that long-period comets originated in an orbiting cloud at the outermost edge of the Solar System.[7] Dutch astronomer Jan Oort independently revived the idea in 1950 as a means to resolve a paradox:[10]
Over the course of the Solar System's existence the orbits of comets are unstable and eventually dynamics dictate that a comet must either collide with the Sun or a planet or else be ejected from the Solar System by planetary perturbations.
Moreover, their volatile composition means that as they repeatedly approach the Sun, radiation gradually boils the volatiles off until the comet splits or develops an insulating crust that prevents further outgassing.
Thus, Oort reasoned, a comet could not have formed while in its current orbit and must have been held in an outer reservoir for almost all of its existence.[10][11][8] He noted that there was a peak in numbers of long-period comets with aphelia (their farthest distance from the Sun) of roughly 20,000 AU, which suggested a reservoir at that distance with a spherical, isotropic distribution. Those relatively rare comets with orbits of about 10,000 AU have probably gone through one or more orbits through the Solar System and have had their orbits drawn inward by the gravity of the planets.[8]
Structure and composition[edit]
The presumed distance of the Oort cloud compared to the rest of the Solar System
The Oort cloud is thought to occupy a vast space from somewhere between 2,000 and 5,000 AU (0.03 and 0.08 ly)[8] to as far as 50,000 AU (0.79 ly)[3] from the Sun. Some estimates place the outer edge at between 100,000 and 200,000 AU (1.58 and 3.16 ly).[8] The region can be subdivided into a spherical outer Oort cloud of 20,000–50,000 AU (0.32–0.79 ly), and a torus-shaped inner Oort cloud of 2,000–20,000 AU (0.0–0.3 ly). The outer cloud is only weakly bound to the Sun and supplies the long-period (and possibly Halley-type) comets to inside the orbit of Neptune.[3] The inner Oort cloud is also known as the Hills cloud, named after Jack G. Hills, who proposed its existence in 1981.[12] Models predict that the inner cloud should have tens or hundreds of times as many cometary nuclei as the outer halo;[12][13][14] it is seen as a possible source of new comets to resupply the tenuous outer cloud as the latter's numbers are gradually depleted. The Hills cloud explains the continued existence of the Oort cloud after billions of years.[15]
The outer Oort cloud may have trillions of objects larger than 1 km (0.62 mi),[3] and billions with absolute magnitudes[16] brighter than 11 (corresponding to approximately 20-kilometre (12 mi) diameter), with neighboring objects tens of millions of kilometres apart.[6][17] Its total mass is not known, but, assuming that Halley's Comet is a suitable prototype for comets within the outer Oort cloud, roughly the combined mass is 3×1025 kilograms (6.6×1025 lb), or five times that of Earth.[3][18] Earlier it was thought to be more massive (up to 380 Earth masses),[19] but improved knowledge of the size distribution of long-period comets led to lower estimates. The mass of the inner Oort cloud has not been characterized.
If analyses of comets are representative of the whole, the vast majority of Oort-cloud objects consist of ices such as water, methane, ethane, carbon monoxide and hydrogen cyanide.[20] However, the discovery of the object 1996 PW, an object whose appearance was consistent with a D-type asteroid[21][22] in an orbit typical of a long-period comet, prompted theoretical research that suggests that the Oort cloud population consists of roughly one to two percent asteroids.[23] Analysis of the carbon and nitrogen isotope ratios in both the long-period and Jupiter-family comets shows little difference between the two, despite their presumably vastly separate regions of origin. This suggests that both originated from the original protosolar cloud,[24] a conclusion also supported by studies of granular size in Oort-cloud comets[25] and by the recent impact study of Jupiter-family comet Tempel 1.[26]
Origin[edit]
The Oort cloud is thought to be a remnant of the original protoplanetary disc that formed around the Sun approximately 4.6 billion years ago.[3] The most widely accepted hypothesis is that the Oort cloud's objects initially coalesced much closer to the Sun as part of the same process that formed the planets and minor planets, but that gravitational interaction with young gas giants such as Jupiter ejected the objects into extremely long elliptic or parabolic orbits.[3][27] Recent research has been cited by NASA hypothesizing that a large number of Oort cloud objects are the product of an exchange of materials between the Sun and its sibling stars as they formed and drifted apart, and it is suggested that many—possibly the majority of—Oort cloud objects did not form in close proximity to the Sun.[28] Simulations of the evolution of the Oort cloud from the beginnings of the Solar System to the present suggest that the cloud's mass peaked around 800 million years after formation, as the pace of accretion and collision slowed and depletion began to overtake supply.[3]
Models by Julio Ángel Fernández suggest that the scattered disc, which is the main source for periodic comets in the Solar System, might also be the primary source for Oort cloud objects. According to the models, about half of the objects scattered travel outward toward the Oort cloud, whereas a quarter are shifted inward to Jupiter's orbit, and a quarter are ejected on hyperbolic orbits. The scattered disc might still be supplying the Oort cloud with material.[29] A third of the scattered disc's population is likely to end up in the Oort cloud after 2.5 billion years.[30]
Computer models suggest that collisions of cometary debris during the formation period play a far greater role than was previously thought. According to these models, the number of collisions early in the Solar System's history was so great that most comets were destroyed before they reached the Oort cloud. Therefore, the current cumulative mass of the Oort cloud is far less than was once suspected.[31] The estimated mass of the cloud is only a small part of the 50–100 Earth masses of ejected material.[3]
Gravitational interaction with nearby stars and galactic tides modified cometary orbits to make them more circular. This explains the nearly spherical shape of the outer Oort cloud.[3] On the other hand, the Hills cloud, which is bound more strongly to the Sun, has not acquired a spherical shape. Recent studies have shown that the formation of the Oort cloud is broadly compatible with the hypothesis that the Solar System formed as part of an embedded cluster of 200–400 stars. These early stars likely played a role in the cloud's formation, since the number of close stellar passages within the cluster was much higher than today, leading to far more frequent perturbations.[32]
In June 2010 Harold F. Levison and others suggested on the basis of enhanced computer simulations that the Sun "captured comets from other stars while it was in its birth cluster". Their results imply that "a substantial fraction of the Oort cloud comets, perhaps exceeding 90%, are from the protoplanetary discs of other stars".[33][34]
Comets[edit]
Comet Hale–Bopp, an archetypical Oort-cloud comet
Comets are thought to have two separate points of origin in the Solar System. Short-period comets (those with orbits of up to 200 years) are generally accepted to have emerged from either the Kuiper belt or the scattered disc, which are two linked flat discs of icy debris beyond Neptune's orbit at 30 AU and jointly extending out beyond 100 AU from the Sun. Long-period comets, such as comet Hale–Bopp, whose orbits last for thousands of years, are thought to originate in the Oort cloud. The orbits within the Kuiper belt are relatively stable, and so very few comets are thought to originate there. The scattered disc, however, is dynamically active, and is far more likely to be the place of origin for comets.[8] Comets pass from the scattered disc into the realm of the outer planets, becoming what are known as centaurs.[35] These centaurs are then sent farther inward to become the short-period comets.[36]
There are two main varieties of short-period comet: Jupiter-family comets (those with semi-major axes of less than 5 AU) and Halley-family comets. Halley-family comets, named for their prototype, Halley's Comet, are unusual in that although they are short-period comets, it is hypothesized that their ultimate origin lies in the Oort cloud, not in the scattered disc. Based on their orbits, it is suggested they were long-period comets that were captured by the gravity of the giant planets and sent into the inner Solar System.[11] This process may have also created the present orbits of a significant fraction of the Jupiter-family comets, although the majority of such comets are thought to have originated in the scattered disc.[6]
Oort noted that the number of returning comets was far less than his model predicted, and this issue, known as "cometary fading", has yet to be resolved. No dynamical process are known to explain the smaller number of observed comets than Oort estimated. Hypotheses for this discrepancy include the destruction of comets due to tidal stresses, impact or heating; the loss of all volatiles, rendering some comets invisible, or the formation of a non-volatile crust on the surface.[37] Dynamical studies of hypothetical Oort cloud comets have estimated that their occurrence in the outer-planet region would be several times higher than in the inner-planet region. This discrepancy may be due to the gravitational attraction of Jupiter, which acts as a kind of barrier, trapping incoming comets and causing them to collide with it, just as it did with Comet Shoemaker–Levy 9 in 1994.[38]
Tidal effects[edit]
Main article: Galactic tide
Most of the comets seen close to the Sun seem to have reached their current positions through gravitational perturbation of the Oort cloud by the tidal force exerted by the Milky Way. Just as the Moon's tidal force deforms Earth's oceans, causing the tides to rise and fall, the galactic tide also distorts the orbits of bodies in the outer Solar System. In the charted regions of the Solar System, these effects are negligible compared to the gravity of the Sun, but in the outer reaches of the system, the Sun's gravity is weaker and the gradient of the Milky Way's gravitational field has substantial effects. Galactic tidal forces stretch the cloud along an axis directed toward the galactic centre and compress it along the other two axes; these small perturbations can shift orbits in the Oort cloud to bring objects close to the Sun.[39] The point at which the Sun's gravity concedes its influence to the galactic tide is called the tidal truncation radius. It lies at a radius of 100,000 to 200,000 AU, and marks the outer boundary of the Oort cloud.[8]
Some scholars theorise that the galactic tide may have contributed to the formation of the Oort cloud by increasing the perihelia (smallest distances to the Sun) of planetesimals with large aphelia (largest distances to the Sun).[40] The effects of the galactic tide are quite complex, and depend heavily on the behaviour of individual objects within a planetary system. Cumulatively, however, the effect can be quite significant: up to 90% of all comets originating from the Oort cloud may be the result of the galactic tide.[41] Statistical models of the observed orbits of long-period comets argue that the galactic tide is the principal means by which their orbits are perturbed toward the inner Solar System.[42]
Stellar perturbations and stellar companion hypotheses[edit]
Besides the galactic tide, the main trigger for sending comets into the inner Solar System is thought to be interaction between the Sun's Oort cloud and the gravitational fields of nearby stars[3] or giant molecular clouds.[38] The orbit of the Sun through the plane of the Milky Way sometimes brings it in relatively close proximity to other stellar systems. For example, it is hypothesized that 70 thousand years ago, perhaps Scholz's star passed through the outer Oort cloud (although its low mass and high relative velocity limited its effect).[43] During the next 10 million years the known star with the greatest possibility of perturbing the Oort cloud is Gliese 710.[44] This process could also scatter Oort cloud objects out of the ecliptic plane, potentially also explaining its spherical distribution.[44][45]
In 1984, Physicist Richard A. Muller postulated that the Sun has a heretofore undetected companion, either a brown dwarf or a red dwarf, in an elliptical orbit within the Oort cloud. This object, known as Nemesis, was hypothesized to pass through a portion of the Oort cloud approximately every 26 million years, bombarding the inner Solar System with comets. However, to date no evidence of Nemesis or the Oort cloud have been found, and many lines of evidence (such as crater counts), have thrown their existence into doubt.[46][47] Recent scientific analysis no longer supports the idea that extinctions on Earth happen at regular, repeating intervals.[48] Thus, the Nemesis hypothesis is no longer needed to explain current assumptions.[48]
A somewhat similar hypothesis was advanced by astronomer John J. Matese of the University of Louisiana at Lafayette in 2002. He contends that more comets are arriving in the inner Solar System from a particular region of the postulated Oort cloud than can be explained by the galactic tide or stellar perturbations alone, and that the most likely cause would be a Jupiter-mass object in a distant orbit.[49] This hypothetical gas giant was nicknamed Tyche. The WISE mission, an all-sky survey using parallax measurements in order to clarify local star distances, was capable of proving or disproving the Tyche hypothesis.[48] In 2014, NASA announced that the WISE survey had ruled out any object as they had defined it.[50]
Future exploration[edit]
Artist's impression of the TAU spacecraft
Space probes have yet to reach the area of the Oort cloud. Voyager 1, the fastest[51] and farthest[52][53] of the interplanetary space probes currently leaving the Solar System, will reach the Oort cloud in about 300 years[4][54] and would take about 30,000 years to pass through it.[55][56] However, around 2025, the radioisotope thermoelectric generators on Voyager 1 will no longer supply enough power to operate any of its scientific instruments, preventing any exploration by Voyager 1. The other four probes currently escaping the Solar System either are already or are predicted to be non-functional when they reach the Oort cloud; however, it may be possible to find an object from the cloud that has been knocked into the inner Solar System.
In the 1980s there was a concept for a probe to reach 1,000 AU in 50 years called TAU; among its missions would be to look for the Oort cloud.[57]
In the 2014 Announcement of Opportunity for the Discovery program, an observatory to detect the objects in the Oort cloud (and Kuiper belt) called the "Whipple Mission" was proposed.[58] It would monitor distant stars with a photometer, looking for transits up to 10,000 AU away.[58] The observatory was proposed for halo orbiting around L2 with a suggested 5-year mission.[58] It has been suggested that the Kepler observatory may also be able to detect objects in the Oort cloud.[59]
See also[edit]
Book: Solar System
Solar System portal
Astronomy portal
Heliosphere
Interstellar comet
List of possible dwarf planets
List of trans-Neptunian objects
Planets beyond Neptune
Scattered disc
Tyche (hypothetical planet)
References[edit]
Jump up ^ "Oort". Oxford English Dictionary (3rd ed.). Oxford University Press. September 2005. (Subscription or UK public library membership required.)
Jump up ^ Whipple, F. L.; Turner, G.; McDonnell, J. A. M.; Wallis, M. K. (1987-09-30). "A Review of Cometary Sciences". Philosophical Transactions of the Royal Society A. 323 (1572): 339–347 [341]. Bibcode:1987RSPTA.323..339W. doi:10.1098/rsta.1987.0090.
^ Jump up to: a b c d e f g h i j k l m n o Alessandro Morbidelli (2006). "Origin and dynamical evolution of comets and their reservoirs of water ammonia and methane". arXiv:astro-ph/0512256  [astro-ph].
^ Jump up to: a b "Catalog Page for PIA17046". Photo Journal. NASA. Retrieved April 27, 2014.
Jump up ^ "Kuiper Belt & Oort Cloud". NASA Solar System Exploration web site. NASA. Retrieved 2011-08-08.
^ Jump up to: a b c d V. V. Emelyanenko; D. J. Asher; M. E. Bailey (2007). "The fundamental role of the Oort Cloud in determining the flux of comets through the planetary system". Monthly Notices of the Royal Astronomical Society. 381 (2): 779–789. Bibcode:2007MNRAS.381..779E. CiteSeerX 10.1.1.558.9946  . doi:10.1111/j.1365-2966.2007.12269.x.
^ Jump up to: a b Ernst Julius Öpik (1932). "Note on Stellar Perturbations of Nearby Parabolic Orbits". Proceedings of the American Academy of Arts and Sciences. 67 (6): 169–182. doi:10.2307/20022899. JSTOR 20022899.
^ Jump up to: a b c d e f g Harold F. Levison; Luke Donnes (2007). "Comet Populations and Cometary Dynamics". In Lucy Ann Adams McFadden; Lucy-Ann Adams; Paul Robert Weissman; Torrence V. Johnson. Encyclopedia of the Solar System (2nd ed.). Amsterdam; Boston: Academic Press. pp. 575–588. ISBN 978-0-12-088589-3.
Jump up ^ Ley, Willy (April 1967). "The Orbits of the Comets". For Your Information. Galaxy Science Fiction. pp. 55–63.
^ Jump up to: a b Jan Oort (1950). "The structure of the cloud of comets surrounding the Solar System and a hypothesis concerning its origin". Bulletin of the Astronomical Institutes of the Netherlands. 11: 91–110. Bibcode:1950BAN....11...91O.
^ Jump up to: a b David C. Jewitt (2001). "From Kuiper Belt to Cometary Nucleus: The Missing Ultrared Matter". Astronomical Journal. 123 (2): 1039–1049. Bibcode:2002AJ....123.1039J. doi:10.1086/338692.
^ Jump up to: a b Jack G. Hills (1981). "Comet showers and the steady-state infall of comets from the Oort Cloud". Astronomical Journal. 86: 1730–1740. Bibcode:1981AJ.....86.1730H. doi:10.1086/113058.
Jump up ^ Harold F. Levison; Luke Dones; Martin J. Duncan (2001). "The Origin of Halley-Type Comets: Probing the Inner Oort Cloud". Astronomical Journal. 121 (4): 2253–2267. Bibcode:2001AJ....121.2253L. doi:10.1086/319943.
Jump up ^ Thomas M. Donahue, ed. (1991). Planetary Sciences: American and Soviet Research, Proceedings from the U.S.–U.S.S.R. Workshop on Planetary Sciences. Kathleen Kearney Trivers, and David M. Abramson. National Academy Press. p. 251. ISBN 978-0-309-04333-5. Retrieved 2008-03-18.
Jump up ^ Julio A. Fernéndez (1997). "The Formation of the Oort Cloud and the Primitive Galactic Environment" (PDF). Icarus. 219: 106–119. Bibcode:1997Icar..129..106F. doi:10.1006/icar.1997.5754. Retrieved 2008-03-18.
Jump up ^ Absolute magnitude is a measure of how bright an object would be if it were 1 AU from the Sun and Earth; as opposed to apparent magnitude, which measures how bright an object appears from Earth. Because all measurements of absolute magnitude assume the same distance, absolute magnitude is in effect a measurement of an object's brightness. The lower an object's absolute magnitude, the brighter it is.
Jump up ^ Paul R. Weissman (1998). "The Oort Cloud". Scientific American. Retrieved 2007-05-26.
Jump up ^ Paul R. Weissman (1983). "The mass of the Oort Cloud". Astronomy and Astrophysics. 118 (1): 90–94. Bibcode:1983A&A...118...90W.
Jump up ^ Sebastian Buhai. "On the Origin of the Long Period Comets: Competing theories" (PDF). Utrecht University College. Archived from the original (PDF) on 2006-09-30. Retrieved 2008-03-29.
Jump up ^ E. L. Gibb; M. J. Mumma; N. Dello Russo; M. A. DiSanti & K. Magee-Sauer (2003). "Methane in Oort Cloud comets". Icarus. 165 (2): 391–406. Bibcode:2003Icar..165..391G. doi:10.1016/S0019-1035(03)00201-X.
Jump up ^ Rabinowitz, D. L. (August 1996). "1996 PW". IAU Circular. 6466: 2. Bibcode:1996IAUC.6466....2R.
Jump up ^ Davies, John K.; McBride, Neil; Green, Simon F.; Mottola, Stefano; et al. (April 1998). "The Lightcurve and Colors of Unusual Minor Planet 1996 PW". Icarus. 132 (2): 418–430. Bibcode:1998Icar..132..418D. doi:10.1006/icar.1998.5888. (Subscription required (help)).
Jump up ^ Paul R. Weissman; Harold F. Levison (1997). "Origin and Evolution of the Unusual Object 1996 PW: Asteroids from the Oort Cloud?". Astrophysical Journal. 488 (2): L133–L136. Bibcode:1997ApJ...488L.133W. doi:10.1086/310940.
Jump up ^ D. Hutsemekers; J. Manfroid; E. Jehin; C. Arpigny; A. Cochran; R. Schulz; J.A. Stüwe & J.M. Zucconi (2005). "Isotopic abundances of carbon and nitrogen in Jupiter-family and Oort Cloud comets". Astronomy and Astrophysics. 440 (2): L21–L24. arXiv:astro-ph/0508033  . Bibcode:2005A&A...440L..21H. doi:10.1051/0004-6361:200500160.
Jump up ^ Takafumi Ootsubo; Jun-ichi Watanabe; Hideyo Kawakita; Mitsuhiko Honda & Reiko Furusho (2007). "Grain properties of Oort Cloud comets: Modeling the mineralogical composition of cometary dust from mid-infrared emission features". Highlights in Planetary Science, 2nd General Assembly of Asia Oceania Geophysical Society. 55 (9): 1044–1049. Bibcode:2007P&SS...55.1044O. doi:10.1016/j.pss.2006.11.012.
Jump up ^ Michael J. Mumma; Michael A. DiSanti; Karen Magee-Sauer; et al. (2005). "Parent Volatiles in Comet 9P/Tempel 1: Before and After Impact" (Submitted manuscript). Science Express. 310 (5746): 270–274. Bibcode:2005Sci...310..270M. doi:10.1126/science.1119337. PMID 16166477.
Jump up ^ "Oort Cloud & Sol b?". SolStation. Retrieved 2007-05-26.
Jump up ^ "The Sun Steals Comets from Other Stars". NASA. 2010.
Jump up ^ Julio A. Fernández; Tabaré Gallardo & Adrián Brunini (2004). "The scattered disc population as a source of Oort Cloud comets: evaluation of its current and past role in populating the Oort Cloud". Icarus. 172 (2): 372–381. Bibcode:2004Icar..172..372F. doi:10.1016/j.icarus.2004.07.023.
Jump up ^ Davies, J. K.; Barrera, L. H. (2004). The First Decadal Review of the Edgeworth-Kuiper Belt. Kluwer Academic Publishers. ISBN 978-1-4020-1781-0.
Jump up ^ S. Alan Stern; Paul R. Weissman (2001). "Rapid collisional evolution of comets during the formation of the Oort Cloud". Nature. 409 (6820): 589–591. Bibcode:2001Natur.409..589S. doi:10.1038/35054508. PMID 11214311.
Jump up ^ R. Brasser; M. J. Duncan; H.F. Levison (2006). "Embedded star clusters and the formation of the Oort Cloud". Icarus. 184 (1): 59–82. Bibcode:2006Icar..184...59B. doi:10.1016/j.icarus.2006.04.010.
Jump up ^ Levison, Harold; et al. (10 June 2010). "Capture of the Sun's Oort Cloud from Stars in Its Birth Cluster". Science. 329 (5988): 187–190. Bibcode:2010Sci...329..187L. doi:10.1126/science.1187535. PMID 20538912.
Jump up ^ "Many famous comets originally formed in other solar systems". Southwest Research Institute® (SwRI®) News. 10 June 2010. Archived from the original on 5 June 2013.
Jump up ^ Harold E. Levison & Luke Dones (2007). "Comet Populations and Cometary dynamics". Encyclopedia of the Solar System: 575–588. Bibcode:2007ess..book..575L. doi:10.1016/B978-012088589-3/50035-9. ISBN 978-0-12-088589-3.
Jump up ^ J Horner; NW Evans; ME Bailey; DJ Asher (2003). "The Populations of Comet-like Bodies in the Solar System". Monthly Notices of the Royal Astronomical Society. 343 (4): 1057–1066. doi:10.1046/j.1365-8711.2003.06714.x.
Jump up ^ Luke Dones; Paul R Weissman; Harold F Levison; Martin J Duncan (2004). "Oort Cloud Formation and Dynamics" (PDF). In Michel C. Festou; H. Uwe Keller; Harold A. Weaver. Comets II. University of Arizona Press. pp. 153–173. Retrieved 2008-03-22.
^ Jump up to: a b Julio A. Fernández (2000). "Long-Period Comets and the Oort Cloud". Earth, Moon, and Planets. 89 (1–4): 325–343. Bibcode:2002EM&P...89..325F. doi:10.1023/A:1021571108658.
Jump up ^ Marc Fouchard; Christiane Froeschlé; Giovanni Valsecchi; Hans Rickman (2006). "Long-term effects of the galactic tide on cometary dynamics". Celestial Mechanics and Dynamical Astronomy. 95 (1–4): 299–326. Bibcode:2006CeMDA..95..299F. doi:10.1007/s10569-006-9027-8.
Jump up ^ Higuchi A.; Kokubo E. & Mukai, T. (2005). "Orbital Evolution of Planetesimals by the Galactic Tide". Bulletin of the American Astronomical Society. 37: 521. Bibcode:2005DDA....36.0205H.
Jump up ^ Nurmi P.; Valtonen M.J.; Zheng J.Q. (2001). "Periodic variation of Oort Cloud flux and cometary impacts on the Earth and Jupiter". Monthly Notices of the Royal Astronomical Society. 327 (4): 1367–1376. Bibcode:2001MNRAS.327.1367N. doi:10.1046/j.1365-8711.2001.04854.x.
Jump up ^ John J. Matese & Jack J. Lissauer (2004). "Perihelion evolution of observed new comets implies the dominance of the galactic tide in making Oort Cloud comets discernible" (Submitted manuscript). Icarus. 170 (2): 508–513. Bibcode:2004Icar..170..508M. CiteSeerX 10.1.1.535.1013  . doi:10.1016/j.icarus.2004.03.019.
Jump up ^ Mamajek, Eric E.; Barenfeld, Scott A.; Ivanov, Valentin D. (2015). "The Closest Known Flyby of a Star to the Solar System" (Full text). The Astrophysical Journal. 800 (1): L17. arXiv:1502.04655  . Bibcode:2015ApJ...800L..17M. doi:10.1088/2041-8205/800/1/L17.
^ Jump up to: a b L. A. Molnar; R. L. Mutel (1997). Close Approaches of Stars to the Oort Cloud: Algol and Gliese 710. American Astronomical Society 191st meeting. American Astronomical Society. Bibcode:1997AAS...191.6906M.
Jump up ^ A. Higuchi; E. Kokubo & T. Mukai (2006). "Scattering of Planetesimals by a Planet: Formation of Comet Cloud Candidates" (PDF). Astronomical Journal. 131 (2): 1119–1129. Bibcode:2006AJ....131.1119H. doi:10.1086/498892.
Jump up ^ J. G. Hills (1984). "Dynamical constraints on the mass and perihelion distance of Nemesis and the stability of its orbit". Nature. 311 (5987): 636–638. Bibcode:1984Natur.311..636H. doi:10.1038/311636a0.
Jump up ^ "Nemesis is a myth". Max Planck Institute. 2011. Retrieved 2011-08-11.
^ Jump up to: a b c "Can WISE Find the Hypothetical 'Tyche'?". NASA/JPL. February 18, 2011. Retrieved 2011-06-15.
Jump up ^ John J. Matese & Jack J. Lissauer (2002-05-06). "Continuing Evidence of an Impulsive Component of Oort Cloud Cometary Flux" (PDF). University of Louisiana at Lafayette, and NASA Ames Research Center. Retrieved 2008-03-21.
Jump up ^ K. L., Luhman (7 March 2014). "A Search For A Distant Companion To The Sun With The Wide-field Infrared Survey Explorer". The Astrophysical Journal. 781 (1): 4. Bibcode:2014ApJ...781....4L. doi:10.1088/0004-637X/781/1/4. Retrieved 20 March 2014.
Jump up ^ "New Horizons Salutes Voyager". New Horizons. August 17, 2006. Archived from the original on March 9, 2011. Retrieved November 3, 2009.
Jump up ^ Clark, Stuart (September 13, 2013). "Voyager 1 leaving solar system matches feats of great human explorers". The Guardian.
Jump up ^ "Voyagers are leaving the Solar System". Space Today. 2011. Retrieved May 29, 2014.
Jump up ^ "It's Official: Voyager 1 Is Now In Interstellar Space". UniverseToday. Retrieved April 27, 2014.
Jump up ^ Ghose, Tia (September 13, 2013). "Voyager 1 Really Is In Interstellar Space: How NASA Knows". Space.com. TechMedia Network. Retrieved September 14, 2013.
Jump up ^ Cook, J.-R (September 12, 2013). "How Do We Know When Voyager Reaches Interstellar Space?". NASA / Jet Propulsion Lab. Retrieved September 15, 2013.
Jump up ^ TAU (Thousand Astronomical Unit) mission
^ Jump up to: a b c "Archived copy" (PDF). Archived from the original (PDF) on 2015-11-17. Retrieved 2015-11-12.
Jump up ^ Scientific American – Kepler Spacecraft May Be Able to Spot Elusive Oort Cloud Objects – 2010
Notes[edit]
Jump up ^ The Oort cloud's outer limit is difficult to define as it varies over the millennia as different stars pass the Sun and thus is subject to variation. Estimates of its distance range from 50,000 to 200,000 AU.
External links[edit]
Listen to this article (info/dl)

This audio file was created from a revision of the article "Oort cloud" dated 2012-04-02, and does not reflect subsequent edits to the article. (Audio help)
More spoken articles
Wikimedia Commons has media related to Oort cloud.
Oort Cloud Profile by NASA's Solar System Exploration
The Kuiper Belt and The Oort Cloud
The effect of perturbations by the Alpha Cen A/B system on the Oort Cloud
Reassessing the formation of the Inner Oort cloud in an embedded star cluster II: Probing the inner edge (Brasser; Schwamb : 7 Nov 2014 : arXiv:1411.1844)
show
v
t
e
The Solar System
The Sun
Mercury
Venus
Earth
Mars
Ceres
Jupiter
Saturn
Uranus
Neptune
Pluto
Haumea
Makemake
Eris
Planets and
Dwarf planets
Terrestrial planets
Mercury
Venus
Earth
Mars
Giant planets
Jupiter
Saturn
Uranus
Neptune
Dwarf planets
Ceres
Pluto
Haumea
Makemake
Eris
Rings
Jovian
Saturnian (Rhean)
Charikloan
Chironean
Uranian
Neptunian
Haumean
Moons
Terrestrial
Moon
other near-Earth objects
Martian
Phobos
Deimos
Jovian
Ganymede
Callisto
Io
Europa
all 79
Saturnian
Titan
Rhea
Iapetus
Dione
Tethys
Enceladus
Mimas
Hyperion
Phoebe
all 62
Uranian
Titania
Oberon
Umbriel
Ariel
Miranda
all 27
Neptunian
Triton
Proteus
Nereid
all 14
Plutonian
Charon
Nix
Hydra
Kerberos
Styx
Haumean
Hiʻiaka
Namaka
Makemakean
S/2015 (136472) 1
Eridian
Dysnomia
Lists
Solar System objects
By size
By discovery date
Minor planets
Gravitationally rounded objects
Possible dwarf planets
Natural satellites
Comets
Small Solar
System bodies
Meteoroids
Minor planets
moons
Comets
Damocloids
Mercury-crossers
Venus-crossers
Venus trojans
Near-Earth objects
Earth-crossers
Earth trojans
Mars-crossers
Mars trojans
Asteroid belt
Asteroids
first discovered: Ceres
Pallas
Juno
Vesta
Families
Notable asteroids
Kirkwood gap
Main-belt comets
Jupiter trojans
Jupiter-crossers
Centaurs
Saturn-crossers
Uranus trojans
Uranus-crossers
Neptune trojans
Cis-Neptunian objects
Trans-Neptunian objects
Neptune-crossers
Plutoids
Kuiper belt
Plutinos
Cubewanos
Scattered disc
Detached objects
Sednoids
Hills cloud
Oort cloud
Hypothetical
objects
Vulcan
Vulcanoids
Phaeton
Planet V
Theia
Fifth giant
Planets beyond Neptune
Tyche
Nemesis
Planet Nine
Exploration
(outline)
Discovery
Astronomy
Timeline
Spaceflight
Robotic spacecraft
Human spaceflight
List of crewed spacecraft
Colonization
List of probes
Timeline
Mercury
Venus
Moon
Mars
Ceres
Asteroids
Mining
Comets
Jupiter
Saturn
Uranus
Neptune
Pluto
Deep space
Outline of the Solar System
Portals
Solar System
Astronomy
Earth sciences
Mars
Jupiter
Uranus
Cosmology
Solar System → Local Interstellar Cloud → Local Bubble → Gould Belt → Orion Arm → Milky Way → Milky Way subgroup → Local Group → Virgo Supercluster → Laniakea Supercluster → Observable universe → Universe
Each arrow (→) may be read as "within" or "part of".
show
v
t
e
Small Solar System bodies
Minor planets
Designation
Groups
List
Moon
Meanings of names
Asteroid
Aten asteroid
Asteroid belt
Family
Jupiter trojan
Near-Earth
Spectral types
Distant minor planet
Centaur
Damocloid
Neptune trojan
Trans-Neptunian object
Detached
Kuiper belt
Oort cloud
Scattered disc
Comets
Extinct
Great
Halley-type
Hyperbolic
Long-period
Lost
Main-belt
Near-parabolic
Periodic
Sungrazing
Other
Meteoroids
show
v
t
e
Dwarf planets
Asteroid belt
IAU: Ceres
No longer rounded and therefore no longer dwarf planets (Vesta)

Centaurs
Possibly: Chariklo
Chiron
Centaurs (extended)
Possibly: 1995 SN55 (lost)
Ceto
2010 TY53
Plutinos
IAU: Pluto
Additional objects proposed by Brown and Tancredi: Orcus
Ixion
2003 AZ84
2004 UX10
Huya
Possibly: 2003 UZ413
2003 VS2
2002 VR128
2004 PF115
2002 XV93
2007 JH43
2001 QF298
Twotinos
Possibly: 2002 WC19
Other resonances/
unknown resonances:
IAU: Haumea
Possibly: 2002 XW93
1999 DE9
1999 KR16
2001 YH140
2011 GM27
2010 VK201
2013 FZ27
2014 UM33
1999 CD158
Cubewanos:
IAU: Makemake
Additional objects proposed by Brown and Tancredi: 2002 MS4
Salacia
Quaoar
Varuna
Varda
2004 GV9
2002 AW197
2002 TX300
2005 RR43
2003 OP32
2005 RN43
Possibly: Chaos
Altjira
Sila-Nunam
2002 UX25
2007 JJ43
2005 UQ513
2004 TY364
2003 QW90
1998 SN165
2002 KX14
Praamzius
2004 NT33
2010 FX86
2002 CY248
2010 VR11
Rhadamanthus
Scattered disc
IAU: Eris
Additional objects proposed by Brown and Tancredi: 2007 OR10
1996 TL66
2001 UR163
2005 RM43
Possibly: 2002 TC302
2004 XA192
2005 QU182
2006 QH181
2007 UK126
2010 EK139
2010 KZ39
2010 RE64
2010 RF43
2010 TJ
2013 FY27
2008 OG19
1996 GQ21
2012 HH2
1999 CC158
2010 VZ98
Area uncertain
Captured satellites that were once dwarf planets: Triton (captured by Neptune)
Phoebe (captured by Saturn, and no longer rounded)
Possibly: 2011 FW62 (lost)
2000 YW134
V774104
Detached objects
Possibly: 2004 XR190
2010 GB174
2008 ST291
1995 TL8
2005 TB190
2003 QX113
2003 FY128
2004 VN112
2000 CR105
Sednoids
Objects proposed by Brown and Tancredi: Sedna
Possibly: 2012 VP113
See also: Charon
Vanth
Dysnomia
Hiʻiaka
Mesoplanet
Planemo
List of trans-Neptunian objects
List of possible dwarf planets
List of Solar System objects
List of Solar System objects by size
show
v
t
e
Comets
Features
Nucleus
Coma
Tails
Antitail
Comet dust
Meteor shower

Types
Periodic
Numbered
Lost
Long period
Halley-type
Jupiter-family
Encke-type
Main-belt
Non-periodic
Near-parabolic
Hyperbolic
Unknown-orbit
Great Comet
Sungrazing (Kreutz)
Extinct
Rock
Exocomet
Interstellar
Related
Naming of comets
Centaur
Comet discoverers
LINEAR
Extraterrestrial atmosphere
Oort cloud
Small Solar System body
Asteroid
Space
missions
Planned and proposed
DESTINY+
CAESAR
Comet Hopper
CONDOR
CORSAIR
CRAF
Hayabusa Mk2
Marco Polo
Vesta
Past and current
CONTOUR
Deep Impact/EPOXI
Deep Space 1
Giotto
ICE
Rosetta
Philae
Timeline
Sakigake
Stardust/NeXT
Suisei
Ulysses
Vega program
Vega 1
Vega 2
Latest
C/2016 U1 (NEOWISE)
C/2015 G2 (MASTER)
C/2015 F5 (SWAN-XingMing)
C/2015 F3
C/2014 Q2 (Lovejoy)
C/2014 E2 (Jacques)
C/2013 US10 (Catalina)
C/2013 A1 (Siding Spring)
C/2012 S4 (PANSTARRS)
C/2012 K1 (PANSTARRS)
Culture and
speculation
Antimatter comet
Comets in fiction
Fictional comets
Comet vintages
show
Lists of comets (more)
Periodic
comets
Until 1985
(all)
1P/Halley
2P/Encke
3D/Biela
4P/Faye
5D/Brorsen
6P/d'Arrest
7P/Pons–Winnecke
8P/Tuttle
9P/Tempel
10P/Tempel
11P/Tempel–Swift–LINEAR
12P/Pons–Brooks
13P/Olbers
14P/Wolf
15P/Finlay
16P/Brooks
17P/Holmes
18D/Perrine–Mrkos
19P/Borrelly
20D/Westphal
21P/Giacobini–Zinner
22P/Kopff
23P/Brorsen–Metcalf
24P/Schaumasse
25D/Neujmin
26P/Grigg–Skjellerup
27P/Crommelin
28P/Neujmin
29P/Schwassmann–Wachmann
30P/Reinmuth
31P/Schwassmann–Wachmann
32P/Comas Solà
33P/Daniel
34D/Gale
35P/Herschel–Rigollet
36P/Whipple
37P/Forbes
38P/Stephan–Oterma
39P/Oterma
40P/Väisälä
41P/Tuttle–Giacobini–Kresák
42P/Neujmin
43P/Wolf–Harrington
44P/Reinmuth
45P/Honda–Mrkos–Pajdušáková
46P/Wirtanen
47P/Ashbrook–Jackson
48P/Johnson
49P/Arend–Rigaux
50P/Arend
51P/Harrington
52P/Harrington–Abell
53P/Van Biesbroeck
54P/de Vico–Swift–NEAT
55P/Tempel–Tuttle
56P/Slaughter–Burnham
57P/du Toit–Neujmin–Delporte
58P/Jackson–Neujmin
59P/Kearns–Kwee
60P/Tsuchinshan
61P/Shajn–Schaldach
62P/Tsuchinshan
63P/Wild
64P/Swift–Gehrels
65P/Gunn
66P/du Toit
67P/Churyumov–Gerasimenko
68P/Klemola
69P/Taylor
70P/Kojima
71P/Clark
72P/Denning–Fujikawa
73P/Schwassmann–Wachmann
74P/Smirnova–Chernykh
75D/Kohoutek
76P/West–Kohoutek–Ikemura
77P/Longmore
78P/Gehrels
79P/du Toit–Hartley
80P/Peters–Hartley
81P/Wild
82P/Gehrels
83D/Russell
84P/Giclas
85D/Boethin
86P/Wild
87P/Bus
88P/Howell
89P/Russell
90P/Gehrels
91P/Russell
92P/Sanguin
93P/Lovas
94P/Russell
95P/Chiron
96P/Machholz
97P/Metcalf–Brewington
98P/Takamizawa
99P/Kowal
100P/Hartley
101P/Chernykh
102P/Shoemaker
After 1985
(notable)
103P/Hartley
105P/Singer Brewster
107P/Wilson–Harrington
109P/Swift–Tuttle
111P/Helin–Roman–Crockett
114P/Wiseman–Skiff
128P/Shoemaker–Holt
139P/Väisälä–Oterma
144P/Kushida
147P/Kushida–Muramatsu
153P/Ikeya–Zhang
163P/NEAT
168P/Hergenrother
169P/NEAT
177P/Barnard
178P/Hug–Bell
205P/Giacobini
209P/LINEAR
238P/Read
246P/NEAT
252P/LINEAR
255P/Levy
273P/Pons–Gambart
276P/Vorobjov
289P/Blanpain
311P/PANSTARRS
322P/SOHO
332P/Ikeya-Murakami
354P/LINEAR
P/1997 B1 (Kobayashi)
P/2010 B2 (WISE)
P/2011 NO1 (Elenin)
Comet-like
asteroids
596 Scheila
2060 Chiron (95P)
4015 Wilson–Harrington (107P)
7968 Elst–Pizarro (133P)
165P/LINEAR
166P/NEAT
167P/CINEOS
60558 Echeclus (174P)
118401 LINEAR (176P)
238P/Read
259P/Garradd
311P/PANSTARRS
324P/La Sagra
P/2010 A2 (LINEAR)
P/2012 F5 (Gibbs)
P/2012 T1 (PANSTARRS)
P/2013 R3 (Catalina-PANSTARRS)
(300163) 2006 VW139
Lost
Recovered
11P/Tempel–Swift–LINEAR
15P/Finlay
17P/Holmes
27P/Crommelin
54P/de Vico–Swift–NEAT
55P/Tempel–Tuttle
57P/du Toit–Neujmin–Delporte
69P/Taylor
72P/Denning–Fujikawa
80P/Peters–Hartley
97P/Metcalf–Brewington
107P/Wilson–Harrington
109P/Swift–Tuttle
113P/Spitaler
122P/de Vico
157P/Tritton
177P/Barnard
205P/Giacobini
206P/Barnard–Boattini
271P/van Houten–Lemmon
273P/Pons–Gambart
289P/Blanpain
Destroyed
3D/Biela
73P/Schwassmann–Wachmann
D/1993 F2 (Shoemaker–Levy 9)
Not found
D/1770 L1 (Lexell)
5D/Brorsen
18D/Perrine–Mrkos
20D/Westphal
25D/Neujmin
34D/Gale
75D/Kohoutek
83D/Russell
85D/Boethin
Visited by
spacecraft
21P/Giacobini–Zinner (1985)
1P/Halley (1986)
26P/Grigg–Skjellerup (1992)
19P/Borrelly (2001)
81P/Wild (2004)
9P/Tempel (2005, 2011)
C/2006 P1 (2007)
103P/Hartley (2010)
67P/Churyumov–Gerasimenko (2014)
Non-Periodic
comets
(notable)
Until 1910
C/-43 K1 (Caesar's Comet)
X/1106 C1 (Great Comet of 1106)
C/1577 V1 (Great Comet of 1577)
C/1652 Y1
C/1680 V1 (Great Comet of 1680, Kirsch's Comet, Newton's Comet))
C/1702 H1 (Comet of 1702)
C/1729 P1 (Comet of 1729, Comet Sarabat)
C/1743 X1 (Great Comet of 1744, Comet Klinkenberg-Chéseaux)
C/1760 A1 (Great Comet of 1760)
C/1769 P1 (Great Comet of 1769)
C/1807 R1 (Great Comet of 1807)
C/1811 F1 (Great Comet of 1811)
C/1819 N1 (Great Comet of 1819)
C/1823 Y1 (Great Comet of 1823)
C/1843 D1 (Great March Comet of 1843)
C/1847 T1 (Miss Mitchell's Comet)
C/1858 L1 (Comet Donati)
C/1861 G1 (Comet Thatcher)
C/1861 J1 (Great Comet of 1861)
C/1865 B1 (Great Southern Comet of 1865)
X/1872 X1 (Pogson's Comet)
C/1874 H1 (Comet Coggia)
C/1881 K1 (Comet Tebbutt)
C/1882 R1 (Great Comet of 1882)
C/1887 B1 (Great Southern Comet of 1887)
C/1890 V1 (Comet Zona)
C/1901 G1 (Great Comet of 1901)
C/1910 A1 (Great January Comet of 1910)
After 1910
C/1911 O1 (Brooks)
C/1911 S3 (Beljawsky)
C/1927 X1 (Skjellerup–Maristany)
C/1931 P1 (Ryves)
C/1941 B2 (de Kock-Paraskevopoulos) (de)
C/1947 X1 (Southern Comet) (de)
C/1948 V1 (Eclipse)
C/1956 R1 (Arend–Roland)
C/1957 P1 (Mrkos) (de)
C/1961 O1 (Wilson-Hubbard) (de)
C/1961 R1 (Humason)
C/1962 C1 (Seki-Lines) (de)
C/1963 R1 (Pereyra)
C/1965 S1 (Ikeya-Seki)
C/1969 Y1 (Bennett)
C/1970 K1 (White–Ortiz–Bolelli)
C/1973 E1 (Kohoutek)
C/1975 V1 (West)
C/1980 E1 (Bowell)
C/1983 H1 (IRAS–Araki–Alcock)
C/1989 X1 (Austin)
C/1989 Y1 (Skorichenko–George)
C/1992 J1 (Spacewatch–Rabinowitz)
C/1993 Y1 (McNaught–Russell)
C/1995 O1 (Hale–Bopp)
C/1996 B2 (Hyakutake)
C/1997 L1 (Zhu–Balam)
C/1998 H1 (Stonehouse)
C/1998 J1 (SOHO)
C/1999 F1 (Catalina)
C/1999 S4 (LINEAR)
C/2000 U5 (LINEAR)
C/2000 W1 (Utsunomiya-Jones)
C/2001 OG108 (LONEOS)
C/2001 Q4 (NEAT)
C/2002 T7 (LINEAR)
C/2004 F4 (Bradfield) (de)
C/2004 Q2 (Machholz)
C/2006 A1 (Pojmański)
C/2006 M4 (SWAN)
C/2006 P1 (McNaught)
C/2007 E2 (Lovejoy)
C/2007 F1 (LONEOS)
C/2007 K5 (Lovejoy)
C/2007 N3 (Lulin)
C/2007 Q3 (Siding Spring)
C/2007 W1 (Boattini)
C/2008 Q1 (Matičič)
C/2009 F6 (Yi–SWAN)
C/2009 R1 (McNaught)
C/2010 X1 (Elenin)
C/2011 L4 (PANSTARRS)
C/2011 W3 (Lovejoy)
C/2012 E2 (SWAN)
C/2012 F6 (Lemmon)
C/2012 K1 (PANSTARRS)
C/2012 S1 (ISON)
C/2012 S4 (PANSTARRS)
C/2013 A1 (Siding Spring)
C/2013 R1 (Lovejoy)
C/2013 US10 (Catalina)
C/2013 V5 (Oukaimeden)
C/2014 E2 (Jacques)
C/2014 Q2 (Lovejoy)
C/2015 V2 (Johnson)
After 1910
(by name)
Arend–Roland
Austin
Beljawsky
Bennett
Boattini
Bowell
Bradfield (de)
Brooks
Catalina
C/1999 F1
C/2013 US10
de Kock–Paraskevopoulos (de)
Eclipse
Elenin
Hale-Bopp
Humason
Hyakutake
Ikeya-Seki
IRAS–Araki–Alcock
ISON
Jacques
Johnson
Kohoutek
Lemmon
LINEAR
C/1999 S4
C/2000 U5
C/2002 T7
LONEOS
C/2001 OG108
C/2007 F1
Lovejoy
C/2007 E2
C/2007 K5
C/2011 W3
C/2013 R1
C/2014 Q2
Lulin
Machholz
Matičič
McNaught
C/2006 P1
C/2009 R1
McNaught–Russell
Mrkos (de)
NEAT
Oukaimeden
Pan-STARRS
C/2011 L4
C/2012 K1
C/2012 S4
311P
Pereyra
Pojmański
Ryves
Seki–Lines (de)
Siding Spring
C/2007 Q3
C/2013 A1
Skjellerup–Maristany
Skorichenko–George
SOHO
Southern (de)
Spacewatch–Rabinowitz
Stonehouse
SWAN
C/2006 M4
C/2012 E2
Utsunomiya–Jones
West
White–Ortiz–Bolelli
Wilson–Hubbard (de)
Yi–SWAN
Zhu–Balam
Category
Commons
Wikinews
Authority control
WorldCat Identities
LCCN: sh86000523
VIAF: 315161594
Retrieved from "https://en.wikipedia.org/w/index.php?title=Oort_cloud&oldid=853531395"
Categories:
Astronomical hypotheses
Comets
Discoveries by Jan Oort
Hypothetical trans-Neptunian objects
Minor planets
Oort cloud
Trans-Neptunian region
Jan Oort
Hidden categories:
Pages containing links to subscription-only content
Spoken articles
Articles with hAudio microformats
Interlanguage link template link number
Wikipedia articles with LCCN identifiers
Wikipedia articles with VIAF identifiers
Featured articles
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
In other projects
Wikimedia Commons
Languages
Afrikaans
العربية
অসমীয়া
Asturianu
Avañe'ẽ
Azərbaycanca
বাংলা
Bân-lâm-gú
Basa Banyumasan
Беларуская
Беларуская (тарашкевіца)
Български
Boarisch
Bosanski
Brezhoneg
Català
Čeština
Cymraeg
Dansk
Deutsch
Eesti
Ελληνικά
Español
Esperanto
Euskara
فارسی
Français
Gaeilge
Gàidhlig
Galego
한국어
Հայերեն
हिन्दी
Hrvatski
Bahasa Indonesia
Íslenska
Italiano
עברית
Basa Jawa
ಕನ್ನಡ
ქართული
Kiswahili
Latina
Latviešu
Lëtzebuergesch
Lietuvių
Lumbaart
Magyar
Македонски
മലയാളം
मराठी
მარგალური
Bahasa Melayu
မြန်မာဘာသာ
Nederlands
日本語
Norsk
Norsk nynorsk
Occitan
Oʻzbekcha/ўзбекча
پنجابی
Plattdüütsch
Polski
Português
Ripoarisch
Română
Русский
Scots
Sicilianu
Simple English
Slovenčina
Slovenščina
Српски / srpski
Srpskohrvatski / српскохрватски
Suomi
Svenska
Tagalog
Татарча/tatarça
తెలుగు
ไทย
Тоҷикӣ
Türkçe
Українська
اردو
Vèneto
Tiếng Việt
Winaray
粵語
中文
80 more
Edit links
This page was last edited on 5 August 2018, at 11:58 (UTC).
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view
Enable previews

values: mw-page-base noprint

values: mw-head-base noprint

values: This is a featured article. Click here for more information.

values: mw-indicator-featured-star mw-indicator

values: mw-indicator-spoken-icon mw-indicator

values: firstHeading firstHeading en

values: siteSub noprint

values: mw-jump-link #mw-head

values: mw-jump-link #p-search

values:
note
hatnote navigation-not-searchable

values: padding:0.3em 0.4em 0.3em;font-weight:bold;font-weight: normal;

values: Template talk:Distant minor planets sidebar

values: float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f9f9f9;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%;width: auto;

values:
/wiki/Inner_Solar_System
mw-redirect
Inner Solar System

values:
/wiki/Short-period_comet
mw-redirect
Short-period comet

values: Formation and evolution of the Solar System

values:
/wiki/Long-period_comet
mw-redirect
Long-period comet

values:
/wiki/Centaur_(planetoid)
mw-redirect
Centaur (planetoid)

values: checkbox button toctogglecheckbox toctogglecheckbox display:none

values:
/wiki/Plane_of_the_ecliptic
mw-redirect
Plane of the ecliptic

values:
/wiki/A._O._Leuschner
mw-redirect
A. O. Leuschner

values:
/wiki/Dynamics_(physics)
mw-redirect
Dynamics (physics)

values:
/wiki/Protoplanetary_disc
mw-redirect
Protoplanetary disc

values:
/wiki/Parabolic_orbit
mw-redirect
Parabolic orbit

values:
/wiki/Periodic_comet
mw-redirect
Periodic comet

values:
/wiki/Semi-major_axis
mw-redirect
Semi-major axis

values:
/wiki/Outer_Solar_System
mw-redirect
Outer Solar System

values: Edit section: Stellar perturbations and stellar companion hypotheses

values:
/wiki/Scholz%27s_star
mw-redirect
Scholz's star

values:
/wiki/WISE_mission
mw-redirect
WISE mission

values:
/wiki/All-sky_survey
mw-redirect
All-sky survey

values: Category:Spacecraft escaping the Solar System

values:
/wiki/Discovery_program
mw-redirect
Discovery program

values: display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle

values: margin:0.5em 0 0.5em 1em;border:solid #aaa 1px

values:
/wiki/Interstellar_comet
mw-redirect
Interstellar comet

values: Philosophical Transactions of the Royal Society A

values:
nofollow
external text
//doi.org/10.1098/rsta.1987.0090

values:
nofollow
external text
//arxiv.org/abs/astro-ph/0512256

attrs: alt src title width height srcset data-file-width data-file-height

values:
nofollow
external text
//arxiv.org/archive/astro-ph

values: Monthly Notices of the Royal Astronomical Society

values: Proceedings of the American Academy of Arts and Sciences

values:
nofollow
external text
//doi.org/10.2307/20022899

values:
nofollow
external text
//www.jstor.org/stable/20022899

values:
/wiki/Astronomical_Journal
mw-redirect
Astronomical Journal

values:
nofollow
external text
//doi.org/10.1086/338692

values:
nofollow
external text
//doi.org/10.1086/113058

values:
nofollow
external text
//doi.org/10.1086/319943

values:
nofollow
external text
//doi.org/10.1006/icar.1997.5754

values:
/wiki/Astronomy_and_Astrophysics
mw-redirect
Astronomy and Astrophysics

values:
nofollow
external text
//doi.org/10.1006/icar.1998.5888

values: The site requires a paid subscription to access this page.

values:
/wiki/Astrophysical_Journal
mw-redirect
Astrophysical Journal

values:
nofollow
external text
//doi.org/10.1086/310940

values:
nofollow
external text
//arxiv.org/abs/astro-ph/0508033

values:
nofollow
external text
//doi.org/10.1016/j.pss.2006.11.012

values:
nofollow
external text
//doi.org/10.1126/science.1119337

values:
/wiki/PubMed_Identifier
mw-redirect
PubMed Identifier

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/16166477

values:
nofollow
external text
//doi.org/10.1016/j.icarus.2004.07.023

values:
nofollow
external text
//doi.org/10.1038/35054508

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/11214311

values:
nofollow
external text
//doi.org/10.1016/j.icarus.2006.04.010

values:
nofollow
external text
//doi.org/10.1126/science.1187535

values:
nofollow
external text
//www.ncbi.nlm.nih.gov/pubmed/20538912

values:
nofollow
external text
//doi.org/10.1023/A%3A1021571108658

values: Celestial Mechanics and Dynamical Astronomy

values: Bulletin of the American Astronomical Society

values:
nofollow
external text
//doi.org/10.1016/j.icarus.2004.03.019

values:
nofollow
external text
//arxiv.org/abs/1502.04655

values:
nofollow
external text
//doi.org/10.1086/498892

values:
nofollow
external text
//doi.org/10.1038/311636a0

values: -moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;

values:
reflist mw-references-wrap
list-style-type: decimal;

values: position: absolute; top: 0px; left: 100px; right: 0px; bottom: 0px; height: 0px; width: 0px;

values: left: 50%; top: 50%; margin-left: -35px; margin-top: -27.5px;

values:
mwPlayerContainer k-player videoHolder
width: 200px; position: relative;

values:
float: left; margin-left: 5px;
floatnone

values:
/wiki/Wikipedia:Media_help
mw-redirect
Wikipedia:Media help

values: font-size: xx-small; line-height: 1.6em; margin-left: 60px;

values:
nofollow
http://solarsystem.nasa.gov/
external text

values:
nofollow
external text
http://www.nineplanets.org/kboc.html

values:
nofollow
external text
https://arxiv.org/abs/1411.1844

attrs: alt src width height data-file-width data-file-height usemap

values:
*_The_Sun
*_Mercury
*_Venus
*_Earth
*_Mars
*_Ceres
*_Jupiter
*_Saturn
*_Uranus
*_Neptune
*_Pluto
*_Haumea
*_Makemake
*_Eris

values:
/wiki/Hi%CA%BBiaka_(moon)
mw-redirect
Hiʻiaka (moon)

values:
/wiki/Namaka_(moon)
mw-redirect
Namaka (moon)

values: Timeline of discovery of Solar System planets and their moons

values: List of gravitationally rounded objects of the Solar System

values: List of hypothetical Solar System objects

values: Discovery and exploration of the Solar System

values: nowraplinks hlist collapsible autocollapse navbox-inner mw-collapsible mw-made-collapsible mw-collapsed

values:
row
navbox-group
text-align: center;;width:1%

values: Ceres - RC3 - Haulani Crater (22381131691) (cropped).jpg

values: width:1px;padding:0px 0px 0px 2px;padding-left: 0.5em;

values:
/wiki/Vanth_(moon)
mw-redirect
Vanth (moon)

values:
row
navbox-group
width:1%;text-align: center;

values:
/wiki/File:Hyakutake_Color.jpg
image
Comet C/1996 B2 (Hyakutake)

values:
navbox-image
6
width:1px;padding:0px 0px 0px 2px

values:
/wiki/Jupiter-family_comet
mw-redirect
Jupiter-family comet

values:
/wiki/List_of_non-periodic_comets
mw-redirect
List of non-periodic comets

values: List of comets discovered by the LINEAR project

values:
/wiki/DESTINY_PLUS
mw-redirect
DESTINY PLUS

values: Comet Rendezvous, Sample Acquisition, Investigation, and Return

values:
/wiki/C/2012_S4_(PANSTARRS)
mw-redirect
C/2012 S4 (PANSTARRS)

values:
/wiki/324P/La_Sagra
mw-redirect
324P/La Sagra

values:
/wiki/P/2010_A2_(LINEAR)
mw-redirect
P/2010 A2 (LINEAR)

values: P/2012 T1 (PANSTARRS) (page does not exist)

values: P/2013 R3 (Catalina-PANSTARRS) (page does not exist)

values:
/wiki/Lost_comets
mw-redirect
Lost comets

values: List of minor planets and comets visited by spacecraft

values: C/1941 B2 (de Kock-Paraskevopoulos) (page does not exist)

values:
noprint
font-size:85%; font-style: normal;

values: C/1947 X1 (Southern Comet) (page does not exist)

values: C/1961 O1 (Wilson-Hubbard) (page does not exist)

values: C/1962 C1 (Seki-Lines) (page does not exist)

values:
/wiki/C/2002_T7_(LINEAR)
mw-redirect
C/2002 T7 (LINEAR)

values: C/2004 F4 (Bradfield) (page does not exist)

values:
/wiki/C/2007_F1_(LONEOS)
mw-redirect
C/2007 F1 (LONEOS)

values: C/2008 Q1 (Matičič) (page does not exist)

values:
/wiki/C/2013_R1_(Lovejoy)
mw-redirect
C/2013 R1 (Lovejoy)

values: Lowell Observatory Near-Earth-Object Search

values: nowraplinks collapsible autocollapse navbox-subgroup mw-collapsible mw-made-collapsible mw-collapsed

attrs: alt src width height style srcset data-file-width data-file-height

values:
nofollow
external text
https://viaf.org/viaf/315161594

values: Category:Pages containing links to subscription-only content

values: Category:Articles with hAudio microformats

values: Category:Interlanguage link template link number

values: Category:Wikipedia articles with LCCN identifiers

values: Category:Wikipedia articles with VIAF identifiers

values: Discussion about edits from this IP address [ctrl-alt-n]

values: A list of edits made from this IP address [ctrl-alt-y]

values: You are encouraged to create an account and log in; however, it is not mandatory

values: You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o]

values:
/wiki/Oort_cloud
View the content page [ctrl-alt-c]
c

values: Discussion about the content page [ctrl-alt-t]

values: p-namespaces navigation vectorTabs p-namespaces-label

values:
p-variants
navigation
vectorMenu emptyPortlet
p-variants-label

values: Past revisions of this page [ctrl-alt-h]

values: A list of recent changes in the wiki [ctrl-alt-r]

values: portal navigation p-interaction p-interaction-label

values: List of all English Wikipedia pages containing links to this page [ctrl-alt-j]

values: Recent changes in pages linked from this page [ctrl-alt-k]

values:
/wiki/Wikipedia:File_Upload_Wizard
Upload files [ctrl-alt-u]
u

values: A list of all special pages [ctrl-alt-q]

values: Permanent link to this revision of the page

values: Link to connected data repository item [ctrl-alt-g]

values: Printable version of this page [ctrl-alt-p]

values:
https://af.wikipedia.org/wiki/Oortwolk
Oortwolk – Afrikaans
af
af
interlanguage-link-target

values:
interlanguage-link interwiki-af
display: none;

values: سحابة أورط – Arabic

values: উৰ্ট মেঘ – Assamese

values:
interlanguage-link interwiki-as
display: none;

values:
interlanguage-link interwiki-ast
display: none;

values:
https://gn.wikipedia.org/wiki/Arai_Oort
Arai Oort – Guarani
gn
gn
interlanguage-link-target

values:
interlanguage-link interwiki-gn
display: none;

values:
interlanguage-link interwiki-az
display: none;

values: উর্ট মেঘ – Bangla

values:
interlanguage-link interwiki-bn
display: none;

values:
interlanguage-link interwiki-zh-min-nan
display: none;

values:
interlanguage-link interwiki-map-bms
display: none;

values: Воблака Оарта – Belarusian

values:
interlanguage-link interwiki-be
display: none;

values: Воблака Оорта – Belarusian (Taraškievica orthography)

values:
interlanguage-link interwiki-be-x-old
display: none;

values: Облак на Оорт – Bulgarian

values:
interlanguage-link interwiki-bg
display: none;

values:
interlanguage-link interwiki-bar
display: none;

values:
interlanguage-link interwiki-bs
display: none;

values:
interlanguage-link interwiki-br
display: none;

values: interlanguage-link interwiki-ca badge-Q17437796 badge-featuredarticle

values:
interlanguage-link interwiki-cs
display: none;

values:
interlanguage-link interwiki-cy
display: none;

values:
https://da.wikipedia.org/wiki/Oortskyen
Oortskyen – Danish
da
da
interlanguage-link-target

values:
interlanguage-link interwiki-da
display: none;

values:
interlanguage-link interwiki-de
display: none;

values:
interlanguage-link interwiki-et
display: none;

values: Νέφος του Όορτ – Greek

values:
interlanguage-link interwiki-el
display: none;

values: interlanguage-link interwiki-es badge-Q17437796 badge-featuredarticle

values:
interlanguage-link interwiki-eo
display: none;

values: interlanguage-link interwiki-eu badge-Q17437796 badge-featuredarticle

values: ابر اورت – Persian

values:
interlanguage-link interwiki-fa
display: none;

values:
interlanguage-link interwiki-fr
display: none;

values:
interlanguage-link interwiki-ga
display: none;

values:
https://gd.wikipedia.org/wiki/Neul_Oort
Neul Oort – Scottish Gaelic
gd
gd
interlanguage-link-target

values:
interlanguage-link interwiki-gd
display: none;

values:
interlanguage-link interwiki-gl
display: none;

values: 오르트 구름 – Korean

values:
interlanguage-link interwiki-ko
display: none;

values: Օորտի ամպ – Armenian

values:
interlanguage-link interwiki-hy
display: none;

values: और्ट बादल – Hindi

values:
interlanguage-link interwiki-hr
display: none;

values:
https://id.wikipedia.org/wiki/Awan_Oort
Awan Oort – Indonesian
id
id
interlanguage-link-target

values:
interlanguage-link interwiki-id
display: none;

values:
interlanguage-link interwiki-is
display: none;

values:
interlanguage-link interwiki-it
display: none;

values: עננת אורט – Hebrew

values:
interlanguage-link interwiki-he
display: none;

values:
interlanguage-link interwiki-jv
display: none;

values: ಊರ್ಟ್ ಮೋಡ – Kannada

values:
interlanguage-link interwiki-kn
display: none;

values: ორტის ღრუბელი – Georgian

values:
interlanguage-link interwiki-ka
display: none;

values:
interlanguage-link interwiki-sw
display: none;

values:
interlanguage-link interwiki-la
display: none;

values:
interlanguage-link interwiki-lv
display: none;

values:
interlanguage-link interwiki-lb
display: none;

values:
interlanguage-link interwiki-lt
display: none;

values:
interlanguage-link interwiki-lmo
display: none;

values:
interlanguage-link interwiki-hu
display: none;

values: Ортов Облак – Macedonian

values:
interlanguage-link interwiki-mk
display: none;

values: ഒർട്ട് മേഘം – Malayalam

values:
interlanguage-link interwiki-ml
display: none;

values: ऊर्टचा मेघ – Marathi

values:
interlanguage-link interwiki-mr
display: none;

values: ოორტაშ მუნაფა – Mingrelian

values:
interlanguage-link interwiki-xmf
display: none;

values:
https://ms.wikipedia.org/wiki/Awan_Oort
Awan Oort – Malay
ms
ms
interlanguage-link-target

values:
interlanguage-link interwiki-ms
display: none;

values:
interlanguage-link interwiki-my
display: none;

values:
https://nl.wikipedia.org/wiki/Oortwolk
Oortwolk – Dutch
nl
nl
interlanguage-link-target

values:
interlanguage-link interwiki-nl
display: none;

values:
interlanguage-link interwiki-ja
display: none;

values:
https://no.wikipedia.org/wiki/Oorts_sky
Oorts sky – Norwegian
no
no
interlanguage-link-target

values:
interlanguage-link interwiki-no
display: none;

values:
https://nn.wikipedia.org/wiki/Oortskya
Oortskya – Norwegian Nynorsk
nn
nn
interlanguage-link-target

values:
interlanguage-link interwiki-nn
display: none;

values:
interlanguage-link interwiki-oc
display: none;

values:
interlanguage-link interwiki-uz
display: none;

values:
interlanguage-link interwiki-pnb
display: none;

values:
interlanguage-link interwiki-nds
display: none;

values: interlanguage-link interwiki-pl badge-Q17437796 badge-featuredarticle

values: interlanguage-link interwiki-pt badge-Q17437796 badge-featuredarticle

values:
interlanguage-link interwiki-ksh
display: none;

values:
interlanguage-link interwiki-ro
display: none;

values: Облако Оорта – Russian

values:
interlanguage-link interwiki-ru
display: none;

values:
interlanguage-link interwiki-sco
display: none;

values:
interlanguage-link interwiki-scn
display: none;

values:
interlanguage-link interwiki-simple
display: none;

values:
interlanguage-link interwiki-sk
display: none;

values:
interlanguage-link interwiki-sl
display: none;

values: Ортов облак – Serbian

values:
interlanguage-link interwiki-sr
display: none;

values:
interlanguage-link interwiki-sh
display: none;

values:
interlanguage-link interwiki-fi
display: none;

values:
interlanguage-link interwiki-sv
display: none;

values:
interlanguage-link interwiki-tl
display: none;

values: Оорт болыты – Tatar

values:
interlanguage-link interwiki-tt
display: none;

values: ఊర్ట్ మేఘం – Telugu

values:
interlanguage-link interwiki-te
display: none;

values: เมฆออร์ต – Thai

values:
interlanguage-link interwiki-th
display: none;

values: Абри оорт – Tajik

values:
interlanguage-link interwiki-tg
display: none;

values:
interlanguage-link interwiki-tr
display: none;

values: Хмара Оорта – Ukrainian

values:
interlanguage-link interwiki-uk
display: none;

values: اورت بادل – Urdu

values:
interlanguage-link interwiki-vec
display: none;

values:
interlanguage-link interwiki-vi
display: none;

values:
interlanguage-link interwiki-war
display: none;

values:
interlanguage-link interwiki-zh-yue
display: none;

values: All languages (initial selection from common choices by you and others)

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Oort_cloud rootpage-Oort_cloud skin-vector action-view


text:
Central tendency
From Wikipedia, the free encyclopedia
Jump to: navigation, search
For the graph/network concept, see Centrality.
In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution.[1] It may also be called a center or location of the distribution. Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late 1920s.[2]
The most common measures of central tendency are the arithmetic mean, the median and the mode. A central tendency can be calculated for either a finite set of values or for a theoretical distribution, such as the normal distribution. Occasionally authors use central tendency to denote "the tendency of quantitative data to cluster around some central value."[2][3]
The central tendency of a distribution is typically contrasted with its dispersion or variability; dispersion and central tendency are the often characterized properties of distributions. Analysts may judge whether data has a strong or a weak central tendency based on its dispersion.
Contents
[hide]
1 Measures
2 Solutions to variational problems
2.1 Uniqueness
3 Relationships between the mean, median and mode
4 See also
5 References
Measures[edit]
The following may be applied to one-dimensional data. Depending on the circumstances, it may be appropriate to transform the data before calculating a central tendency. Examples are squaring the values or taking logarithms. Whether a transformation is appropriate and what it should be, depend heavily on the data being analyzed.
Arithmetic mean or simply, mean
the sum of all measurements divided by the number of observations in the data set.
Median
the middle value that separates the higher half from the lower half of the data set. The median and the mode are the only measures of central tendency that can be used for ordinal data, in which values are ranked relative to each other but are not measured absolutely.
Mode
the most frequent value in the data set. This is the only central tendency measure that can be used with nominal data, which have purely qualitative category assignments.
Geometric mean
the nth root of the product of the data values, where there are n of these. This measure is valid only for data that are measured absolutely on a strictly positive scale.
Harmonic mean
the reciprocal of the arithmetic mean of the reciprocals of the data values. This measure too is valid only for data that are measured absolutely on a strictly positive scale.
Weighted arithmetic mean
an arithmetic mean that incorporates weighting to certain data elements.
Truncated mean or trimmed mean
the arithmetic mean of data values after a certain number or proportion of the highest and lowest data values have been discarded.
Interquartile mean
a truncated mean based on data within the interquartile range.
Midrange
the arithmetic mean of the maximum and minimum values of a data set.
Midhinge
the arithmetic mean of the two quartiles.
Trimean
the weighted arithmetic mean of the median and two quartiles.
Winsorized mean
an arithmetic mean in which extreme values are replaced by values closer to the median.
Any of the above may be applied to each dimension of multi-dimensional data, but the results may not be invariant to rotations of the multi-dimensional space. In addition, there are the
Geometric median
which minimizes the sum of distances to the data points. This is the same as the median when applied to one-dimensional data, but it is not the same as taking the median of each dimension independently. It is not invariant to different rescaling of the different dimensions.
Quadratic mean (often known as the root mean square)
useful in engineering, but not often used in statistics. This is because it is not a good indicator of the center of the distribution when the distribution includes negative values.
Simplicial depth
the probability that a randomly chosen simplex with vertices from the given distribution will contain the given center
Tukey median
a point with the property that every halfspace containing it also contains many sample points
Solutions to variational problems[edit]
Several measures of central tendency can be characterized as solving a variational problem, in the sense of the calculus of variations, namely minimizing variation from the center. That is, given a measure of statistical dispersion, one asks for a measure of central tendency that minimizes variation: such that variation from the center is minimal among all choices of center. In a quip, "dispersion precedes location". This center may or may not be unique. In the sense of Lp spaces, the correspondence is:
Lp
dispersion
central tendency
L0
variation ratio mode
L1
average absolute deviation median
L2
standard deviation mean
L∞
maximum deviation midrange
The associated functions are called p-norms: respectively 0-"norm", 1-norm, 2-norm, and ∞-norm. The function corresponding to the L0 space is not a norm, and is thus often referred to in quotes: 0-"norm".
In equations, for a given (finite) data set X, thought of as a vector x = ( x 1 , … , x n ) {\displaystyle \mathbf {x} =(x_{1},\ldots ,x_{n})} , the dispersion about a point c is the "distance" from x to the constant vector c = ( c , … , c ) {\displaystyle \mathbf {c} =(c,\ldots ,c)} in the p-norm (normalized by the number of points n):
f p ( c ) = ‖ x − c ‖ p := ( 1 n ∑ i = 1 n | x i − c | p ) 1 / p . {\displaystyle f_{p}(c)=\left\|\mathbf {x} -\mathbf {c} \right\|_{p}:={\bigg (}{\frac {1}{n}}\sum _{i=1}^{n}\left|x_{i}-c\right|^{p}{\bigg )}^{1/p}.}
Note that for p = 0 {\displaystyle p=0} and p = ∞ {\displaystyle p=\infty } these functions are defined by taking limits, respectively as p → 0 {\displaystyle p\to 0} and p → ∞ {\displaystyle p\to \infty } . For p = 0 {\displaystyle p=0} the limiting values are 0 0 = 0 {\displaystyle 0^{0}=0} and a 0 = 1 {\displaystyle a^{0}=1} for a ≠ 0 {\displaystyle a\neq 0} , so the difference becomes simply equality, so the 0-norm counts the number of unequal points. For p = ∞ {\displaystyle p=\infty } the largest number dominates, and thus the ∞-norm is the maximum difference.
Uniqueness[edit]
The mean (L2 center) and midrange (L∞ center) are unique (when they exist), while the median (L1 center) and mode (L0 center) are not in general unique. This can be understood in terms of convexity of the associated functions (coercive functions).
The 2-norm and ∞-norm are strictly convex, and thus (by convex optimization) the minimizer is unique (if it exists), and exists for bounded distributions. Thus standard deviation about the mean is lower than standard deviation about any other point, and the maximum deviation about the midrange is lower than the maximum deviation about any other point.
The 1-norm is not strictly convex, whereas strict convexity is needed to ensure uniqueness of the minimizer. Correspondingly, the median (in this sense of minimizing) is not in general unique, and in fact any point between the two central points of a discrete distribution minimizes average absolute deviation.
The 0-"norm" is not convex (hence not a norm). Correspondingly, the mode is not unique – for example, in a uniform distribution any point is the mode.
Relationships between the mean, median and mode[edit]
Main article: Nonparametric skew § Relationships between the mean, median and mode
For unimodal distributions the following bounds are known and are sharp:[4]
| θ − μ | σ ≤ 3 , {\displaystyle {\frac {|\theta -\mu |}{\sigma }}\leq {\sqrt {3}},}
| ν − μ | σ ≤ 0.6 , {\displaystyle {\frac {|\nu -\mu |}{\sigma }}\leq {\sqrt {0.6}},}
| θ − ν | σ ≤ 3 , {\displaystyle {\frac {|\theta -\nu |}{\sigma }}\leq {\sqrt {3}},}
where μ is the mean, ν is the median, θ is the mode, and σ is the standard deviation.
For every distribution,[5][6]
| ν − μ | σ ≤ 1. {\displaystyle {\frac {|\nu -\mu |}{\sigma }}\leq 1.}
See also[edit]
Expected value
Location parameter
References[edit]
Jump up ^ Weisberg H.F (1992) Central Tendency and Variability, Sage University Paper Series on Quantitative Applications in the Social Sciences, ISBN 0-8039-4007-6 p.2
^ Jump up to: a b Upton, G.; Cook, I. (2008) Oxford Dictionary of Statistics, OUP ISBN 978-0-19-954145-4 (entry for "central tendency")
Jump up ^ Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP for International Statistical Institute. ISBN 0-19-920613-9 (entry for "central tendency")
Jump up ^ Johnson NL, Rogers CA (1951) "The moment problem for unimodal distributions". Annals of Mathematical Statistics, 22 (3) 433–439
Jump up ^ Hotelling H, Solomons LM (1932) The limits of a measure of skewness. Annals Math Stat 3, 141–114
Jump up ^ Garver (1932) Concerning the limits of a mesuare of skewness. Ann Math Stats 3(4) 141–142
[hide]
v
t
e
Statistics
Outline
Index
[hide]
Descriptive statistics
Continuous data
Center
Mean
arithmetic
geometric
harmonic
Median
Mode
Dispersion
Variance
Standard deviation
Coefficient of variation
Percentile
Range
Interquartile range
Shape
Central limit theorem
Moments
Skewness
Kurtosis
L-moments
Count data
Index of dispersion
Summary tables
Grouped data
Frequency distribution
Contingency table
Dependence
Pearson product-moment correlation
Rank correlation
Spearman's rho
Kendall's tau
Partial correlation
Scatter plot
Graphics
Bar chart
Biplot
Box plot
Control chart
Correlogram
Fan chart
Forest plot
Histogram
Pie chart
Q–Q plot
Run chart
Scatter plot
Stem-and-leaf display
Radar chart
[show]
Data collection
Study design
Population
Statistic
Effect size
Statistical power
Sample size determination
Missing data
Survey methodology
Sampling
stratified
cluster
Standard error
Opinion poll
Questionnaire
Controlled experiments
Design
control
optimal
Controlled trial
Randomized
Random assignment
Replication
Blocking
Interaction
Factorial experiment
Uncontrolled studies
Observational study
Natural experiment
Quasi-experiment
[show]
Statistical inference
Statistical theory
Population
Statistic
Probability distribution
Sampling distribution
Order statistic
Empirical distribution
Density estimation
Statistical model
Lp space
Parameter
location
scale
shape
Parametric family
Likelihood (monotone)
Location–scale family
Exponential family
Completeness
Sufficiency
Statistical functional
Bootstrap
U
V
Optimal decision
loss function
Efficiency
Statistical distance
divergence
Asymptotics
Robustness
Frequentist inference
Point estimation
Estimating equations
Maximum likelihood
Method of moments
M-estimator
Minimum distance
Unbiased estimators
Mean-unbiased minimum-variance
Rao–Blackwellization
Lehmann–Scheffé theorem
Median unbiased
Plug-in
Interval estimation
Confidence interval
Pivot
Likelihood interval
Prediction interval
Tolerance interval
Resampling
Bootstrap
Jackknife
Testing hypotheses
1- & 2-tails
Power
Uniformly most powerful test
Permutation test
Randomization test
Multiple comparisons
Parametric tests
Likelihood-ratio
Wald
Score
Specific tests
Z-test (normal)
Student's t-test
F-test
Goodness of fit
Chi-squared
G-test
Kolmogorov–Smirnov
Anderson–Darling
Lilliefors
Jarque–Bera
Normality (Shapiro–Wilk)
Likelihood-ratio test
Model selection
Cross validation
AIC
BIC
Rank statistics
Sign
Sample median
Signed rank (Wilcoxon)
Hodges–Lehmann estimator
Rank sum (Mann–Whitney)
Nonparametric anova
1-way (Kruskal–Wallis)
2-way (Friedman)
Ordered alternative (Jonckheere–Terpstra)
Bayesian inference
Bayesian probability
prior
posterior
Credible interval
Bayes factor
Bayesian estimator
Maximum posterior estimator
[show]
Correlation
Regression analysis
Correlation
Pearson product-moment
Partial correlation
Confounding variable
Coefficient of determination
Regression analysis
Errors and residuals
Regression model validation
Mixed effects models
Simultaneous equations models
Multivariate adaptive regression splines (MARS)
Linear regression
Simple linear regression
Ordinary least squares
General linear model
Bayesian regression
Non-standard predictors
Nonlinear regression
Nonparametric
Semiparametric
Isotonic
Robust
Heteroscedasticity
Homoscedasticity
Generalized linear model
Exponential families
Logistic (Bernoulli) / Binomial / Poisson regressions
Partition of variance
Analysis of variance (ANOVA, anova)
Analysis of covariance
Multivariate ANOVA
Degrees of freedom
[show]
Categorical / Multivariate / Time-series / Survival analysis
Categorical
Cohen's kappa
Contingency table
Graphical model
Log-linear model
McNemar's test
Multivariate
Regression
Manova
Principal components
Canonical correlation
Discriminant analysis
Cluster analysis
Classification
Structural equation model
Factor analysis
Multivariate distributions
Elliptical distributions
Normal
Time-series
General
Decomposition
Trend
Stationarity
Seasonal adjustment
Exponential smoothing
Cointegration
Structural break
Granger causality
Specific tests
Dickey–Fuller
Johansen
Q-statistic (Ljung–Box)
Durbin–Watson
Breusch–Godfrey
Time domain
Autocorrelation (ACF)
partial (PACF)
Cross-correlation (XCF)
ARMA model
ARIMA model (Box–Jenkins)
Autoregressive conditional heteroskedasticity (ARCH)
Vector autoregression (VAR)
Frequency domain
Spectral density estimation
Fourier analysis
Wavelet
Survival
Survival function
Kaplan–Meier estimator (product limit)
Proportional hazards models
Accelerated failure time (AFT) model
First hitting time
Hazard function
Nelson–Aalen estimator
Test
Log-rank test
[show]
Applications
Biostatistics
Bioinformatics
Clinical trials / studies
Epidemiology
Medical statistics
Engineering statistics
Chemometrics
Methods engineering
Probabilistic design
Process / quality control
Reliability
System identification
Social statistics
Actuarial science
Census
Crime statistics
Demography
Econometrics
National accounts
Official statistics
Population statistics
Psychometrics
Spatial statistics
Cartography
Environmental statistics
Geographic information system
Geostatistics
Kriging
Category
Portal
Commons
WikiProject
Retrieved from "https://en.wikipedia.org/w/index.php?title=Central_tendency&oldid=826381045"
Categories:
Summary statistics
Probability theory
Navigation menu
Personal tools
Not logged in
Talk
Contributions
Create account
Log in
Namespaces
Article
Talk
Variants
Views
Read
Edit
View history
More
Search
Navigation
Main page
Contents
Featured content
Current events
Random article
Donate to Wikipedia
Wikipedia store
Interaction
Help
About Wikipedia
Community portal
Recent changes
Contact page
Tools
What links here
Related changes
Upload file
Special pages
Permanent link
Page information
Wikidata item
Cite this page
Print/export
Create a book
Download as PDF
Printable version
In other projects
Wikimedia Commons
Languages
العربية
বাংলা
Català
Deutsch
Español
Euskara
فارسی
Français
Bahasa Indonesia
Italiano
עברית
Bahasa Melayu
Nederlands
Polski
Русский
Simple English
Basa Sunda
Suomi
తెలుగు
Українська
中文
Edit links
This page was last edited on 18 February 2018, at 20:09.
Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization.
Privacy policy
About Wikipedia
Disclaimers
Contact Wikipedia
Developers
Cookie statement
Mobile view
Enable previews

key: html

type: local

value: div

attrs: id class

values: mw-page-base noprint

values: mw-head-base noprint

value: a

attrs: id class lang

values: firstHeading firstHeading en

values: siteSub noprint

values: jump-to-nav mw-jump

attrs: href title

attrs: role class

values:
note
hatnote navigation-not-searchable

value: b

value: sup

attrs: href class title

values: /wiki/Averages mw-redirect Averages

value: i

value: p

values:
/wiki/Quadratic_mean
mw-redirect
Quadratic mean

values:
/wiki/Tukey_median
mw-redirect
Tukey median

values: Edit section: Solutions to variational problems

values:
/wiki/Maximum_deviation
mw-redirect
Maximum deviation

values: vertical-align: -0.838ex; width:16.429ex; height:2.843ex;

values: {\displaystyle \mathbf {c} =(c,\ldots ,c)}

values: vertical-align: -0.838ex; width:13.288ex; height:2.843ex;

values: vertical-align: -3.005ex; width:42.142ex; height:7.176ex;

values: vertical-align: -0.671ex; margin-left: -0.089ex; width:5.52ex; height:2.509ex;

values: vertical-align: -0.671ex; margin-left: -0.089ex; width:6.681ex; height:2.009ex;

values: vertical-align: -0.671ex; margin-left: -0.089ex; width:6.035ex; height:2.509ex;

values: vertical-align: -0.671ex; margin-left: -0.089ex; width:7.197ex; height:2.176ex;

values: vertical-align: -0.338ex; width:6.478ex; height:2.676ex;

values: vertical-align: -0.338ex; width:6.545ex; height:2.676ex;

values: vertical-align: -0.838ex; width:5.491ex; height:2.676ex;

values:
/wiki/Strictly_convex
mw-redirect
Strictly convex

values: Edit section: Relationships between the mean, median and mode

values:
/wiki/Unimodal_distribution
mw-redirect
Unimodal distribution

values: vertical-align: -1.838ex; width:14.306ex; height:5.676ex;

values: vertical-align: -1.838ex; width:16.257ex; height:5.676ex;

values: vertical-align: -1.838ex; width:14.136ex; height:5.676ex;

values: vertical-align: -1.838ex; width:12.512ex; height:5.676ex;

values:
reflist mw-references-wrap
list-style-type: decimal;

values:
/wiki/Shape_of_the_distribution
mw-redirect
Shape of the distribution

values: Kendall tau rank correlation coefficient

values: nowraplinks collapsible uncollapsed navbox-subgroup

values:
/wiki/Population_(statistics)
mw-redirect
Population (statistics)

values: nowraplinks collapsible collapsed navbox-subgroup

values:
/wiki/Maximum_likelihood
mw-redirect
Maximum likelihood

values:
/wiki/Median-unbiased_estimator
mw-redirect
Median-unbiased estimator

values:
/wiki/Likelihood_interval
mw-redirect
Likelihood interval

values:
/wiki/Power_(statistics)
mw-redirect
Power (statistics)

values:
/wiki/Permutation_test
mw-redirect
Permutation test

values:
/wiki/Randomization_test
mw-redirect
Randomization test

values:
/wiki/Multiple_comparisons
mw-redirect
Multiple comparisons

values:
/wiki/Rank_statistics
mw-redirect
Rank statistics

values:
/wiki/Sample_median
mw-redirect
Sample median

values: Kruskal–Wallis one-way analysis of variance

values:
CorrelationRegression_analysis
font-size:114%;margin:0 4em
hlist hlist-separated

values: Pearson product-moment correlation coefficient

values:
/wiki/Regression_model_validation
mw-redirect
Regression model validation

values: Multivariate adaptive regression splines

values:
/wiki/Multivariate_distribution
mw-redirect
Multivariate distribution

values:
/wiki/Trend_estimation
mw-redirect
Trend estimation

values: List of fields of application of statistics

values: nowraplinks hlist collapsible uncollapsed navbox-inner

values: navigation navbox Statistics padding:3px

values:
catlinks mw-normal-catlinks
catlinks mw-normal-catlinks
interface

values: Discussion about edits from this IP address [ctrl-alt-n]

values: A list of edits made from this IP address [ctrl-alt-y]

values: You are encouraged to create an account and log in; however, it is not mandatory

values: You're encouraged to log in; however, it's not mandatory. [ctrl-alt-o]

values:
/wiki/Central_tendency
View the content page [ctrl-alt-c]
c

values: Discussion about the content page [ctrl-alt-t]

values: p-namespaces navigation vectorTabs p-namespaces-label

values:
p-variants
navigation
vectorMenu emptyPortlet
p-variants-label

values: Past revisions of this page [ctrl-alt-h]

values: p-views navigation vectorTabs p-views-label

values:
p-cactions
navigation
vectorMenu emptyPortlet
p-cactions-label

values:
mw-wiki-logo
/wiki/Main_Page
Visit the main page

values:
/wiki/Main_Page
Visit the main page [ctrl-alt-z]
z

values: Featured content – the best of Wikipedia

values: Find background information on current events

values:
/wiki/Special:Random
Load a random article [ctrl-alt-x]
x

values: portal navigation p-navigation p-navigation-label

values: Guidance on how to use and edit Wikipedia

values: About the project, what you can do, where to find things

values: A list of recent changes in the wiki [ctrl-alt-r]

values: portal navigation p-interaction p-interaction-label

values: List of all English Wikipedia pages containing links to this page [ctrl-alt-j]

values: Recent changes in pages linked from this page [ctrl-alt-k]

values:
/wiki/Wikipedia:File_Upload_Wizard
Upload files [ctrl-alt-u]
u

values: A list of all special pages [ctrl-alt-q]

values: Permanent link to this revision of the page

values: Link to connected data repository item [ctrl-alt-g]

values: Printable version of this page [ctrl-alt-p]

values: portal navigation p-wikibase-otherprojects p-wikibase-otherprojects-label

values: نزعة مركزية – Arabic

values: কেন্দ্রীয় প্রবণতা – Bangla

values: شاخص‌های مرکزی – Persian

values: מדד מיקום – Hebrew

values: Меры центральной тенденции – Russian

values:
https://fi.wikipedia.org/wiki/Keskiluku
Keskiluku – Finnish
fi
fi
interlanguage-link-target

values: కేంద్రీయ ప్రవృత్తి మాపనాలు – Telugu

values: Центральна тенденція – Ukrainian

values: /static/images/wikimedia-button-1.5x.png 1.5x, /static/images/wikimedia-button-2x.png 2x

values: /static/images/poweredby_mediawiki_132x47.png 1.5x, /static/images/poweredby_mediawiki_176x62.png 2x

values:
suggestions
display: none; font-size: 13px;

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Central_tendency rootpage-Central_tendency skin-vector action-view