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{{about||Dava Sobel's book about John Harrison|Longitude (book)|the adaptation of Sobel's book| Longitude (TV series)|other uses|Longitude (disambiguation)}}
[[File:Division of the Earth into Gauss-Krueger zones - Globe.svg|thumb|upright=0.9|right|A [[Geographic coordinate system|graticule]] on the [[Earth]] as a [[sphere]] or an [[ellipsoid]]. The lines from pole to pole are lines of constant longitude, or [[meridian (geography)|meridians]]. The circles parallel to the [[Equator]] are circles of constant [[latitude]], or [[circle of latitude|parallels]]. The graticule shows the latitude and longitude of points on the surface. In this example, meridians are spaced at 6° intervals and parallels at 4° intervals.]]
{{longlat}}{{Geodesy|notshowfig=1}}
'''Longitude''' ({{IPAc-en|ˈ|l|ɒ|n|dʒ|ᵻ|tj|uː|d}}, {{small|AU and UK also}} {{IPAc-en|ˈ|l|ɒ|ŋ|ɡ|ᵻ|-}}),<ref>{{cite web |url=http://www.merriam-webster.com/dictionary/longitude |title=Definition of LONGITUDE |website=www.merriam-webster.com |publisher=[[Merriam-Webster]] |access-date=14 March 2018}}</ref><ref>[[Oxford English Dictionary]]</ref> is a [[geographic coordinate system|geographic coordinate]] that specifies the [[east]]–[[west]] position of a point on the [[Earth]]'s surface, or the surface of a celestial body. It is an angular measurement, usually expressed in [[degree (angle)|degrees]] and denoted by the [[Greek alphabet|Greek letter]] [[lambda]] (λ). [[meridian (geography)|Meridians]] (lines running from [[geographical pole|pole]] to pole) connect points with the same longitude. The [[prime meridian]], which passes near the [[Royal Observatory, Greenwich]], England, is defined as 0° longitude by convention. Positive longitudes are east of the prime meridian, and negative ones are west.
Because of the earth's rotation, there is a close connection between longitude and time. Local time (for example from the position of the sun) varies with longitude, a difference of 15° longitude corresponding to a one-hour difference in local time. Comparing local time to an absolute measure of time allows longitude to be determined. Depending on the era, the absolute time might be obtained from a celestial event visible from both locations, such as a lunar eclipse, or from a time signal transmitted by telegraph or wireless. The principle is straightforward, but in practice finding a reliable method of determining longitude took centuries and required the effort of some of the greatest scientific minds.
A location's [[north]]–[[south]] position along a meridian is given by its [[latitude]], which is approximately the angle between the local vertical and the equatorial plane.
Longitude is generally given using the geometrical or astronomical vertical. This can differ slightly from the gravitational vertical because of [[vertical deflection|small variations in Earth's gravitational field]].
== History ==
{{Main|History of longitude}}
The concept of longitude was first developed by ancient Greek astronomers. [[Hipparchus]] (2nd century BCE) used a coordinate system that assumed a spherical earth, and divided it into 360° as we still do today. His [[prime meridian]] passed through [[Alexandria]].<ref name="Dicks">{{cite thesis |type=PhD|last1=Dicks |first1=D.R. |title=Hipparchus : a critical edition of the extant material for his life and works |date=1953 |publisher=Birkbeck College, University of London |url=https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.720566}}</ref>{{rp|31}} He also proposed a method of determining longitude by comparing the local time of a [[lunar eclipse]] at two different places, thus demonstrating an understanding of the relationship between longitude and time.{{r|Dicks|p=11}}.<ref>{{cite book |last1=Hoffman |first1=Susanne M. |title=The Science of Time |chapter=How time served to measure the geographical position since Hellenism|date=2016 |editor-last1=Arias |editor-first1=Elisa Felicitas |editor-last2=Combrinck |editor-first2=Ludwig |editor-last3=Gabor |editor-first3=Pavel |editor-last4=Hohenkerk |editor-first4=Catherine |editor-last5=Seidelmann |editor-first5=P.Kenneth |publisher=Springer International |series=Astrophysics and Space Science Proceedings|volume=50 |doi=10.1007/978-3-319-59909-0_4|pages=25–36|isbn=978-3-319-59908-3 }}</ref> [[Ptolemy|Claudius Ptolemy]] (2nd century CE) developed a mapping system using curved parallels that reduced distortion. He also collected data for many locations, from Britain to the Middle East. He used a prime meridian through the Canary Islands, so that all longitude values would be positive. While Ptolemy's system was sound, the data he used were often poor, leading to a gross over-estimate (by about 70%) of the length of the Mediterranean.<ref>{{cite book |last1=Mittenhuber |first1=Florian |title=Ptolemy in Perspective: Use and Criticism of his Work from Antiquity to the Nineteenth Century|url=https://archive.org/details/ptolemyperspecti00jone |url-access=limited |chapter=The Tradition of Texts and Maps in Ptolemy's Geography |series=Archimedes |date=2010 |volume=23 |editor-last1=Jones | editor-first1=Alexander |publisher=Springer |location=Dordrecht |pages=[https://archive.org/details/ptolemyperspecti00jone/page/n106 95]-119|doi=10.1007/978-90-481-2788-7_4|isbn=978-90-481-2787-0 }}</ref><ref name="Bunbury">{{cite book |last1=Bunbury |first1=E.H. |title=A History of Ancient Geography |volume=2|date=1879 |publisher=John Murray |location=London|url=https://archive.org/details/historyofancientgeographybunburye.h.vol21879_648_H}}</ref>{{rp|551-553}}<ref>{{cite journal |last1=Shcheglov |first1=Dmitry A. |s2cid=129864284 |title=The Error in Longitude in Ptolemy's Geography Revisited |journal=The Cartographic Journal |date=2016 |volume=53 |issue=1 |pages=3–14 |doi=10.1179/1743277414Y.0000000098}}</ref>
After the fall of the Roman Empire, interest in geography greatly declined in Europe.<ref name="Wright1925">{{cite book |last1=Wright |first1=John Kirtland |title=The geographical lore of the time of the Crusades: A study in the history of medieval science and tradition in Western Europe |date=1925 |publisher=American geographical society |location=New York |url=https://archive.org/details/geographicallore00wrig}}</ref>{{rp|65}} Hindu and Muslim astronomers continued to develop these ideas, adding many new locations and often improving on Ptolemy's data.<ref name="Ragep">{{cite book |last1=Ragep |first1=F.Jamil|editor-last=Jones|editor-first=A.|title=Ptolemy in Perspective |publisher=Springer |place=Dordrecht |date=2010 |chapter=Islamic reactions to Ptolemy's imprecisions |series=Archimedes|volume=23|isbn=978-90-481-2788-7 |doi=10.1007/978-90-481-2788-7}}</ref><ref name="Tibbett">{{cite book |last1=Tibbetts|first1=Gerald R.|editor1-last=Harley|editor1-first=J.B.|editor2-last=Woodward
|editor2-first=David |title=The History of Cartography Vol. 2 Cartography in the Traditional Islamic and South Asian Societies |publisher=University of Chicago Press |date=1992 |chapter=The Beginnings of a Cartographic Tradition |chapter-url=https://press.uchicago.edu/books/HOC/HOC_V2_B1/HOC_VOLUME2_Book1_chapter4.pdf }}</ref> For example [[Al-Battani|al-Battānī]] used simultaneous observations of two lunar eclipses to determine the difference in longitude between [[Antakya]] and [[Raqqa]] with an error of less than 1°. This is considered to be the best that can be achieved with the methods then available - observation of the eclipse with the naked eye, and determination of local time using an [[astrolabe]] to measure the altitude of a suitable "clock star".<ref name="Said2">{{cite journal |last1=Said |first1=S.S. |last2=Stevenson |first2=F.R. |s2cid=117100760 |title=Solar and Lunar Eclipse Measurements by Medieval Muslim Astronomers, II: Observations |journal=Journal for the History of Astronomy |date=1997 |volume=28 |issue=1 |pages=29–48 |doi=10.1177/002182869702800103|bibcode=1997JHA....28...29S }}</ref><ref name="Steele">{{cite thesis |type=PhD |last=Steele|first=John Michael |date=1998 |title=Observations and predictions of eclipse times by astronomers in the pre-telescopic period |publisher=University of Durham (United Kingdom)}}</ref>
In the later Middle Ages, interest in geography revived in the west, as travel increased, and Arab scholarship began to be known through contact with Spain and North Africa. In the 12th Century, astronomical tables were prepared for a number of European cities, based on the work of [[Abū Ishāq Ibrāhīm al-Zarqālī|al-Zarqālī]] in [[Toledo, Spain|Toledo]]. The lunar eclipse of September 12, 1178 was used to establish the longitude differences between Toledo, [[Marseille]]s, and [[Hereford]].<ref name="Wright1923">{{cite journal |last1=Wright |first1=John Kirtland |title=Notes on the Knowledge of Latitudes and Longitudes in the Middle Ages |journal=Isis |date=1923 |volume=5 |issue=1 |bibcode=1922nkll.book.....W |url=https://archive.org/details/wright-1923-isisacad-05acaduoft}}</ref>{{rp|85}}
Christopher Columbus made two attempts to use lunar eclipses to discover his longitude, the first in [[Saona Island]], on 14 September 1494 (second voyage), and the second in [[Jamaica]] on 29 February 1504 (fourth voyage). It is assumed that he used astronomical tables for reference. His determinations of longitude showed large errors of 13 and 38° W respectively.<ref name="Pickering">{{cite journal |last1=Pickering |first1=Keith |title=Columbus's Method of Determining Longitude: An Analytical View |journal=The Journal of Navigation |date=1996 |volume=49 |issue=1 |pages=96–111 |doi=10.1017/S037346330001314X|bibcode=1996JNav...49...95P }}</ref> Randles (1985) documents longitude measurement by the Portuguese and Spanish between 1514 and 1627 both in the Americas and Asia. Errors ranged from 2-25°.<ref name="Randles">{{cite journal |last1=Randles |first1=W.G.L. |title=Portuguese and Spanish attempts to measure longitude in the 16th century |journal=Vistas in Astronomy |date=1985 |volume=28 |issue=1 |pages=235–241|doi=10.1016/0083-6656(85)90031-5 |bibcode=1985VA.....28..235R }}</ref>
The telescope was invented in the early 17th-century. Initially an observation device, developments over the next half century transformed it into an accurate measurement tool.<ref name="Pannekoek">{{cite book |last1=Pannekoek |first1=Anton |title=A history of astronomy |date=1989 |publisher=Courier Corporation |pages=259–276 |url=https://archive.org/details/historyofastrono0000pann}}</ref><ref name="Van Helden">{{cite journal |last1=Van Helden |first1=Albert |title=The Telescope in the Seventeenth Century |journal=Isis |date=1974 |volume=65 |issue=1 |pages=38–58 |doi=10.1086/351216 |jstor=228880 }}</ref> The [[pendulum clock]] was patented by [[Christiaan Huygens]] in 1657<ref name="Grimbergen">{{cite conference |last1=Grimbergen |first1=Kees |title=Huygens and the advancement of time measurements |journal=Titan - from Discovery to Encounter |conference=Titan - From Discovery to Encounter |editor-last=Fletcher | editor-first=Karen |location=ESTEC, Noordwijk, Netherlands |date=2004 |volume=1278 |pages=91–102 |publisher=ESA Publications Division |bibcode=2004ESASP1278...91G |isbn=92-9092-997-9 }}</ref> and gave an increase in accuracy of about 30 fold over previous mechanical clocks.<ref>{{cite journal |last1=Blumenthal |first1=Aaron S. |last2=Nosonovsky |first2=Michael |title=Friction and Dynamics of Verge and Foliot: How the Invention of the Pendulum Made Clocks Much More Accurate |journal=Applied Mechanics |date=2020 |volume=1 |issue=2 |pages=111–122 |doi=10.3390/applmech1020008|doi-access=free }}</ref> These two inventions would revolutionize observational astronomy and cartography.<ref name="Olmsted">{{cite journal |last1=Olmsted |first1=J.W. |title=The Voyage of Jean Richer to Acadia in 1670: A Study in the Relations of Science and Navigation under Colbert |journal=Proceedings of the American Philosophical Society |date=1960 |volume=104 |issue=6 |pages=612–634 |jstor=985537 }}</ref>
The main methods for dermining longitude are listed below. With one exception (magnetic declination) they all depend on a common principle, which was to determine an absolute time from an event or measurement and to compare the corresponding local time at two different locations.
* [[Lunar distance (navigation)|Lunar distances]]. In its orbit around the earth, the moon moves relative to the stars at a rate of just over 0.5°/hour. The angle between the moon and a suitable star is measured with a [[sextant]], and (after consultation with tables and lengthy calculations) gives a value for absolute time.
*Satellites of Jupiter. [[Galileo Galilei|Galileo]] proposed that with sufficiently accurate knowledge of the orbits of the satellites, their positions could provide a measure of absolute time. The method requires a telescope, as the moons are not visible to the naked eye.
*Appulses, occultations, and eclipses. An [[appulse]] is the least apparent distance between two objects (the moon a star or a planet), an [[occultation]] occurs when a star or planet passes behind the moon — essentially a type of eclipse. Lunar eclipses continued to be used. The times of any of these events can be used as the measure of absolute time.
*[[Marine chronometer|Chronometers]]. A clock is set to the local time of a starting point whose longitude is known, and the longitude of any other place can be determined by comparing its local time with the clock time.
*Magnetic declination. A compass needle does not in general point exactly north. The [[Magnetic declination|variation]] from true north varies with location, and it was suggested that this could provide a basis for determination of longitude.
With the exception of magnetic declination, all proved practicable methods. Developments on land and sea, however, were very different.
On land, the period from the development of telescopes and pendulum clocks until the mid 18th-Century saw a steady increase in the number of places whose longitude had been determined with reasonable accuracy, often with errors of less than a degree, and nearly always within 2-3°. By the 1720s errors were consistently less than 1°.<ref>See, for example, Port Royal, Jamaica: {{cite journal |last1=Halley |first1=Edmond |title=Observations on the Eclipse of the Moon, June 18, 1722. and the Longitude of Port Royal in Jamaica |journal=Philosophical Transactions |date=1722 |volume=32 |issue=370–380 |pages=235–236 |url=https://archive.org/details/jstor-103607}}; Buenos Aires: {{cite journal |last1=Halley |first1=Edm. |title=The Longitude of Buenos Aires, Determin'd from an Observation Made There by Père Feuillée |journal=Philosophical Transactions |date=1722 |volume=32 |issue=370–380 |pages=2–4 |url=https://archive.org/details/jstor-103565}}Santa Catarina, Brazil: {{cite journal |last1=Legge |first1=Edward |last2=Atwell |first2=Joseph |title=Extract of a letter from the Honble Edward Legge, Esq; F. R. S. Captain of his Majesty's ship the Severn, containing an observation of the eclipse of the moon, Dec. 21. 1740. at the Island of St. Catharine on the Coast of Brasil |journal=Philosophical Transactions |date=1743 |volume=42 |issue=462 |pages=18–19 |url=https://archive.org/details/jstor-104132}}</ref> At sea during the same period, the situation was very different. Two problems proved intractable. The first was the need of a navigator for immediate results. The second was the marine environment. Making accurate observations in an ocean swell is much harder than on land, and pendulum clocks do not work well in these conditions.
In response to the problems of navigation, a number of European maritime powers offered prizes for a method to determine longitude at sea. The best-known of these is the [[Longitude Act]] passed by the British parliament in 1714.<ref name="Siegel">{{cite journal |last1=Siegel |first1=Jonathan R. |title=Law and Longitude |journal=Tulane Law Review |date=2009 |volume=84 |pages=1–66}}</ref>{{rp|8}} It offered two levels of rewards, for solutions within 1° and 0.5°. Rewards were given for two solutions: lunar distances, made practicable by the tables of [[Tobias Mayer]]<ref name="Forbes2006">{{cite journal |last1=Forbes |first1=Eric Gray |title=Tobias Mayer's lunar tables|journal=Annals of Science |volume=22 |issue=2 |year=2006 |pages=105–116 |issn=0003-3790|doi=10.1080/00033796600203075}}</ref> developed into an [[nautical almanac]] by the [[Astronomer Royal]] [[Neville Maskelyne]]; and for the chronometers developed by the Yorkshire carpenter and clock-maker [[John Harrison]]. Harrison built five chronometers over more than three decades. However, he was not awarded the prize by the Longitude Board and was forced to fight for his reward, finally receiving payment in 1773, after the intervention of parliament{{r|"Siegel"|p=26}}. It was some while before either method became widely used in navigation. In the early years, chronometers were very expensive, and the calculations required for lunar distances were still complex and time-consuming. Lunar distances came into general use after 1790.<ref name="Wess2015">{{cite book|title=Navigational Enterprises in Europe and its Empires, 1730-1850 |editor1-last=Dunn |editor1-first=Richard |editor2-last=Higgitt |editor2-first=Rebekah |last1=Wess|first1=Jane|chapter=Navigation and Mathematics: A Match Made in the Heavens?|year=2015|pages=201–222|publisher=Palgrave Macmillan UK |location=London |doi=10.1057/9781137520647_11|isbn=978-1-349-56744-7 }}</ref> Chronometers had the advantages that both the observations and the calculations were simpler, and as they became cheaper in the early 19th-Century they started to replace lunars, which were seldom used after 1850.<ref name="Littlehales">{{cite journal |last1=Littlehales |first1=G.W. |title=The Decline of the Lunar Distance for the Determination of the Time and Longitude at |journal=Bulletin of the American Geographical Society |date=1909 |volume=41 |issue=2 |pages=83–86 |doi=10.2307/200792 |jstor=200792 |url=https://archive.org/details/jstor-200792}}</ref>
The first working telegraphs were established in Britain by [[Charles Wheatstone|Wheatstone]] and [[William Fothergill Cooke|Cooke]] in 1839, and in the US by [[Samuel Morse|Morse]] in 1844. It was quickly realised that the telegraph could be used to transmit a time signal for longitude determination.<ref name="Walker 1850">{{cite journal |last1=Walker |first1=Sears C |title=Report on the experience of the Coast Survey in regard to telegraph operations, for determination of longitude &c. |journal=American Journal of Science and Arts |date=1850 |volume=10 |issue=28 |pages=151–160 |url=https://archive.org/details/appendix-telegraphic-longitude-the-american-journal-of-science-and-arts }}</ref> The method was soon in practical use for longitude determination, especially in North America, and over longer and longer distances as the telegraph network expanded, including western Europe with the completion of transatlantic cables. The [[U.S. National Geodetic Survey|US Coast Survey]] was particularly active in this development, and not just in the United States. The Survey established chains of mapped locations through Central and South America, and the West Indies, and as far as Japan and China in the years 1874–90. This contributed greatly to the accurate mapping of these areas.<ref name="Knox">{{cite journal |last1=Knox |first1=Robert W. |title=Precise Determination of Longitude in the United States |journal=Geographical Review |date=1957 |volume=47 |pages=555-563 |jstor=211865}}</ref><ref name="Green1883">{{cite book |last1=Green |first1=Francis Mathews |last2=Davis |first2=Charles Henry |last3=Norris |first3=John Alexander |title=Telegraphic Determination of Longitudes in Japan, China, and the East Indies: Embracing the Meridians of Yokohama, Nagasaki, Wladiwostok, Shanghai, Amoy, Hong-Kong, Manila, Cape St. James, Singapore, Batavia, and Madras, with the Latitude of the Several Stations |date=1883 |publisher=US Hydrographic Office |location=Washington |url=https://archive.org/details/in.ernet.dli.2015.177254}}</ref>
While mariners benefited from the accurate charts, they could not receive telegraph signals while under way, and so could not use the method for navigation. This changed when wireless telegraphy became available in the early 20th-Century.<ref name="Munro1902">{{cite journal|last1=Munro|first1=John|s2cid=4021629|title=Time-Signals by Wireless Telegraphy |journal=Nature |volume=66 |issue=1713 |year=1902 |pages=416 |issn=0028-0836 |doi=10.1038/066416d0 |bibcode=1902Natur..66..416M |url=https://zenodo.org/record/2080631}}</ref> Wireless time signals for the use of ships were transmitted from [[Halifax, Nova Scotia]], starting in 1907<ref name="Hutchnson">{{cite journal |last1=Hutchinson |first1=D.L. |title=Wireless Time Signals from the St. John Observatory of the Canadian Meteorological Service. |journal=Proceedings and Transactions of the Royal Society of Canada |date=1908 |volume=Ser. 3 Vol. 2 |pages=153–154 |url=https://archive.org/details/hutchinson-1908-proceedingstrans-32roya}}</ref> and from the [[Eiffel Tower]] in Paris from 1910.<ref name="Lockyer1913">{{cite journal|last1=Lockyer|first1=William J. S.|s2cid=3977506|title=International Time and Weather Radio-Telegraphic Signals |journal=Nature |volume=91 |issue=2263 |year=1913 |pages=33–36 |issn=0028-0836 |doi=10.1038/091033b0 |bibcode=1913Natur..91...33L |doi-access=free}}</ref> These signals allowed navigators to check and adjust their chronometers on a frequent basis.<ref name="Zimmerman">{{cite web |last1=Zimmerman |first1=Arthur E. |title=The first wireless time signals to ships at sea |url=https://www.antiquewireless.org/wp-content/uploads/50-the_first_wireless_time_signals_to_ships_at_sea.pdf |website=antiquewireless.org |publisher=Antique Wireless Association |access-date=9 July 2020}}</ref>
[[Radio navigation]] systems came into general use after [[World War II]]. The systems all depended on transmissions from fixed navigational beacons. A ship-board receiver calculated the vessel's position from these transmissions.<ref name="Pierce">{{cite journal |last1=Pierce |first1=J.A. |s2cid=20739091 |title=An introduction to Loran |journal=Proceedings of the IRE |date=1946 |volume=34 |issue=5 |pages=216–234 |doi=10.1109/JRPROC.1946.234564}}</ref> They allowed accurate navigation when poor visibility prevented astronomical observations, and became the established method for commercial shipping until replaced by [[Global Positioning System|GPS]] in the early 1990s.
==Noting and calculating longitude==
Longitude is given as an [[angle|angular measurement]] ranging from 0° at the Prime Meridian to +180° eastward and −180° westward. The Greek letter λ (lambda),<ref>{{cite web|url=http://www.colorado.edu/geography/gcraft/notes/datum/gif/llhxyz.gif|title=Coordinate Conversion|website=colorado.edu|access-date=14 March 2018|archive-url=https://web.archive.org/web/20090929121405/http://www.colorado.edu/geography/gcraft/notes/datum/gif/llhxyz.gif|archive-date=29 September 2009|url-status=dead}}</ref><ref>"λ = Longitude east of Greenwich (for longitude west of Greenwich, use a minus sign)."<br>John P. Snyder, ''[https://pubs.er.usgs.gov/usgspubs/pp/pp1395 Map Projections, A Working Manual]'', [[USGS]] Professional Paper 1395, page ix</ref> is used to denote the location of a place on Earth east or west of the Prime Meridian.
Each degree of longitude is sub-divided into 60 [[minute of arc|minutes]], each of which is divided into 60 [[arcsecond|seconds]]. A longitude is thus specified in [[sexagesimal]] notation as 23° 27′ 30″ E. For higher precision, the seconds are specified with a [[Decimal#Decimal fractions|decimal fraction]]. An alternative representation uses degrees and minutes, where parts of a minute are expressed in decimal notation with a fraction, thus: 23° 27.5′ E. Degrees may also be expressed as a decimal fraction: 23.45833° E. For calculations, the angular measure may be converted to [[radian]]s, so longitude may also be expressed in this manner as a signed fraction of {{pi}} ([[pi]]), or an unsigned fraction of 2{{pi}}.
For calculations, the West/East suffix is replaced by a negative sign in the [[western hemisphere]]. The international standard convention ([[ISO 6709]])—that East is positive—is consistent with a right-handed [[Cartesian coordinate system]], with the North Pole up. A specific longitude may then be combined with a specific latitude (positive in the [[northern hemisphere]]) to give a precise position on the Earth's surface. Confusingly, the convention of negative for East is also sometimes seen, most commonly in the [[United States]]; the [[Earth System Research Laboratory]] used it on an older version of one of their pages, in order "to make coordinate entry less awkward" for applications confined to the [[Western Hemisphere]]. They have since shifted to the standard approach.<ref>[https://www.esrl.noaa.gov/gmd/grad/solcalc/sunrise.html NOAA ESRL Sunrise/Sunset Calculator] (deprecated). ''[[Earth System Research Laboratory]]''. Retrieved October 18, 2019.</ref>
There is no other physical principle determining longitude directly but with time. Longitude at a point may be determined by calculating the time difference between that at its location and [[Coordinated Universal Time]] (UTC). Since there are 24 hours in a day and 360 degrees in a circle, the sun moves across the sky at a rate of 15 degrees per hour (360° ÷ 24 hours = 15° per hour). So if the [[time zone]] a person is in is three hours ahead of UTC then that person is near 45° longitude (3 hours × 15° per hour = 45°). The word ''near'' is used because the point might not be at the center of the time zone; also the time zones are defined politically, so their centers and boundaries often do not lie on meridians at multiples of 15°. In order to perform this calculation, however, a person needs to have a [[marine chronometer|chronometer]] (watch) set to UTC and needs to determine local time by solar or astronomical observation. The details are more complex than described here: see the articles on [[Universal Time]] and on the [[equation of time]] for more details.
===Singularity and discontinuity of longitude===
Note that the longitude is [[mathematical singularity|singular]] at the [[Geographical pole|Poles]] and calculations that are sufficiently accurate for other positions may be inaccurate at or near the Poles. Also the [[Discontinuity (mathematics)|discontinuity]] at the ±[[180th meridian|180° meridian]] must be handled with care in calculations. An example is a calculation of east displacement by subtracting two longitudes, which gives the wrong answer if the two positions are on either side of this meridian. To avoid these complexities, consider replacing latitude and longitude with another [[horizontal position representation]] in calculation.
==Plate movement and longitude== <!-- http://en.wikipedia.org/enwiki/w/index.php?title=Wikipedia:Reference_desk/Science&oldid=231745680#Plate_movement_and_longitude -->
The Earth's [[plate tectonics|tectonic plates]] move relative to one another in different directions at speeds on the order of {{cvt|50 to 100|mm}} per year.<ref>{{cite book |author=Read HH, Watson Janet |title=Introduction to Geology |place=New York |publisher=Halsted |year=1975 |pages=13–15}}</ref> <!-- Adapted from http://en.wikipedia.org/enwiki/w/index.php?title=Plate_tectonics&oldid=226650343 --> So points on the Earth's surface on different plates are always in motion relative to one another. For example, the longitudinal difference between a point on the Equator in Uganda, on the [[African Plate]], and a point on the Equator in Ecuador, on the [[South American Plate]], is increasing by about 0.0014 [[Minute of arc#Symbols and abbreviations|arcseconds]] per year. These tectonic movements likewise affect latitude.
If a [[geodetic datum|global reference frame]] (such as [[WGS84]], for example) is used, the longitude of a place on the surface will change from year to year. To minimize this change, when dealing just with points on a single plate, a different reference frame can be used, whose coordinates are fixed to a particular plate, such as "[[NAD83]]" for North America or "[[ETRS89]]" for Europe.
==Length of a degree of longitude==
The length of a degree of longitude (east–west distance) depends only on the radius of a circle of latitude. For a sphere of radius {{mvar|a}} that radius at latitude {{mvar|φ}} is {{math|''a'' [[cosine|cos]] ''φ''}}, and the length of a one-degree (or {{sfrac|{{pi}}|180}} [[radian]]) arc along a circle of latitude is
:<math>\Delta^1_{\rm long}= \frac{\pi}{180^\circ}a \cos \phi </math>
{| class="wikitable" style="float: right; margin-left:1em; text-align:right;"
!{{mvar|φ}}||{{math|Δ{{su|p=1|b=lat}}}}||{{math|Δ{{su|p=1|b=long}}}}
|-
| 0° || 110.574 km || 111.320 km
|-
| 15° || 110.649 km || 107.551 km
|-
| 30° || 110.852 km || 96.486 km
|-
| 45° || 111.133 km || 78.847 km
|-
| 60° || 111.412 km || 55.800 km
|-
| 75° || 111.618 km || 28.902 km
|-
| 90° || 111.694 km || 0.000 km
|}
{{WGS84_angle_to_distance_conversion.svg}}
When the Earth is modelled by an [[ellipsoid]] this arc length becomes<ref name=osborne>{{Cite book |last=Osborne |first=Peter |year=2013 |url=http://www.mercator99.webspace.virginmedia.com/mercator.pdf |doi=10.5281/zenodo.35392 |title=The Mercator Projections: The Normal and Transverse Mercator Projections on the Sphere and the Ellipsoid with Full Derivations of all Formulae |chapter=Chapter 5: The geometry of the ellipsoid |location=Edinburgh |access-date=2016-01-24 |archive-url=https://web.archive.org/web/20160509180529/http://www.mercator99.webspace.virginmedia.com/mercator.pdf |archive-date=2016-05-09 |url-status=dead }}</ref><ref name=rapp>{{cite book |last=Rapp |first=Richard H. |date=April 1991 |title=Geometric Geodesy Part I |chapter=Chapter 3: Properties of the Ellipsoid |publisher=Department of Geodetic Science and Surveying, Ohio State University |location=Columbus, Ohio. |hdl=1811/24333 }}</ref>
:<math>\Delta^1_{\rm long}=\frac{\pi a\cos\phi}{180^\circ \sqrt{1 - e^2 \sin^2 \phi}}</math>
where {{mvar|e}}, the eccentricity of the ellipsoid, is related to the major and minor axes (the equatorial and polar radii respectively) by
:<math>e^2=\frac{a^2-b^2}{a^2}</math>
An alternative formula is
:<math>\Delta^1_{\rm long}= \frac{\pi}{180^\circ}a \cos \beta \quad \mbox{where }\tan \beta = \frac{b}{a} \tan \phi</math>; here <math>\beta</math> is the so-called [[Latitude#Parametric_(or_reduced)_latitude|<strong>parametric</strong> or <strong>reduced</strong> latitude]].
Cos {{mvar|φ}} decreases from 1 at the equator to 0 at the poles, which measures how circles of latitude shrink from the equator to a point at the pole, so the length of a degree of longitude decreases likewise. This contrasts with the small (1%) increase in the [[length of a degree of latitude]] (north–south distance), equator to pole. The table shows both for the [[WGS84]] ellipsoid with {{mvar|a}} = {{val|6378137.0|u=m}} and {{mvar|b}} = {{val|6356752.3142|u=m}}. Note that the distance between two points 1 degree apart on the same circle of latitude, measured along that circle of latitude, is slightly more than the shortest ([[geodesic]]) distance between those points (unless on the equator, where these are equal); the difference is less than {{convert|0.6|m|ft|0|abbr=on}}.
A [[geographical mile]] is defined to be the length of one [[minute of arc]] along the equator (one equatorial minute of longitude), therefore a degree of longitude along the equator is exactly 60 geographical miles or 111.3 kilometers, as there are 60 minutes in a degree. The length of 1 minute of longitude along the equator is 1 geographical mile or {{convert|1.855|km|mi|disp=or|abbr=in}}, while the length of 1 second of it is 0.016 geographical mile or {{convert|30.916|m|ft|disp=or|abbr=in}}.
==Longitude on bodies other than Earth{{anchor|Planets}}==<!-- This section is linked from [[Viking 2]] -->
{{see also|Prime meridian (planets)}}
{{More citations needed section|date=January 2020}}
[[Planet]]ary coordinate systems are defined relative to their mean [[axis of rotation]] and various definitions of longitude depending on the body. The longitude systems of most of those bodies with observable rigid surfaces have been defined by references to a surface feature such as a [[Impact crater|crater]]. The [[north pole]] is that pole of rotation that lies on the north side of the [[invariable plane]] of the solar system (near the [[ecliptic]]). The location of the prime meridian as well as the position of the body's north pole on the celestial sphere may vary with time due to precession of the axis of rotation of the planet (or satellite). If the position angle of the body's prime meridian increases with time, the body has a direct (or [[direct motion|prograde]]) rotation; otherwise the rotation is said to be [[retrograde motion|retrograde]].
In the absence of other information, the axis of rotation is assumed to be normal to the mean [[Orbital plane (astronomy)|orbital plane]]; [[Mercury (planet)|Mercury]] and most of the satellites are in this category. For many of the satellites, it is assumed that the rotation rate is equal to the mean [[orbital period]]. In the case of the [[gas giant|giant planets]], since their surface features are constantly changing and moving at various rates, the rotation of their [[magnetic field]]s is used as a reference instead. In the case of the [[Sun]], even this criterion fails (because its magnetosphere is very complex and does not really rotate in a steady fashion), and an agreed-upon value for the rotation of its equator is used instead.
For ''planetographic longitude'', west longitudes (i.e., longitudes measured positively to the west) are used when the rotation is prograde, and east longitudes (i.e., longitudes measured positively to the east) when the rotation is retrograde. In simpler terms, imagine a distant, non-orbiting observer viewing a planet as it rotates. Also suppose that this observer is within the plane of the planet's equator. A point on the Equator that passes directly in front of this observer later in time has a higher planetographic longitude than a point that did so earlier in time.
However, ''planetocentric longitude'' is always measured positively to the east, regardless of which way the planet rotates. ''East'' is defined as the counter-clockwise direction around the planet, as seen from above its north pole, and the north pole is whichever pole more closely aligns with the Earth's north pole. Longitudes traditionally have been written using "E" or "W" instead of "+" or "−" to indicate this polarity. For example, −91°, 91°W, +269° and 269°E all mean the same thing.
The reference surfaces for some planets (such as Earth and [[Mars]]) are [[ellipsoid]]s of revolution for which the equatorial radius is larger than the polar radius, such that they are [[oblate spheroid]]s. Smaller bodies ([[Io (moon)|Io]], [[Mimas (moon)|Mimas]], etc.) tend to be better approximated by [[triaxial ellipsoid]]s; however, triaxial ellipsoids would render many computations more complicated, especially those related to [[map projection]]s. Many projections would lose their elegant and popular properties. For this reason spherical reference surfaces are frequently used in mapping programs.
The modern standard for maps of Mars (since about 2002) is to use planetocentric coordinates. Guided by the works of historical astronomers, [[Merton E. Davies]] established the meridian of Mars at [[Airy-0]] crater.<ref>[http://www.esa.int/SPECIALS/Mars_Express/SEM0VQV4QWD_0.html Where is zero degrees longitude on Mars?] – Copyright 2000 – 2010 © European Space Agency. All rights reserved.</ref><ref>Davies, M. E., and R. A. Berg, "Preliminary Control Net of Mars,"Journal of Geophysical Research, Vol. 76, No. 2, pps. 373-393, January 10, 1971.</ref> For [[Mercury (planet)|Mercury]], the only other planet with a solid surface visible from Earth, a thermocentric coordinate is used: the prime meridian runs through the point on the equator where the planet is hottest (due to the planet's rotation and orbit, the sun briefly [[Apparent retrograde motion|retrogrades]] at noon at this point during [[perihelion]], giving it more sun). By convention, this meridian is defined as exactly twenty degrees of longitude east of [[Hun Kal (crater)|Hun Kal]].<ref>Davies, M. E., "Surface Coordinates and Cartography of Mercury," Journal of Geophysical Research, Vol. 80, No. 17, June 10, 1975.</ref><ref name="ArchinalA’Hearn2010">{{cite journal |last1=Archinal |first1=Brent A. |display-authors=4 |last2=A'Hearn |first2=Michael F. |last3=Bowell |first3=Edward L. |last4=Conrad |first4=Albert R. |last5=Consolmagno |first5=Guy J. |last6=Courtin |first6=Régis |last7=Fukushima |first7=Toshio |last8=Hestroffer |first8=Daniel |last9=Hilton |first9=James L. |last10=Krasinsky |first10=George A. |last11=Neumann |first11=Gregory A. |last12=Oberst |first12=Jürgen |last13=Seidelmann |first13=P. Kenneth |last14=Stooke |first14=Philip J. |last15=Tholen |first15=David J. |last16=Thomas |first16=Peter C. |last17=Williams |first17=Iwan P. |title=Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2009 |journal=Celestial Mechanics and Dynamical Astronomy |volume=109 |issue=2 |date=2010 |pages=101–135 |issn=0923-2958 |doi=10.1007/s10569-010-9320-4 |bibcode=2011CeMDA.109..101A}}</ref><ref name="usgs">{{cite web |url=https://astrogeology.usgs.gov/Projects/WGCCRE/constants/iau2000_table1.html |access-date=October 22, 2009 |title=USGS Astrogeology: Rotation and pole position for the Sun and planets (IAU WGCCRE) |archive-url=https://web.archive.org/web/20111024101856/http://astrogeology.usgs.gov/Projects/WGCCRE/constants/iau2000_table1.html |archive-date=October 24, 2011 |url-status=dead}}</ref>
[[Tidal lock|Tidally-locked]] bodies have a natural reference longitude passing through the point nearest to their parent body: 0° the center of the primary-facing hemisphere, 90° the center of the leading hemisphere, 180° the center of the anti-primary hemisphere, and 270° the center of the trailing hemisphere.<ref>[http://www.cfa.harvard.edu/image_archive/2007/31/lores.jpg First map of extraterrestrial planet] – Center of Astrophysics.</ref> However, [[libration]] due to non-circular orbits or axial tilts causes this point to move around any fixed point on the celestial body like an [[analemma]].
==See also==
{{div col|colwidth=20em}}
* [[American Practical Navigator]]
* [[Cardinal direction]]
* [[Ecliptic longitude]]
* [[Geodesy]]
* [[Geodetic system]]
* [[Geographic coordinate system]]
* [[Geographical distance]]
* [[Geotagging]]
* [[Great-circle distance]]
* [[History of longitude]]
* ''[[The Island of the Day Before]]''
* [[Latitude]]
* [[Meridian arc]]
* [[Natural Area Code]]
* [[Navigation]]
* [[Orders of magnitude (length)|Orders of magnitude]]
* [[Right ascension]] on [[celestial sphere]]
* [[World Geodetic System]]
{{div col end}}
==References==
{{reflist}}
==External links==
{{sisterlinks}}
* [http://jan.ucc.nau.edu/~cvm/latlon_find_location.html Resources for determining your latitude and longitude]
* [http://www.hnsky.org/iau-iag.htm IAU/IAG Working Group On Cartographic Coordinates and Rotational Elements of the Planets and Satellites]
* [http://entertainment.timesonline.co.uk/tol/arts_and_entertainment/the_tls/article5136819.ece "Longitude forged"]: an essay exposing a hoax solution to the problem of calculating longitude, undetected in Dava Sobel's Longitude, from [http://www.the-tls.co.uk TLS], November 12, 2008.
* [http://cudl.lib.cam.ac.uk/collections/longitude Board of Longitude Collection, Cambridge Digital Library] – complete digital version of the Board's archive
* [http://www.thegpscoordinates.com Longitude And Latitude Of Points of Interest]
* [http://www.csgnetwork.com/degreelenllavcalc.html Length Of A Degree Of Latitude And Longitude Calculator]
* [http://articles.adsabs.harvard.edu/full/seri/RA.../0002//0000185.000.html Esame critico intorno alla scoperta di Vespucci ...]
* [https://exhibits.museogalileo.it/waldseemuller/ewal.php?c%5B%5D=54117 A land beyond the stars - Museo Galileo]
{{Map projection}}
{{TimeSig}}
{{Time Topics}}
{{Time measurement and standards}}
{{Authority control}}
[[Category:Meridians (geography)|*]]
[[Category:Navigation]]
[[Category:Geodesy]]' |
New page wikitext, after the edit (new_wikitext) | '{{short description|geographic coordinate that specifies the east-west position of a point on the Earth hahaha dont care
[[File:Division of the Earth into Gauss-Krueger zones - Globe.svg|thumb|upright=0.9|right|A [[Geographic coordinate system|graticule]] on the [[Earth]] as a [[sphere]] or an [[ellipsoid]]. The lines from pole to pole are lines of constant longitude, or [[meridian (geography)|meridians]]. The circles parallel to the [[Equator]] are circles of constant [[latitude]], or [[circle of latitude|parallels]]. The graticule shows the latitude and longitude of pointsrface. In this example, meridians are spaced at 6° intervals and parallels at 4° intervals.]]
{{longlat}}{{Geodesy|notshowfig=1}}
'''Longitude''' ({{IPAc-en|ˈ|l|ɒ|n|dʒ|ᵻ|tj|uː|d}}, {{small|AU and UK also}} {{IPAc-en|ˈ|l|ɒ|ŋ|ɡ|ᵻ|-}}),<ref>{{cite web |url=http://www.merriam-webster.com/dictionary/longitude |title=Definition of LONGITUDE |website=www.merriam-webster.com'''Bold text''' It is an angular measurement, usually expressed in [[degree (angle)|degrees]] and denoted by the [[Greek alphabet|Greek letter]] [[lambda]] ([[Lal Bahadur Shastri]]λ). [[meridian (geography)|Meridians]] (lines running from [[geographical pole|pole]] to pole) connect points with the same longitude. The [[prime meridian]], which passes near the [[Royal Observatory, Greenwich]], England, is defined as 0° longitude by convention. Positive longitudes are east of the prime meridian, and negative ones are west.
Because of the earth's rotation, there is a close connection between longitude and time. Local time (for example from the position of the sun) varies with longitude, a difference of 15° longitude corresponding to a one-hour difference in local time. Comparing local time to an absolute measure of time allows longitude to be determined. Depending on the era, the absolute time might be obtained from a celestial event visible from both locations, such as a lunar eclipse, or from a time signal transmitted by telegraph or wireless. The principle is straightforward, but in practice finding a reliable method of determining longitude took centuries and required the effort of some of the greatest scientific minds.
A location's [[north]]–[[south]] position along a meridian is given by its [[latitude]], which is approximately the angle between the local vertical and the equatorial plane.
Longitude is generally given using the geometrical or astronomical vertical. This can differ slightly from the gravitational vertical because of [[vertical deflection|small variations in Earth's gravitational field]].
== History ==
{{Main|History of longitude}}
The concept of longitude was first developed by ancient Greek astronomers. [[Hipparchus]] (2nd century BCE) used a coordinate system that assumed a spherical earth, and divided it into 360° as we still do today. His [[prime meridian]] passed through [[Alexandria]].<ref name="Dicks">{{cite thesis |type=PhD|last1=Dicks |first1=D.R. |title=Hipparchus : a critical edition of the extant material for his life and works |date=1953 |publisher=Birkbeck College, University of London |url=https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.720566}}</ref>{{rp|31}} He also proposed a method of determining longitude by comparing the local time of a [[lunar eclipse]] at two different places, thus demonstrating an understanding of the relationship between longitude and time.{{r|Dicks|p=11}}.<ref>{{cite book |last1=Hoffman |first1=Susanne M. |title=The Science of Time |chapter=How time served to measure the geographical position since Hellenism|date=2016 |editor-last1=Arias |editor-first1=Elisa Felicitas |editor-last2=Combrinck |editor-first2=Ludwig |editor-last3=Gabor |editor-first3=Pavel |editor-last4=Hohenkerk |editor-first4=Catherine |editor-last5=Seidelmann |editor-first5=P.Kenneth |publisher=Springer International |series=Astrophysics and Space Science Proceedings|volume=50 |doi=10.1007/978-3-319-59909-0_4|pages=25–36|isbn=978-3-319-59908-3 }}</ref> [[Ptolemy|Claudius Ptolemy]] (2nd century CE) developed a mapping system using curved parallels that reduced distortion. He also collected data for many locations, from Britain to the Middle East. He used a prime meridian through the Canary Islands, so that all longitude values would be positive. While Ptolemy's system was sound, the data he used were often poor, leading to a gross over-estimate (by about 70%) of the length of the Mediterranean.<ref>{{cite book |last1=Mittenhuber |first1=Florian |title=Ptolemy in Perspective: Use and Criticism of his Work from Antiquity to the Nineteenth Century|url=https://archive.org/details/ptolemyperspecti00jone |url-access=limited |chapter=The Tradition of Texts and Maps in Ptolemy's Geography |series=Archimedes |date=2010 |volume=23 |editor-last1=Jones | editor-first1=Alexander |publisher=Springer |location=Dordrecht |pages=[https://archive.org/details/ptolemyperspecti00jone/page/n106 95]-119|doi=10.1007/978-90-481-2788-7_4|isbn=978-90-481-2787-0 }}</ref><ref name="Bunbury">{{cite book |last1=Bunbury |first1=E.H. |title=A History of Ancient Geography |volume=2|date=1879 |publisher=John Murray |location=London|url=https://archive.org/details/historyofancientgeographybunburye.h.vol21879_648_H}}</ref>{{rp|551-553}}<ref>{{cite journal |last1=Shcheglov |first1=Dmitry A. |s2cid=129864284 |title=The Error in Longitude in Ptolemy's Geography Revisited |journal=The Cartographic Journal |date=2016 |volume=53 |issue=1 |pages=3–14 |doi=10.1179/1743277414Y.0000000098}}</ref>
After the fall of the Roman Empire, interest in geography greatly declined in Europe.<ref name="Wright1925">{{cite book |last1=Wright |first1=John Kirtland |title=The geographical lore of the time of the Crusades: A study in the history of medieval science and tradition in Western Europe |date=1925 |publisher=American geographical society |location=New York |url=https://archive.org/details/geographicallore00wrig}}</ref>{{rp|65}} Hindu and Muslim astronomers continued to develop these ideas, adding many new locations and often improving on Ptolemy's data.<ref name="Ragep">{{cite book |last1=Ragep |first1=F.Jamil|editor-last=Jones|editor-first=A.|title=Ptolemy in Perspective |publisher=Springer |place=Dordrecht |date=2010 |chapter=Islamic reactions to Ptolemy's imprecisions |series=Archimedes|volume=23|isbn=978-90-481-2788-7 |doi=10.1007/978-90-481-2788-7}}</ref><ref name="Tibbett">{{cite book |last1=Tibbetts|first1=Gerald R.|editor1-last=Harley|editor1-first=J.B.|editor2-last=Woodward
|editor2-first=David |title=The History of Cartography Vol. 2 Cartography in the Traditional Islamic and South Asian Societies |publisher=University of Chicago Press |date=1992 |chapter=The Beginnings of a Cartographic Tradition |chapter-url=https://press.uchicago.edu/books/HOC/HOC_V2_B1/HOC_VOLUME2_Book1_chapter4.pdf }}</ref> For example [[Al-Battani|al-Battānī]] used simultaneous observations of two lunar eclipses to determine the difference in longitude between [[Antakya]] and [[Raqqa]] with an error of less than 1°. This is considered to be the best that can be achieved with the methods then available - observation of the eclipse with the naked eye, and determination of local time using an [[astrolabe]] to measure the altitude of a suitable "clock star".<ref name="Said2">{{cite journal |last1=Said |first1=S.S. |last2=Stevenson |first2=F.R. |s2cid=117100760 |title=Solar and Lunar Eclipse Measurements by Medieval Muslim Astronomers, II: Observations |journal=Journal for the History of Astronomy |date=1997 |volume=28 |issue=1 |pages=29–48 |doi=10.1177/002182869702800103|bibcode=1997JHA....28...29S }}</ref><ref name="Steele">{{cite thesis |type=PhD |last=Steele|first=John Michael |date=1998 |title=Observations and predictions of eclipse times by astronomers in the pre-telescopic period |publisher=University of Durham (United Kingdom)}}</ref>
In the later Middle Ages, interest in geography revived in the west, as travel increased, and Arab scholarship began to be known through contact with Spain and North Africa. In the 12th Century, astronomical tables were prepared for a number of European cities, based on the work of [[Abū Ishāq Ibrāhīm al-Zarqālī|al-Zarqālī]] in [[Toledo, Spain|Toledo]]. The lunar eclipse of September 12, 1178 was used to establish the longitude differences between Toledo, [[Marseille]]s, and [[Hereford]].<ref name="Wright1923">{{cite journal |last1=Wright |first1=John Kirtland |title=Notes on the Knowledge of Latitudes and Longitudes in the Middle Ages |journal=Isis |date=1923 |volume=5 |issue=1 |bibcode=1922nkll.book.....W |url=https://archive.org/details/wright-1923-isisacad-05acaduoft}}</ref>{{rp|85}}
Christopher Columbus made two attempts to use lunar eclipses to discover his longitude, the first in [[Saona Island]], on 14 September 1494 (second voyage), and the second in [[Jamaica]] on 29 February 1504 (fourth voyage). It is assumed that he used astronomical tables for reference. His determinations of longitude showed large errors of 13 and 38° W respectively.<ref name="Pickering">{{cite journal |last1=Pickering |first1=Keith |title=Columbus's Method of Determining Longitude: An Analytical View |journal=The Journal of Navigation |date=1996 |volume=49 |issue=1 |pages=96–111 |doi=10.1017/S037346330001314X|bibcode=1996JNav...49...95P }}</ref> Randles (1985) documents longitude measurement by the Portuguese and Spanish between 1514 and 1627 both in the Americas and Asia. Errors ranged from 2-25°.<ref name="Randles">{{cite journal |last1=Randles |first1=W.G.L. |title=Portuguese and Spanish attempts to measure longitude in the 16th century |journal=Vistas in Astronomy |date=1985 |volume=28 |issue=1 |pages=235–241|doi=10.1016/0083-6656(85)90031-5 |bibcode=1985VA.....28..235R }}</ref>
The telescope was invented in the early 17th-century. Initially an observation device, developments over the next half century transformed it into an accurate measurement tool.<ref name="Pannekoek">{{cite book |last1=Pannekoek |first1=Anton |title=A history of astronomy |date=1989 |publisher=Courier Corporation |pages=259–276 |url=https://archive.org/details/historyofastrono0000pann}}</ref><ref name="Van Helden">{{cite journal |last1=Van Helden |first1=Albert |title=The Telescope in the Seventeenth Century |journal=Isis |date=1974 |volume=65 |issue=1 |pages=38–58 |doi=10.1086/351216 |jstor=228880 }}</ref> The [[pendulum clock]] was patented by [[Christiaan Huygens]] in 1657<ref name="Grimbergen">{{cite conference |last1=Grimbergen |first1=Kees |title=Huygens and the advancement of time measurements |journal=Titan - from Discovery to Encounter |conference=Titan - From Discovery to Encounter |editor-last=Fletcher | editor-first=Karen |location=ESTEC, Noordwijk, Netherlands |date=2004 |volume=1278 |pages=91–102 |publisher=ESA Publications Division |bibcode=2004ESASP1278...91G |isbn=92-9092-997-9 }}</ref> and gave an increase in accuracy of about 30 fold over previous mechanical clocks.<ref>{{cite journal |last1=Blumenthal |first1=Aaron S. |last2=Nosonovsky |first2=Michael |title=Friction and Dynamics of Verge and Foliot: How the Invention of the Pendulum Made Clocks Much More Accurate |journal=Applied Mechanics |date=2020 |volume=1 |issue=2 |pages=111–122 |doi=10.3390/applmech1020008|doi-access=free }}</ref> These two inventions would revolutionize observational astronomy and cartography.<ref name="Olmsted">{{cite journal |last1=Olmsted |first1=J.W. |title=The Voyage of Jean Richer to Acadia in 1670: A Study in the Relations of Science and Navigation under Colbert |journal=Proceedings of the American Philosophical Society |date=1960 |volume=104 |issue=6 |pages=612–634 |jstor=985537 }}</ref>
The main methods for dermining longitude are listed below. With one exception (magnetic declination) they all depend on a common principle, which was to determine an absolute time from an event or measurement and to compare the corresponding local time at two different locations.
* [[Lunar distance (navigation)|Lunar distances]]. In its orbit around the earth, the moon moves relative to the stars at a rate of just over 0.5°/hour. The angle between the moon and a suitable star is measured with a [[sextant]], and (after consultation with tables and lengthy calculations) gives a value for absolute time.
*Satellites of Jupiter. [[Galileo Galilei|Galileo]] proposed that with sufficiently accurate knowledge of the orbits of the satellites, their positions could provide a measure of absolute time. The method requires a telescope, as the moons are not visible to the naked eye.
*Appulses, occultations, and eclipses. An [[appulse]] is the least apparent distance between two objects (the moon a star or a planet), an [[occultation]] occurs when a star or planet passes behind the moon — essentially a type of eclipse. Lunar eclipses continued to be used. The times of any of these events can be used as the measure of absolute time.
*[[Marine chronometer|Chronometers]]. A clock is set to the local time of a starting point whose longitude is known, and the longitude of any other place can be determined by comparing its local time with the clock time.
*Magnetic declination. A compass needle does not in general point exactly north. The [[Magnetic declination|variation]] from true north varies with location, and it was suggested that this could provide a basis for determination of longitude.
With the exception of magnetic declination, all proved practicable methods. Developments on land and sea, however, were very different.
On land, the period from the development of telescopes and pendulum clocks until the mid 18th-Century saw a steady increase in the number of places whose longitude had been determined with reasonable accuracy, often with errors of less than a degree, and nearly always within 2-3°. By the 1720s errors were consistently less than 1°.<ref>See, for example, Port Royal, Jamaica: {{cite journal |last1=Halley |first1=Edmond |title=Observations on the Eclipse of the Moon, June 18, 1722. and the Longitude of Port Royal in Jamaica |journal=Philosophical Transactions |date=1722 |volume=32 |issue=370–380 |pages=235–236 |url=https://archive.org/details/jstor-103607}}; Buenos Aires: {{cite journal |last1=Halley |first1=Edm. |title=The Longitude of Buenos Aires, Determin'd from an Observation Made There by Père Feuillée |journal=Philosophical Transactions |date=1722 |volume=32 |issue=370–380 |pages=2–4 |url=https://archive.org/details/jstor-103565}}Santa Catarina, Brazil: {{cite journal |last1=Legge |first1=Edward |last2=Atwell |first2=Joseph |title=Extract of a letter from the Honble Edward Legge, Esq; F. R. S. Captain of his Majesty's ship the Severn, containing an observation of the eclipse of the moon, Dec. 21. 1740. at the Island of St. Catharine on the Coast of Brasil |journal=Philosophical Transactions |date=1743 |volume=42 |issue=462 |pages=18–19 |url=https://archive.org/details/jstor-104132}}</ref> At sea during the same period, the situation was very different. Two problems proved intractable. The first was the need of a navigator for immediate results. The second was the marine environment. Making accurate observations in an ocean swell is much harder than on land, and pendulum clocks do not work well in these conditions.
In response to the problems of navigation, a number of European maritime powers offered prizes for a method to determine longitude at sea. The best-known of these is the [[Longitude Act]] passed by the British parliament in 1714.<ref name="Siegel">{{cite journal |last1=Siegel |first1=Jonathan R. |title=Law and Longitude |journal=Tulane Law Review |date=2009 |volume=84 |pages=1–66}}</ref>{{rp|8}} It offered two levels of rewards, for solutions within 1° and 0.5°. Rewards were given for two solutions: lunar distances, made practicable by the tables of [[Tobias Mayer]]<ref name="Forbes2006">{{cite journal |last1=Forbes |first1=Eric Gray |title=Tobias Mayer's lunar tables|journal=Annals of Science |volume=22 |issue=2 |year=2006 |pages=105–116 |issn=0003-3790|doi=10.1080/00033796600203075}}</ref> developed into an [[nautical almanac]] by the [[Astronomer Royal]] [[Neville Maskelyne]]; and for the chronometers developed by the Yorkshire carpenter and clock-maker [[John Harrison]]. Harrison built five chronometers over more than three decades. However, he was not awarded the prize by the Longitude Board and was forced to fight for his reward, finally receiving payment in 1773, after the intervention of parliament{{r|"Siegel"|p=26}}. It was some while before either method became widely used in navigation. In the early years, chronometers were very expensive, and the calculations required for lunar distances were still complex and time-consuming. Lunar distances came into general use after 1790.<ref name="Wess2015">{{cite book|title=Navigational Enterprises in Europe and its Empires, 1730-1850 |editor1-last=Dunn |editor1-first=Richard |editor2-last=Higgitt |editor2-first=Rebekah |last1=Wess|first1=Jane|chapter=Navigation and Mathematics: A Match Made in the Heavens?|year=2015|pages=201–222|publisher=Palgrave Macmillan UK |location=London |doi=10.1057/9781137520647_11|isbn=978-1-349-56744-7 }}</ref> Chronometers had the advantages that both the observations and the calculations were simpler, and as they became cheaper in the early 19th-Century they started to replace lunars, which were seldom used after 1850.<ref name="Littlehales">{{cite journal |last1=Littlehales |first1=G.W. |title=The Decline of the Lunar Distance for the Determination of the Time and Longitude at |journal=Bulletin of the American Geographical Society |date=1909 |volume=41 |issue=2 |pages=83–86 |doi=10.2307/200792 |jstor=200792 |url=https://archive.org/details/jstor-200792}}</ref>
The first working telegraphs were established in Britain by [[Charles Wheatstone|Wheatstone]] and [[William Fothergill Cooke|Cooke]] in 1839, and in the US by [[Samuel Morse|Morse]] in 1844. It was quickly realised that the telegraph could be used to transmit a time signal for longitude determination.<ref name="Walker 1850">{{cite journal |last1=Walker |first1=Sears C |title=Report on the experience of the Coast Survey in regard to telegraph operations, for determination of longitude &c. |journal=American Journal of Science and Arts |date=1850 |volume=10 |issue=28 |pages=151–160 |url=https://archive.org/details/appendix-telegraphic-longitude-the-american-journal-of-science-and-arts }}</ref> The method was soon in practical use for longitude determination, especially in North America, and over longer and longer distances as the telegraph network expanded, including western Europe with the completion of transatlantic cables. The [[U.S. National Geodetic Survey|US Coast Survey]] was particularly active in this development, and not just in the United States. The Survey established chains of mapped locations through Central and South America, and the West Indies, and as far as Japan and China in the years 1874–90. This contributed greatly to the accurate mapping of these areas.<ref name="Knox">{{cite journal |last1=Knox |first1=Robert W. |title=Precise Determination of Longitude in the United States |journal=Geographical Review |date=1957 |volume=47 |pages=555-563 |jstor=211865}}</ref><ref name="Green1883">{{cite book |last1=Green |first1=Francis Mathews |last2=Davis |first2=Charles Henry |last3=Norris |first3=John Alexander |title=Telegraphic Determination of Longitudes in Japan, China, and the East Indies: Embracing the Meridians of Yokohama, Nagasaki, Wladiwostok, Shanghai, Amoy, Hong-Kong, Manila, Cape St. James, Singapore, Batavia, and Madras, with the Latitude of the Several Stations |date=1883 |publisher=US Hydrographic Office |location=Washington |url=https://archive.org/details/in.ernet.dli.2015.177254}}</ref>
While mariners benefited from the accurate charts, they could not receive telegraph signals while under way, and so could not use the method for navigation. This changed when wireless telegraphy became available in the early 20th-Century.<ref name="Munro1902">{{cite journal|last1=Munro|first1=John|s2cid=4021629|title=Time-Signals by Wireless Telegraphy |journal=Nature |volume=66 |issue=1713 |year=1902 |pages=416 |issn=0028-0836 |doi=10.1038/066416d0 |bibcode=1902Natur..66..416M |url=https://zenodo.org/record/2080631}}</ref> Wireless time signals for the use of ships were transmitted from [[Halifax, Nova Scotia]], starting in 1907<ref name="Hutchnson">{{cite journal |last1=Hutchinson |first1=D.L. |title=Wireless Time Signals from the St. John Observatory of the Canadian Meteorological Service. |journal=Proceedings and Transactions of the Royal Society of Canada |date=1908 |volume=Ser. 3 Vol. 2 |pages=153–154 |url=https://archive.org/details/hutchinson-1908-proceedingstrans-32roya}}</ref> and from the [[Eiffel Tower]] in Paris from 1910.<ref name="Lockyer1913">{{cite journal|last1=Lockyer|first1=William J. S.|s2cid=3977506|title=International Time and Weather Radio-Telegraphic Signals |journal=Nature |volume=91 |issue=2263 |year=1913 |pages=33–36 |issn=0028-0836 |doi=10.1038/091033b0 |bibcode=1913Natur..91...33L |doi-access=free}}</ref> These signals allowed navigators to check and adjust their chronometers on a frequent basis.<ref name="Zimmerman">{{cite web |last1=Zimmerman |first1=Arthur E. |title=The first wireless time signals to ships at sea |url=https://www.antiquewireless.org/wp-content/uploads/50-the_first_wireless_time_signals_to_ships_at_sea.pdf |website=antiquewireless.org |publisher=Antique Wireless Association |access-date=9 July 2020}}</ref>
[[Radio navigation]] systems came into general use after [[World War II]]. The systems all depended on transmissions from fixed navigational beacons. A ship-board receiver calculated the vessel's position from these transmissions.<ref name="Pierce">{{cite journal |last1=Pierce |first1=J.A. |s2cid=20739091 |title=An introduction to Loran |journal=Proceedings of the IRE |date=1946 |volume=34 |issue=5 |pages=216–234 |doi=10.1109/JRPROC.1946.234564}}</ref> They allowed accurate navigation when poor visibility prevented astronomical observations, and became the established method for commercial shipping until replaced by [[Global Positioning System|GPS]] in the early 1990s.
==Noting and calculating longitude==
Longitude is given as an [[angle|angular measurement]] ranging from 0° at the Prime Meridian to +180° eastward and −180° westward. The Greek letter λ (lambda),<ref>{{cite web|url=http://www.colorado.edu/geography/gcraft/notes/datum/gif/llhxyz.gif|title=Coordinate Conversion|website=colorado.edu|access-date=14 March 2018|archive-url=https://web.archive.org/web/20090929121405/http://www.colorado.edu/geography/gcraft/notes/datum/gif/llhxyz.gif|archive-date=29 September 2009|url-status=dead}}</ref><ref>"λ = Longitude east of Greenwich (for longitude west of Greenwich, use a minus sign)."<br>John P. Snyder, ''[https://pubs.er.usgs.gov/usgspubs/pp/pp1395 Map Projections, A Working Manual]'', [[USGS]] Professional Paper 1395, page ix</ref> is used to denote the location of a place on Earth east or west of the Prime Meridian.
Each degree of longitude is sub-divided into 60 [[minute of arc|minutes]], each of which is divided into 60 [[arcsecond|seconds]]. A longitude is thus specified in [[sexagesimal]] notation as 23° 27′ 30″ E. For higher precision, the seconds are specified with a [[Decimal#Decimal fractions|decimal fraction]]. An alternative representation uses degrees and minutes, where parts of a minute are expressed in decimal notation with a fraction, thus: 23° 27.5′ E. Degrees may also be expressed as a decimal fraction: 23.45833° E. For calculations, the angular measure may be converted to [[radian]]s, so longitude may also be expressed in this manner as a signed fraction of {{pi}} ([[pi]]), or an unsigned fraction of 2{{pi}}.
For calculations, the West/East suffix is replaced by a negative sign in the [[western hemisphere]]. The international standard convention ([[ISO 6709]])—that East is positive—is consistent with a right-handed [[Cartesian coordinate system]], with the North Pole up. A specific longitude may then be combined with a specific latitude (positive in the [[northern hemisphere]]) to give a precise position on the Earth's surface. Confusingly, the convention of negative for East is also sometimes seen, most commonly in the [[United States]]; the [[Earth System Research Laboratory]] used it on an older version of one of their pages, in order "to make coordinate entry less awkward" for applications confined to the [[Western Hemisphere]]. They have since shifted to the standard approach.<ref>[https://www.esrl.noaa.gov/gmd/grad/solcalc/sunrise.html NOAA ESRL Sunrise/Sunset Calculator] (deprecated). ''[[Earth System Research Laboratory]]''. Retrieved October 18, 2019.</ref>
There is no other physical principle determining longitude directly but with time. Longitude at a point may be determined by calculating the time difference between that at its location and [[Coordinated Universal Time]] (UTC). Since there are 24 hours in a day and 360 degrees in a circle, the sun moves across the sky at a rate of 15 degrees per hour (360° ÷ 24 hours = 15° per hour). So if the [[time zone]] a person is in is three hours ahead of UTC then that person is near 45° longitude (3 hours × 15° per hour = 45°). The word ''near'' is used because the point might not be at the center of the time zone; also the time zones are defined politically, so their centers and boundaries often do not lie on meridians at multiples of 15°. In order to perform this calculation, however, a person needs to have a [[marine chronometer|chronometer]] (watch) set to UTC and needs to determine local time by solar or astronomical observation. The details are more complex than described here: see the articles on [[Universal Time]] and on the [[equation of time]] for more details.
===Singularity and discontinuity of longitude===
Note that the longitude is [[mathematical singularity|singular]] at the [[Geographical pole|Poles]] and calculations that are sufficiently accurate for other positions may be inaccurate at or near the Poles. Also the [[Discontinuity (mathematics)|discontinuity]] at the ±[[180th meridian|180° meridian]] must be handled with care in calculations. An example is a calculation of east displacement by subtracting two longitudes, which gives the wrong answer if the two positions are on either side of this meridian. To avoid these complexities, consider replacing latitude and longitude with another [[horizontal position representation]] in calculation.
==Plate movement and longitude== <!-- http://en.wikipedia.org/enwiki/w/index.php?title=Wikipedia:Reference_desk/Science&oldid=231745680#Plate_movement_and_longitude -->
The Earth's [[plate tectonics|tectonic plates]] move relative to one another in different directions at speeds on the order of {{cvt|50 to 100|mm}} per year.<ref>{{cite book |author=Read HH, Watson Janet |title=Introduction to Geology |place=New York |publisher=Halsted |year=1975 |pages=13–15}}</ref> <!-- Adapted from http://en.wikipedia.org/enwiki/w/index.php?title=Plate_tectonics&oldid=226650343 --> So points on the Earth's surface on different plates are always in motion relative to one another. For example, the longitudinal difference between a point on the Equator in Uganda, on the [[African Plate]], and a point on the Equator in Ecuador, on the [[South American Plate]], is increasing by about 0.0014 [[Minute of arc#Symbols and abbreviations|arcseconds]] per year. These tectonic movements likewise affect latitude.
If a [[geodetic datum|global reference frame]] (such as [[WGS84]], for example) is used, the longitude of a place on the surface will change from year to year. To minimize this change, when dealing just with points on a single plate, a different reference frame can be used, whose coordinates are fixed to a particular plate, such as "[[NAD83]]" for North America or "[[ETRS89]]" for Europe.
==Length of a degree of longitude==
The length of a degree of longitude (east–west distance) depends only on the radius of a circle of latitude. For a sphere of radius {{mvar|a}} that radius at latitude {{mvar|φ}} is {{math|''a'' [[cosine|cos]] ''φ''}}, and the length of a one-degree (or {{sfrac|{{pi}}|180}} [[radian]]) arc along a circle of latitude is
:<math>\Delta^1_{\rm long}= \frac{\pi}{180^\circ}a \cos \phi </math>
{| class="wikitable" style="float: right; margin-left:1em; text-align:right;"
!{{mvar|φ}}||{{math|Δ{{su|p=1|b=lat}}}}||{{math|Δ{{su|p=1|b=long}}}}
|-
| 0° || 110.574 km || 111.320 km
|-
| 15° || 110.649 km || 107.551 km
|-
| 30° || 110.852 km || 96.486 km
|-
| 45° || 111.133 km || 78.847 km
|-
| 60° || 111.412 km || 55.800 km
|-
| 75° || 111.618 km || 28.902 km
|-
| 90° || 111.694 km || 0.000 km
|}
{{WGS84_angle_to_distance_conversion.svg}}
When the Earth is modelled by an [[ellipsoid]] this arc length becomes<ref name=osborne>{{Cite book |last=Osborne |first=Peter |year=2013 |url=http://www.mercator99.webspace.virginmedia.com/mercator.pdf |doi=10.5281/zenodo.35392 |title=The Mercator Projections: The Normal and Transverse Mercator Projections on the Sphere and the Ellipsoid with Full Derivations of all Formulae |chapter=Chapter 5: The geometry of the ellipsoid |location=Edinburgh |access-date=2016-01-24 |archive-url=https://web.archive.org/web/20160509180529/http://www.mercator99.webspace.virginmedia.com/mercator.pdf |archive-date=2016-05-09 |url-status=dead }}</ref><ref name=rapp>{{cite book |last=Rapp |first=Richard H. |date=April 1991 |title=Geometric Geodesy Part I |chapter=Chapter 3: Properties of the Ellipsoid |publisher=Department of Geodetic Science and Surveying, Ohio State University |location=Columbus, Ohio. |hdl=1811/24333 }}</ref>
:<math>\Delta^1_{\rm long}=\frac{\pi a\cos\phi}{180^\circ \sqrt{1 - e^2 \sin^2 \phi}}</math>
where {{mvar|e}}, the eccentricity of the ellipsoid, is related to the major and minor axes (the equatorial and polar radii respectively) by
:<math>e^2=\frac{a^2-b^2}{a^2}</math>
An alternative formula is
:<math>\Delta^1_{\rm long}= \frac{\pi}{180^\circ}a \cos \beta \quad \mbox{where }\tan \beta = \frac{b}{a} \tan \phi</math>; here <math>\beta</math> is the so-called [[Latitude#Parametric_(or_reduced)_latitude|<strong>parametric</strong> or <strong>reduced</strong> latitude]].
Cos {{mvar|φ}} decreases from 1 at the equator to 0 at the poles, which measures how circles of latitude shrink from the equator to a point at the pole, so the length of a degree of longitude decreases likewise. This contrasts with the small (1%) increase in the [[length of a degree of latitude]] (north–south distance), equator to pole. The table shows both for the [[WGS84]] ellipsoid with {{mvar|a}} = {{val|6378137.0|u=m}} and {{mvar|b}} = {{val|6356752.3142|u=m}}. Note that the distance between two points 1 degree apart on the same circle of latitude, measured along that circle of latitude, is slightly more than the shortest ([[geodesic]]) distance between those points (unless on the equator, where these are equal); the difference is less than {{convert|0.6|m|ft|0|abbr=on}}.
A [[geographical mile]] is defined to be the length of one [[minute of arc]] along the equator (one equatorial minute of longitude), therefore a degree of longitude along the equator is exactly 60 geographical miles or 111.3 kilometers, as there are 60 minutes in a degree. The length of 1 minute of longitude along the equator is 1 geographical mile or {{convert|1.855|km|mi|disp=or|abbr=in}}, while the length of 1 second of it is 0.016 geographical mile or {{convert|30.916|m|ft|disp=or|abbr=in}}.
==Longitude on bodies other than Earth{{anchor|Planets}}==<!-- This section is linked from [[Viking 2]] -->
{{see also|Prime meridian (planets)}}
{{More citations needed section|date=January 2020}}
[[Planet]]ary coordinate systems are defined relative to their mean [[axis of rotation]] and various definitions of longitude depending on the body. The longitude systems of most of those bodies with observable rigid surfaces have been defined by references to a surface feature such as a [[Impact crater|crater]]. The [[north pole]] is that pole of rotation that lies on the north side of the [[invariable plane]] of the solar system (near the [[ecliptic]]). The location of the prime meridian as well as the position of the body's north pole on the celestial sphere may vary with time due to precession of the axis of rotation of the planet (or satellite). If the position angle of the body's prime meridian increases with time, the body has a direct (or [[direct motion|prograde]]) rotation; otherwise the rotation is said to be [[retrograde motion|retrograde]].
In the absence of other information, the axis of rotation is assumed to be normal to the mean [[Orbital plane (astronomy)|orbital plane]]; [[Mercury (planet)|Mercury]] and most of the satellites are in this category. For many of the satellites, it is assumed that the rotation rate is equal to the mean [[orbital period]]. In the case of the [[gas giant|giant planets]], since their surface features are constantly changing and moving at various rates, the rotation of their [[magnetic field]]s is used as a reference instead. In the case of the [[Sun]], even this criterion fails (because its magnetosphere is very complex and does not really rotate in a steady fashion), and an agreed-upon value for the rotation of its equator is used instead.
For ''planetographic longitude'', west longitudes (i.e., longitudes measured positively to the west) are used when the rotation is prograde, and east longitudes (i.e., longitudes measured positively to the east) when the rotation is retrograde. In simpler terms, imagine a distant, non-orbiting observer viewing a planet as it rotates. Also suppose that this observer is within the plane of the planet's equator. A point on the Equator that passes directly in front of this observer later in time has a higher planetographic longitude than a point that did so earlier in time.
However, ''planetocentric longitude'' is always measured positively to the east, regardless of which way the planet rotates. ''East'' is defined as the counter-clockwise direction around the planet, as seen from above its north pole, and the north pole is whichever pole more closely aligns with the Earth's north pole. Longitudes traditionally have been written using "E" or "W" instead of "+" or "−" to indicate this polarity. For example, −91°, 91°W, +269° and 269°E all mean the same thing.
The reference surfaces for some planets (such as Earth and [[Mars]]) are [[ellipsoid]]s of revolution for which the equatorial radius is larger than the polar radius, such that they are [[oblate spheroid]]s. Smaller bodies ([[Io (moon)|Io]], [[Mimas (moon)|Mimas]], etc.) tend to be better approximated by [[triaxial ellipsoid]]s; however, triaxial ellipsoids would render many computations more complicated, especially those related to [[map projection]]s. Many projections would lose their elegant and popular properties. For this reason spherical reference surfaces are frequently used in mapping programs.
The modern standard for maps of Mars (since about 2002) is to use planetocentric coordinates. Guided by the works of historical astronomers, [[Merton E. Davies]] established the meridian of Mars at [[Airy-0]] crater.<ref>[http://www.esa.int/SPECIALS/Mars_Express/SEM0VQV4QWD_0.html Where is zero degrees longitude on Mars?] – Copyright 2000 – 2010 © European Space Agency. All rights reserved.</ref><ref>Davies, M. E., and R. A. Berg, "Preliminary Control Net of Mars,"Journal of Geophysical Research, Vol. 76, No. 2, pps. 373-393, January 10, 1971.</ref> For [[Mercury (planet)|Mercury]], the only other planet with a solid surface visible from Earth, a thermocentric coordinate is used: the prime meridian runs through the point on the equator where the planet is hottest (due to the planet's rotation and orbit, the sun briefly [[Apparent retrograde motion|retrogrades]] at noon at this point during [[perihelion]], giving it more sun). By convention, this meridian is defined as exactly twenty degrees of longitude east of [[Hun Kal (crater)|Hun Kal]].<ref>Davies, M. E., "Surface Coordinates and Cartography of Mercury," Journal of Geophysical Research, Vol. 80, No. 17, June 10, 1975.</ref><ref name="ArchinalA’Hearn2010">{{cite journal |last1=Archinal |first1=Brent A. |display-authors=4 |last2=A'Hearn |first2=Michael F. |last3=Bowell |first3=Edward L. |last4=Conrad |first4=Albert R. |last5=Consolmagno |first5=Guy J. |last6=Courtin |first6=Régis |last7=Fukushima |first7=Toshio |last8=Hestroffer |first8=Daniel |last9=Hilton |first9=James L. |last10=Krasinsky |first10=George A. |last11=Neumann |first11=Gregory A. |last12=Oberst |first12=Jürgen |last13=Seidelmann |first13=P. Kenneth |last14=Stooke |first14=Philip J. |last15=Tholen |first15=David J. |last16=Thomas |first16=Peter C. |last17=Williams |first17=Iwan P. |title=Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2009 |journal=Celestial Mechanics and Dynamical Astronomy |volume=109 |issue=2 |date=2010 |pages=101–135 |issn=0923-2958 |doi=10.1007/s10569-010-9320-4 |bibcode=2011CeMDA.109..101A}}</ref><ref name="usgs">{{cite web |url=https://astrogeology.usgs.gov/Projects/WGCCRE/constants/iau2000_table1.html |access-date=October 22, 2009 |title=USGS Astrogeology: Rotation and pole position for the Sun and planets (IAU WGCCRE) |archive-url=https://web.archive.org/web/20111024101856/http://astrogeology.usgs.gov/Projects/WGCCRE/constants/iau2000_table1.html |archive-date=October 24, 2011 |url-status=dead}}</ref>
[[Tidal lock|Tidally-locked]] bodies have a natural reference longitude passing through the point nearest to their parent body: 0° the center of the primary-facing hemisphere, 90° the center of the leading hemisphere, 180° the center of the anti-primary hemisphere, and 270° the center of the trailing hemisphere.<ref>[http://www.cfa.harvard.edu/image_archive/2007/31/lores.jpg First map of extraterrestrial planet] – Center of Astrophysics.</ref> However, [[libration]] due to non-circular orbits or axial tilts causes this point to move around any fixed point on the celestial body like an [[analemma]].
==See also==
{{div col|colwidth=20em}}
* [[American Practical Navigator]]
* [[Cardinal direction]]
* [[Ecliptic longitude]]
* [[Geodesy]]
* [[Geodetic system]]
* [[Geographic coordinate system]]
* [[Geographical distance]]
* [[Geotagging]]
* [[Great-circle distance]]
* [[History of longitude]]
* ''[[The Island of the Day Before]]''
* [[Latitude]]
* [[Meridian arc]]
* [[Natural Area Code]]
* [[Navigation]]
* [[Orders of magnitude (length)|Orders of magnitude]]
* [[Right ascension]] on [[celestial sphere]]
* [[World Geodetic System]]
{{div col end}}
==References==
{{reflist}}
==External links==
{{sisterlinks}}
* [http://jan.ucc.nau.edu/~cvm/latlon_find_location.html Resources for determining your latitude and longitude]
* [http://www.hnsky.org/iau-iag.htm IAU/IAG Working Group On Cartographic Coordinates and Rotational Elements of the Planets and Satellites]
* [http://entertainment.timesonline.co.uk/tol/arts_and_entertainment/the_tls/article5136819.ece "Longitude forged"]: an essay exposing a hoax solution to the problem of calculating longitude, undetected in Dava Sobel's Longitude, from [http://www.the-tls.co.uk TLS], November 12, 2008.
* [http://cudl.lib.cam.ac.uk/collections/longitude Board of Longitude Collection, Cambridge Digital Library] – complete digital version of the Board's archive
* [http://www.thegpscoordinates.com Longitude And Latitude Of Points of Interest]
* [http://www.csgnetwork.com/degreelenllavcalc.html Length Of A Degree Of Latitude And Longitude Calculator]
* [http://articles.adsabs.harvard.edu/full/seri/RA.../0002//0000185.000.html Esame critico intorno alla scoperta di Vespucci ...]
* [https://exhibits.museogalileo.it/waldseemuller/ewal.php?c%5B%5D=54117 A land beyond the stars - Museo Galileo]
{{Map projection}}
{{TimeSig}}
{{Time Topics}}
{{Time measurement and standards}}
{{Authority control}}
[[Category:Meridians (geography)|*]]
[[Category:Navigation]]
[[Category:Geodesy]]' |
Unified diff of changes made by edit (edit_diff) | '@@ -1,8 +1,7 @@
-{{short description|geographic coordinate that specifies the east-west position of a point on the Earth's surface}}
-{{about||Dava Sobel's book about John Harrison|Longitude (book)|the adaptation of Sobel's book| Longitude (TV series)|other uses|Longitude (disambiguation)}}
-[[File:Division of the Earth into Gauss-Krueger zones - Globe.svg|thumb|upright=0.9|right|A [[Geographic coordinate system|graticule]] on the [[Earth]] as a [[sphere]] or an [[ellipsoid]]. The lines from pole to pole are lines of constant longitude, or [[meridian (geography)|meridians]]. The circles parallel to the [[Equator]] are circles of constant [[latitude]], or [[circle of latitude|parallels]]. The graticule shows the latitude and longitude of points on the surface. In this example, meridians are spaced at 6° intervals and parallels at 4° intervals.]]
+{{short description|geographic coordinate that specifies the east-west position of a point on the Earth hahaha dont care
+[[File:Division of the Earth into Gauss-Krueger zones - Globe.svg|thumb|upright=0.9|right|A [[Geographic coordinate system|graticule]] on the [[Earth]] as a [[sphere]] or an [[ellipsoid]]. The lines from pole to pole are lines of constant longitude, or [[meridian (geography)|meridians]]. The circles parallel to the [[Equator]] are circles of constant [[latitude]], or [[circle of latitude|parallels]]. The graticule shows the latitude and longitude of pointsrface. In this example, meridians are spaced at 6° intervals and parallels at 4° intervals.]]
{{longlat}}{{Geodesy|notshowfig=1}}
-'''Longitude''' ({{IPAc-en|ˈ|l|ɒ|n|dʒ|ᵻ|tj|uː|d}}, {{small|AU and UK also}} {{IPAc-en|ˈ|l|ɒ|ŋ|ɡ|ᵻ|-}}),<ref>{{cite web |url=http://www.merriam-webster.com/dictionary/longitude |title=Definition of LONGITUDE |website=www.merriam-webster.com |publisher=[[Merriam-Webster]] |access-date=14 March 2018}}</ref><ref>[[Oxford English Dictionary]]</ref> is a [[geographic coordinate system|geographic coordinate]] that specifies the [[east]]–[[west]] position of a point on the [[Earth]]'s surface, or the surface of a celestial body. It is an angular measurement, usually expressed in [[degree (angle)|degrees]] and denoted by the [[Greek alphabet|Greek letter]] [[lambda]] (λ). [[meridian (geography)|Meridians]] (lines running from [[geographical pole|pole]] to pole) connect points with the same longitude. The [[prime meridian]], which passes near the [[Royal Observatory, Greenwich]], England, is defined as 0° longitude by convention. Positive longitudes are east of the prime meridian, and negative ones are west.
+'''Longitude''' ({{IPAc-en|ˈ|l|ɒ|n|dʒ|ᵻ|tj|uː|d}}, {{small|AU and UK also}} {{IPAc-en|ˈ|l|ɒ|ŋ|ɡ|ᵻ|-}}),<ref>{{cite web |url=http://www.merriam-webster.com/dictionary/longitude |title=Definition of LONGITUDE |website=www.merriam-webster.com'''Bold text''' It is an angular measurement, usually expressed in [[degree (angle)|degrees]] and denoted by the [[Greek alphabet|Greek letter]] [[lambda]] ([[Lal Bahadur Shastri]]λ). [[meridian (geography)|Meridians]] (lines running from [[geographical pole|pole]] to pole) connect points with the same longitude. The [[prime meridian]], which passes near the [[Royal Observatory, Greenwich]], England, is defined as 0° longitude by convention. Positive longitudes are east of the prime meridian, and negative ones are west.
Because of the earth's rotation, there is a close connection between longitude and time. Local time (for example from the position of the sun) varies with longitude, a difference of 15° longitude corresponding to a one-hour difference in local time. Comparing local time to an absolute measure of time allows longitude to be determined. Depending on the era, the absolute time might be obtained from a celestial event visible from both locations, such as a lunar eclipse, or from a time signal transmitted by telegraph or wireless. The principle is straightforward, but in practice finding a reliable method of determining longitude took centuries and required the effort of some of the greatest scientific minds.
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1 => '[[File:Division of the Earth into Gauss-Krueger zones - Globe.svg|thumb|upright=0.9|right|A [[Geographic coordinate system|graticule]] on the [[Earth]] as a [[sphere]] or an [[ellipsoid]]. The lines from pole to pole are lines of constant longitude, or [[meridian (geography)|meridians]]. The circles parallel to the [[Equator]] are circles of constant [[latitude]], or [[circle of latitude|parallels]]. The graticule shows the latitude and longitude of pointsrface. In this example, meridians are spaced at 6° intervals and parallels at 4° intervals.]]',
2 => ''''Longitude''' ({{IPAc-en|ˈ|l|ɒ|n|dʒ|ᵻ|tj|uː|d}}, {{small|AU and UK also}} {{IPAc-en|ˈ|l|ɒ|ŋ|ɡ|ᵻ|-}}),<ref>{{cite web |url=http://www.merriam-webster.com/dictionary/longitude |title=Definition of LONGITUDE |website=www.merriam-webster.com'''Bold text''' It is an angular measurement, usually expressed in [[degree (angle)|degrees]] and denoted by the [[Greek alphabet|Greek letter]] [[lambda]] ([[Lal Bahadur Shastri]]λ). [[meridian (geography)|Meridians]] (lines running from [[geographical pole|pole]] to pole) connect points with the same longitude. The [[prime meridian]], which passes near the [[Royal Observatory, Greenwich]], England, is defined as 0° longitude by convention. Positive longitudes are east of the prime meridian, and negative ones are west.'
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1 => '{{about||Dava Sobel's book about John Harrison|Longitude (book)|the adaptation of Sobel's book| Longitude (TV series)|other uses|Longitude (disambiguation)}}',
2 => '[[File:Division of the Earth into Gauss-Krueger zones - Globe.svg|thumb|upright=0.9|right|A [[Geographic coordinate system|graticule]] on the [[Earth]] as a [[sphere]] or an [[ellipsoid]]. The lines from pole to pole are lines of constant longitude, or [[meridian (geography)|meridians]]. The circles parallel to the [[Equator]] are circles of constant [[latitude]], or [[circle of latitude|parallels]]. The graticule shows the latitude and longitude of points on the surface. In this example, meridians are spaced at 6° intervals and parallels at 4° intervals.]]',
3 => ''''Longitude''' ({{IPAc-en|ˈ|l|ɒ|n|dʒ|ᵻ|tj|uː|d}}, {{small|AU and UK also}} {{IPAc-en|ˈ|l|ɒ|ŋ|ɡ|ᵻ|-}}),<ref>{{cite web |url=http://www.merriam-webster.com/dictionary/longitude |title=Definition of LONGITUDE |website=www.merriam-webster.com |publisher=[[Merriam-Webster]] |access-date=14 March 2018}}</ref><ref>[[Oxford English Dictionary]]</ref> is a [[geographic coordinate system|geographic coordinate]] that specifies the [[east]]–[[west]] position of a point on the [[Earth]]'s surface, or the surface of a celestial body. It is an angular measurement, usually expressed in [[degree (angle)|degrees]] and denoted by the [[Greek alphabet|Greek letter]] [[lambda]] (λ). [[meridian (geography)|Meridians]] (lines running from [[geographical pole|pole]] to pole) connect points with the same longitude. The [[prime meridian]], which passes near the [[Royal Observatory, Greenwich]], England, is defined as 0° longitude by convention. Positive longitudes are east of the prime meridian, and negative ones are west.'
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Parsed HTML source of the new revision (new_html) | '<div class="mw-parser-output"><p>{{short description|geographic coordinate that specifies the east-west position of a point on the Earth hahaha dont care
</p>
<div class="thumb tright"><div class="thumbinner" style="width:202px;"><a href="/enwiki/wiki/File:Division_of_the_Earth_into_Gauss-Krueger_zones_-_Globe.svg" class="image"><img alt="" src="/upwiki/wikipedia/commons/thumb/4/44/Division_of_the_Earth_into_Gauss-Krueger_zones_-_Globe.svg/200px-Division_of_the_Earth_into_Gauss-Krueger_zones_-_Globe.svg.png" decoding="async" width="200" height="200" class="thumbimage" srcset="/upwiki/wikipedia/commons/thumb/4/44/Division_of_the_Earth_into_Gauss-Krueger_zones_-_Globe.svg/300px-Division_of_the_Earth_into_Gauss-Krueger_zones_-_Globe.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/4/44/Division_of_the_Earth_into_Gauss-Krueger_zones_-_Globe.svg/400px-Division_of_the_Earth_into_Gauss-Krueger_zones_-_Globe.svg.png 2x" data-file-width="948" data-file-height="948" /></a> <div class="thumbcaption"><div class="magnify"><a href="/enwiki/wiki/File:Division_of_the_Earth_into_Gauss-Krueger_zones_-_Globe.svg" class="internal" title="Enlarge"></a></div>A <a href="/enwiki/wiki/Geographic_coordinate_system" title="Geographic coordinate system">graticule</a> on the <a href="/enwiki/wiki/Earth" title="Earth">Earth</a> as a <a href="/enwiki/wiki/Sphere" title="Sphere">sphere</a> or an <a href="/enwiki/wiki/Ellipsoid" title="Ellipsoid">ellipsoid</a>. The lines from pole to pole are lines of constant longitude, or <a href="/enwiki/wiki/Meridian_(geography)" title="Meridian (geography)">meridians</a>. The circles parallel to the <a href="/enwiki/wiki/Equator" title="Equator">Equator</a> are circles of constant <a href="/enwiki/wiki/Latitude" title="Latitude">latitude</a>, or <a href="/enwiki/wiki/Circle_of_latitude" title="Circle of latitude">parallels</a>. The graticule shows the latitude and longitude of pointsrface. In this example, meridians are spaced at 6° intervals and parallels at 4° intervals.</div></div></div>
<table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f8f9fa;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%"><tbody><tr><td style="padding:0.2em 0 0.4em"><a href="/enwiki/wiki/Geodesy" title="Geodesy"><img alt="World map longlat.svg" src="/upwiki/wikipedia/commons/thumb/5/56/World_map_longlat.svg/275px-World_map_longlat.svg.png" decoding="async" width="275" height="157" srcset="/upwiki/wikipedia/commons/thumb/5/56/World_map_longlat.svg/413px-World_map_longlat.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/5/56/World_map_longlat.svg/550px-World_map_longlat.svg.png 2x" data-file-width="1200" data-file-height="684" /></a><div style="padding-top:0.2em;line-height:1.2em"><a href="/enwiki/wiki/Map" title="Map">Map</a> of <a href="/enwiki/wiki/Earth" title="Earth">Earth</a></div></td></tr><tr><th style="padding:0.1em;background:#bbffee; text-align:left;">
<a class="mw-selflink selflink">Longitude</a> (λ)</th></tr><tr><td style="padding:0 0.1em 0.4em;text-align:left;">
Lines of longitude appear <a href="/enwiki/wiki/Vertical_direction" class="mw-redirect" title="Vertical direction">vertical</a> with varying curvature in this projection, but are actually halves of great ellipses, with identical radii at a given latitude.</td>
</tr><tr><th style="padding:0.1em;background:#bbffee; text-align:left;">
<a href="/enwiki/wiki/Latitude" title="Latitude">Latitude</a> (φ)</th></tr><tr><td style="padding:0 0.1em 0.4em;text-align:left;">
Lines of latitude appear <a href="/enwiki/wiki/Horizontal_plane" class="mw-redirect" title="Horizontal plane">horizontal</a> with varying curvature in this projection; but are actually circular with different radii. All locations with a given latitude are collectively referred to as a <a href="/enwiki/wiki/Circle_of_latitude" title="Circle of latitude">circle of latitude</a>.</td>
</tr><tr><td style="padding:0 0.1em 0.4em;text-align:left;;padding-bottom:0;">
<div class="floatright"><a href="/enwiki/wiki/File:World_map_with_equator.svg" class="image"><img alt="World map with equator.svg" src="/upwiki/wikipedia/commons/thumb/e/e5/World_map_with_equator.svg/80px-World_map_with_equator.svg.png" decoding="async" width="80" height="40" srcset="/upwiki/wikipedia/commons/thumb/e/e5/World_map_with_equator.svg/120px-World_map_with_equator.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/e/e5/World_map_with_equator.svg/160px-World_map_with_equator.svg.png 2x" data-file-width="1300" data-file-height="651" /></a></div> The <b><a href="/enwiki/wiki/Equator" title="Equator">equator</a></b> divides the planet into a <a href="/enwiki/wiki/Northern_Hemisphere" title="Northern Hemisphere">Northern Hemisphere</a> and a <a href="/enwiki/wiki/Southern_Hemisphere" title="Southern Hemisphere">Southern Hemisphere</a>, and has a latitude of 0°.</td>
</tr><tr><td style="text-align:right;font-size:115%;padding-top:0;"><style data-mw-deduplicate="TemplateStyles:r992953826">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}.mw-parser-output .infobox .navbar{font-size:100%}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/enwiki/wiki/Template:Longlat" title="Template:Longlat"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/enwiki/wiki/Template_talk:Longlat" title="Template talk:Longlat"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a class="external text" href="https://en.wikipedia.org/enwiki/w/index.php?title=Template:Longlat&action=edit"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table><table class="vertical-navbox nowraplinks" style="float:right;clear:right;width:22.0em;margin:0 0 1.0em 1.0em;background:#f8f9fa;border:1px solid #aaa;padding:0.2em;border-spacing:0.4em 0;text-align:center;line-height:1.4em;font-size:88%"><tbody><tr><th style="padding:0.2em 0.4em 0.2em;font-size:145%;line-height:1.2em;padding-bottom:0.4em;"><a href="/enwiki/wiki/Geodesy" title="Geodesy">Geodesy</a></th></tr><tr><td style="padding:0.2em 0 0.4em"><a href="/enwiki/wiki/File:Azimutalprojektion-schief_kl-cropped.png" class="image"><img alt="Azimutalprojektion-schief kl-cropped.png" src="/upwiki/wikipedia/commons/thumb/4/4c/Azimutalprojektion-schief_kl-cropped.png/120px-Azimutalprojektion-schief_kl-cropped.png" decoding="async" width="120" height="119" srcset="/upwiki/wikipedia/commons/thumb/4/4c/Azimutalprojektion-schief_kl-cropped.png/180px-Azimutalprojektion-schief_kl-cropped.png 1.5x, /upwiki/wikipedia/commons/thumb/4/4c/Azimutalprojektion-schief_kl-cropped.png/240px-Azimutalprojektion-schief_kl-cropped.png 2x" data-file-width="242" data-file-height="240" /></a></td></tr><tr><td style="padding:0 0.1em 0.4em;padding-top:0.2em;padding-bottom:0.7em;">
<div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left">Fundamentals</div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center">
<ul><li><a href="/enwiki/wiki/Geodesy" title="Geodesy">Geodesy</a></li>
<li><a href="/enwiki/wiki/Geodynamics" title="Geodynamics">Geodynamics</a></li>
<li><a href="/enwiki/wiki/Geomatics" title="Geomatics">Geomatics</a></li>
<li><a href="/enwiki/wiki/History_of_geodesy" title="History of geodesy">History</a></li></ul></div></div></td>
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<div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left">Concepts</div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center">
<ul><li><a href="/enwiki/wiki/Geographical_distance" title="Geographical distance">Geographical distance</a></li>
<li><a href="/enwiki/wiki/Geoid" title="Geoid">Geoid</a></li>
<li><a href="/enwiki/wiki/Figure_of_the_Earth" title="Figure of the Earth">Figure of the Earth</a> <small>(<a href="/enwiki/wiki/Earth_radius" title="Earth radius">Earth radius</a> and <a href="/enwiki/wiki/Earth%27s_circumference" title="Earth's circumference">Earth's circumference</a>)</small></li>
<li><a href="/enwiki/wiki/Geodetic_datum" title="Geodetic datum">Geodetic datum</a></li>
<li><a href="/enwiki/wiki/Geodesic" title="Geodesic">Geodesic</a></li>
<li><a href="/enwiki/wiki/Geographic_coordinate_system" title="Geographic coordinate system">Geographic coordinate system</a></li>
<li><a href="/enwiki/wiki/Horizontal_position_representation" title="Horizontal position representation">Horizontal position representation</a></li>
<li><span class="nowrap"><a href="/enwiki/wiki/Latitude" title="Latitude">Latitude</a> / <a class="mw-selflink selflink">Longitude</a></span></li>
<li><a href="/enwiki/wiki/Map_projection" title="Map projection">Map projection</a></li>
<li><a href="/enwiki/wiki/Reference_ellipsoid" title="Reference ellipsoid">Reference ellipsoid</a></li>
<li><a href="/enwiki/wiki/Satellite_geodesy" title="Satellite geodesy">Satellite geodesy</a></li>
<li><a href="/enwiki/wiki/Spatial_reference_system" title="Spatial reference system">Spatial reference system</a></li>
<li><a href="/enwiki/wiki/Spatial_relation" title="Spatial relation">Spatial relations</a></li></ul></div></div></td>
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<div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left">Technologies</div><div class="NavContent hlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center">
<ul><li><a href="/enwiki/wiki/Satellite_navigation" title="Satellite navigation">Global Nav. Sat. Systems (GNSSs)</a></li>
<li><a href="/enwiki/wiki/Global_Positioning_System" title="Global Positioning System">Global Pos. System (GPS)</a></li>
<li><a href="/enwiki/wiki/GLONASS" title="GLONASS">GLONASS <span style="font-size:90%;">(Russia)</span></a></li>
<li><a href="/enwiki/wiki/BeiDou" title="BeiDou">BeiDou (BDS) <span style="font-size:90%;">(China)</span></a></li>
<li><a href="/enwiki/wiki/Galileo_(satellite_navigation)" title="Galileo (satellite navigation)">Galileo <span style="font-size:90%;">(Europe)</span></a></li>
<li><a href="/enwiki/wiki/Indian_Regional_Navigation_Satellite_System" title="Indian Regional Navigation Satellite System">NAVIC <span style="font-size:90%;">(India)</span></a></li>
<li><a href="/enwiki/wiki/Quasi-Zenith_Satellite_System" title="Quasi-Zenith Satellite System">Quasi-Zenith Sat. Sys. (QZSS) <span style="font-size:90%;">(Japan)</span></a></li>
<li><a href="/enwiki/wiki/Discrete_Global_Grid" class="mw-redirect" title="Discrete Global Grid">Discrete Global Grid and Geocoding</a></li></ul></div></div></td>
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<div class="NavFrame collapsed" style="border:none;padding:0"><div class="NavHead" style="font-size:105%;background:transparent;text-align:left">Standards (history)</div><div class="NavContent hlist plainlist" style="font-size:105%;padding:0.2em 0 0.4em;text-align:center"><table class="nowrap" style="width:100%;border-collapse:collapse;border-spacing:0px 0px;border:none;line-height:1.2em;"><tbody><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/enwiki/wiki/Sea_Level_Datum_of_1929" class="mw-redirect" title="Sea Level Datum of 1929">NGVD 29</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Sea Level Datum 1929</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/enwiki/wiki/OSGB36" class="mw-redirect" title="OSGB36">OSGB36</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Ordnance Survey Great Britain 1936</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/enwiki/wiki/SK-42_reference_system" title="SK-42 reference system">SK-42</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Systema Koordinat 1942 goda</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/enwiki/wiki/ED50" title="ED50">ED50</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> European Datum 1950</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/enwiki/wiki/South_American_Datum#SAD69" title="South American Datum">SAD69</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> South American Datum 1969</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/enwiki/wiki/GRS_80" class="mw-redirect" title="GRS 80">GRS 80</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Geodetic Reference System 1980</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/enwiki/wiki/ISO_6709" title="ISO 6709">ISO 6709</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Geographic point coord. 1983</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/enwiki/wiki/North_American_Datum#North_American_Datum_of_1983" title="North American Datum">NAD 83</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> North American Datum 1983</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/enwiki/wiki/World_Geodetic_System" title="World Geodetic System">WGS 84</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> World Geodetic System 1984</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/enwiki/wiki/North_American_Vertical_Datum_of_1988" title="North American Vertical Datum of 1988">NAVD 88</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> N. American Vertical Datum 1988</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/enwiki/wiki/European_Terrestrial_Reference_System_1989" title="European Terrestrial Reference System 1989">ETRS89</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> European Terrestrial Ref. Sys. 1989</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/enwiki/wiki/Restrictions_on_geographic_data_in_China" title="Restrictions on geographic data in China">GCJ-02</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Chinese obfuscated datum 2002</td></tr><tr style="vertical-align:top"><td style="text-align:left;padding-left:0.5em;"> <a href="/enwiki/wiki/Geo_URI_scheme" title="Geo URI scheme">Geo URI</a></td><td style="text-align:right;font-size:90%;padding-right:0.55em;"> Internet link to a point 2010</td></tr></tbody></table>
<ul><li><a href="/enwiki/wiki/International_Terrestrial_Reference_System" class="mw-redirect" title="International Terrestrial Reference System">International Terrestrial Reference System</a></li>
<li><a href="/enwiki/wiki/SRID" class="mw-redirect" title="SRID">Spatial Reference System Identifier (SRID)</a></li>
<li><a href="/enwiki/wiki/Universal_Transverse_Mercator_coordinate_system" title="Universal Transverse Mercator coordinate system">Universal Transverse Mercator (UTM)</a></li></ul></div></div></td>
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<p><b>Longitude</b> (<span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt"><a href="/enwiki/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="/ˈ/: primary stress follows">ˈ</span><span title="'l' in 'lie'">l</span><span title="/ɒ/: 'o' in 'body'">ɒ</span><span title="'n' in 'nigh'">n</span><span title="/dʒ/: 'j' in 'jam'">dʒ</span><span title="/ɪ/: 'i' in 'kit'">ɪ</span><span title="/tj/: 't' in 'tune'">tj</span><span title="/uː/: 'oo' in 'goose'">uː</span><span title="'d' in 'dye'">d</span></span>/</a></span></span>, <span style="font-size:85%;">AU and UK also</span> <span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt"><a href="/enwiki/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="/ˈ/: primary stress follows">ˈ</span><span title="'l' in 'lie'">l</span><span title="/ɒ/: 'o' in 'body'">ɒ</span><span title="/ŋ/: 'ng' in 'sing'">ŋ</span><span title="/ɡ/: 'g' in 'guy'">ɡ</span><span title="/ɪ/: 'i' in 'kit'">ɪ</span></span>-/</a></span></span>),<span class="error mw-ext-cite-error" lang="en" dir="ltr">Cite error: A <code><ref></code> tag is missing the closing <code></ref></code> (see the <a href="/enwiki/wiki/Help:Cite_errors/Cite_error_included_ref" title="Help:Cite errors/Cite error included ref">help page</a>).
</span><sup class="reference" style="white-space:nowrap;">:<span>31</span></sup> He also proposed a method of determining longitude by comparing the local time of a <a href="/enwiki/wiki/Lunar_eclipse" title="Lunar eclipse">lunar eclipse</a> at two different places, thus demonstrating an understanding of the relationship between longitude and time.<sup id="cite_ref-Dicks_1-0" class="reference"><a href="#cite_note-Dicks-1">[1]</a></sup><sup class="reference nowrap">:<span>11</span></sup>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2">[2]</a></sup> <a href="/enwiki/wiki/Ptolemy" title="Ptolemy">Claudius Ptolemy</a> (2nd century CE) developed a mapping system using curved parallels that reduced distortion. He also collected data for many locations, from Britain to the Middle East. He used a prime meridian through the Canary Islands, so that all longitude values would be positive. While Ptolemy's system was sound, the data he used were often poor, leading to a gross over-estimate (by about 70%) of the length of the Mediterranean.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3">[3]</a></sup><sup id="cite_ref-Bunbury_4-0" class="reference"><a href="#cite_note-Bunbury-4">[4]</a></sup><sup class="reference" style="white-space:nowrap;">:<span>551–553</span></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5">[5]</a></sup>
</p><p>After the fall of the Roman Empire, interest in geography greatly declined in Europe.<sup id="cite_ref-Wright1925_6-0" class="reference"><a href="#cite_note-Wright1925-6">[6]</a></sup><sup class="reference" style="white-space:nowrap;">:<span>65</span></sup> Hindu and Muslim astronomers continued to develop these ideas, adding many new locations and often improving on Ptolemy's data.<sup id="cite_ref-Ragep_7-0" class="reference"><a href="#cite_note-Ragep-7">[7]</a></sup><sup id="cite_ref-Tibbett_8-0" class="reference"><a href="#cite_note-Tibbett-8">[8]</a></sup> For example <a href="/enwiki/wiki/Al-Battani" title="Al-Battani">al-Battānī</a> used simultaneous observations of two lunar eclipses to determine the difference in longitude between <a href="/enwiki/wiki/Antakya" title="Antakya">Antakya</a> and <a href="/enwiki/wiki/Raqqa" title="Raqqa">Raqqa</a> with an error of less than 1°. This is considered to be the best that can be achieved with the methods then available - observation of the eclipse with the naked eye, and determination of local time using an <a href="/enwiki/wiki/Astrolabe" title="Astrolabe">astrolabe</a> to measure the altitude of a suitable "clock star".<sup id="cite_ref-Said2_9-0" class="reference"><a href="#cite_note-Said2-9">[9]</a></sup><sup id="cite_ref-Steele_10-0" class="reference"><a href="#cite_note-Steele-10">[10]</a></sup>
</p><p>In the later Middle Ages, interest in geography revived in the west, as travel increased, and Arab scholarship began to be known through contact with Spain and North Africa. In the 12th Century, astronomical tables were prepared for a number of European cities, based on the work of <a href="/enwiki/wiki/Ab%C5%AB_Ish%C4%81q_Ibr%C4%81h%C4%ABm_al-Zarq%C4%81l%C4%AB" title="Abū Ishāq Ibrāhīm al-Zarqālī">al-Zarqālī</a> in <a href="/enwiki/wiki/Toledo,_Spain" title="Toledo, Spain">Toledo</a>. The lunar eclipse of September 12, 1178 was used to establish the longitude differences between Toledo, <a href="/enwiki/wiki/Marseille" title="Marseille">Marseilles</a>, and <a href="/enwiki/wiki/Hereford" title="Hereford">Hereford</a>.<sup id="cite_ref-Wright1923_11-0" class="reference"><a href="#cite_note-Wright1923-11">[11]</a></sup><sup class="reference" style="white-space:nowrap;">:<span>85</span></sup>
</p><p>Christopher Columbus made two attempts to use lunar eclipses to discover his longitude, the first in <a href="/enwiki/wiki/Saona_Island" title="Saona Island">Saona Island</a>, on 14 September 1494 (second voyage), and the second in <a href="/enwiki/wiki/Jamaica" title="Jamaica">Jamaica</a> on 29 February 1504 (fourth voyage). It is assumed that he used astronomical tables for reference. His determinations of longitude showed large errors of 13 and 38° W respectively.<sup id="cite_ref-Pickering_12-0" class="reference"><a href="#cite_note-Pickering-12">[12]</a></sup> Randles (1985) documents longitude measurement by the Portuguese and Spanish between 1514 and 1627 both in the Americas and Asia. Errors ranged from 2-25°.<sup id="cite_ref-Randles_13-0" class="reference"><a href="#cite_note-Randles-13">[13]</a></sup>
</p><p>The telescope was invented in the early 17th-century. Initially an observation device, developments over the next half century transformed it into an accurate measurement tool.<sup id="cite_ref-Pannekoek_14-0" class="reference"><a href="#cite_note-Pannekoek-14">[14]</a></sup><sup id="cite_ref-Van_Helden_15-0" class="reference"><a href="#cite_note-Van_Helden-15">[15]</a></sup> The <a href="/enwiki/wiki/Pendulum_clock" title="Pendulum clock">pendulum clock</a> was patented by <a href="/enwiki/wiki/Christiaan_Huygens" title="Christiaan Huygens">Christiaan Huygens</a> in 1657<sup id="cite_ref-Grimbergen_16-0" class="reference"><a href="#cite_note-Grimbergen-16">[16]</a></sup> and gave an increase in accuracy of about 30 fold over previous mechanical clocks.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17">[17]</a></sup> These two inventions would revolutionize observational astronomy and cartography.<sup id="cite_ref-Olmsted_18-0" class="reference"><a href="#cite_note-Olmsted-18">[18]</a></sup>
</p><p>The main methods for dermining longitude are listed below. With one exception (magnetic declination) they all depend on a common principle, which was to determine an absolute time from an event or measurement and to compare the corresponding local time at two different locations.
</p>
<ul><li><a href="/enwiki/wiki/Lunar_distance_(navigation)" title="Lunar distance (navigation)">Lunar distances</a>. In its orbit around the earth, the moon moves relative to the stars at a rate of just over 0.5°/hour. The angle between the moon and a suitable star is measured with a <a href="/enwiki/wiki/Sextant" title="Sextant">sextant</a>, and (after consultation with tables and lengthy calculations) gives a value for absolute time.</li>
<li>Satellites of Jupiter. <a href="/enwiki/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo</a> proposed that with sufficiently accurate knowledge of the orbits of the satellites, their positions could provide a measure of absolute time. The method requires a telescope, as the moons are not visible to the naked eye.</li>
<li>Appulses, occultations, and eclipses. An <a href="/enwiki/wiki/Appulse" title="Appulse">appulse</a> is the least apparent distance between two objects (the moon a star or a planet), an <a href="/enwiki/wiki/Occultation" title="Occultation">occultation</a> occurs when a star or planet passes behind the moon — essentially a type of eclipse. Lunar eclipses continued to be used. The times of any of these events can be used as the measure of absolute time.</li>
<li><a href="/enwiki/wiki/Marine_chronometer" title="Marine chronometer">Chronometers</a>. A clock is set to the local time of a starting point whose longitude is known, and the longitude of any other place can be determined by comparing its local time with the clock time.</li>
<li>Magnetic declination. A compass needle does not in general point exactly north. The <a href="/enwiki/wiki/Magnetic_declination" title="Magnetic declination">variation</a> from true north varies with location, and it was suggested that this could provide a basis for determination of longitude.</li></ul>
<p>With the exception of magnetic declination, all proved practicable methods. Developments on land and sea, however, were very different.
</p><p>On land, the period from the development of telescopes and pendulum clocks until the mid 18th-Century saw a steady increase in the number of places whose longitude had been determined with reasonable accuracy, often with errors of less than a degree, and nearly always within 2-3°. By the 1720s errors were consistently less than 1°.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19">[19]</a></sup> At sea during the same period, the situation was very different. Two problems proved intractable. The first was the need of a navigator for immediate results. The second was the marine environment. Making accurate observations in an ocean swell is much harder than on land, and pendulum clocks do not work well in these conditions.
</p><p>In response to the problems of navigation, a number of European maritime powers offered prizes for a method to determine longitude at sea. The best-known of these is the <a href="/enwiki/wiki/Longitude_Act" title="Longitude Act">Longitude Act</a> passed by the British parliament in 1714.<sup id="cite_ref-Siegel_20-0" class="reference"><a href="#cite_note-Siegel-20">[20]</a></sup><sup class="reference" style="white-space:nowrap;">:<span>8</span></sup> It offered two levels of rewards, for solutions within 1° and 0.5°. Rewards were given for two solutions: lunar distances, made practicable by the tables of <a href="/enwiki/wiki/Tobias_Mayer" title="Tobias Mayer">Tobias Mayer</a><sup id="cite_ref-Forbes2006_21-0" class="reference"><a href="#cite_note-Forbes2006-21">[21]</a></sup> developed into an <a href="/enwiki/wiki/Nautical_almanac" title="Nautical almanac">nautical almanac</a> by the <a href="/enwiki/wiki/Astronomer_Royal" title="Astronomer Royal">Astronomer Royal</a> <a href="/enwiki/wiki/Neville_Maskelyne" class="mw-redirect" title="Neville Maskelyne">Neville Maskelyne</a>; and for the chronometers developed by the Yorkshire carpenter and clock-maker <a href="/enwiki/wiki/John_Harrison" title="John Harrison">John Harrison</a>. Harrison built five chronometers over more than three decades. However, he was not awarded the prize by the Longitude Board and was forced to fight for his reward, finally receiving payment in 1773, after the intervention of parliament<sup id="cite_ref-Siegel_20-1" class="reference"><a href="#cite_note-Siegel-20">[20]</a></sup><sup class="reference nowrap">:<span>26</span></sup>. It was some while before either method became widely used in navigation. In the early years, chronometers were very expensive, and the calculations required for lunar distances were still complex and time-consuming. Lunar distances came into general use after 1790.<sup id="cite_ref-Wess2015_22-0" class="reference"><a href="#cite_note-Wess2015-22">[22]</a></sup> Chronometers had the advantages that both the observations and the calculations were simpler, and as they became cheaper in the early 19th-Century they started to replace lunars, which were seldom used after 1850.<sup id="cite_ref-Littlehales_23-0" class="reference"><a href="#cite_note-Littlehales-23">[23]</a></sup>
</p><p>The first working telegraphs were established in Britain by <a href="/enwiki/wiki/Charles_Wheatstone" title="Charles Wheatstone">Wheatstone</a> and <a href="/enwiki/wiki/William_Fothergill_Cooke" title="William Fothergill Cooke">Cooke</a> in 1839, and in the US by <a href="/enwiki/wiki/Samuel_Morse" title="Samuel Morse">Morse</a> in 1844. It was quickly realised that the telegraph could be used to transmit a time signal for longitude determination.<sup id="cite_ref-Walker_1850_24-0" class="reference"><a href="#cite_note-Walker_1850-24">[24]</a></sup> The method was soon in practical use for longitude determination, especially in North America, and over longer and longer distances as the telegraph network expanded, including western Europe with the completion of transatlantic cables. The <a href="/enwiki/wiki/U.S._National_Geodetic_Survey" title="U.S. National Geodetic Survey">US Coast Survey</a> was particularly active in this development, and not just in the United States. The Survey established chains of mapped locations through Central and South America, and the West Indies, and as far as Japan and China in the years 1874–90. This contributed greatly to the accurate mapping of these areas.<sup id="cite_ref-Knox_25-0" class="reference"><a href="#cite_note-Knox-25">[25]</a></sup><sup id="cite_ref-Green1883_26-0" class="reference"><a href="#cite_note-Green1883-26">[26]</a></sup>
</p><p>While mariners benefited from the accurate charts, they could not receive telegraph signals while under way, and so could not use the method for navigation. This changed when wireless telegraphy became available in the early 20th-Century.<sup id="cite_ref-Munro1902_27-0" class="reference"><a href="#cite_note-Munro1902-27">[27]</a></sup> Wireless time signals for the use of ships were transmitted from <a href="/enwiki/wiki/Halifax,_Nova_Scotia" title="Halifax, Nova Scotia">Halifax, Nova Scotia</a>, starting in 1907<sup id="cite_ref-Hutchnson_28-0" class="reference"><a href="#cite_note-Hutchnson-28">[28]</a></sup> and from the <a href="/enwiki/wiki/Eiffel_Tower" title="Eiffel Tower">Eiffel Tower</a> in Paris from 1910.<sup id="cite_ref-Lockyer1913_29-0" class="reference"><a href="#cite_note-Lockyer1913-29">[29]</a></sup> These signals allowed navigators to check and adjust their chronometers on a frequent basis.<sup id="cite_ref-Zimmerman_30-0" class="reference"><a href="#cite_note-Zimmerman-30">[30]</a></sup>
</p><p><a href="/enwiki/wiki/Radio_navigation" title="Radio navigation">Radio navigation</a> systems came into general use after <a href="/enwiki/wiki/World_War_II" title="World War II">World War II</a>. The systems all depended on transmissions from fixed navigational beacons. A ship-board receiver calculated the vessel's position from these transmissions.<sup id="cite_ref-Pierce_31-0" class="reference"><a href="#cite_note-Pierce-31">[31]</a></sup> They allowed accurate navigation when poor visibility prevented astronomical observations, and became the established method for commercial shipping until replaced by <a href="/enwiki/wiki/Global_Positioning_System" title="Global Positioning System">GPS</a> in the early 1990s.
</p>
<div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div>
<ul>
<li class="toclevel-1 tocsection-1"><a href="#Noting_and_calculating_longitude"><span class="tocnumber">1</span> <span class="toctext">Noting and calculating longitude</span></a>
<ul>
<li class="toclevel-2 tocsection-2"><a href="#Singularity_and_discontinuity_of_longitude"><span class="tocnumber">1.1</span> <span class="toctext">Singularity and discontinuity of longitude</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-3"><a href="#Plate_movement_and_longitude"><span class="tocnumber">2</span> <span class="toctext">Plate movement and longitude</span></a></li>
<li class="toclevel-1 tocsection-4"><a href="#Length_of_a_degree_of_longitude"><span class="tocnumber">3</span> <span class="toctext">Length of a degree of longitude</span></a></li>
<li class="toclevel-1 tocsection-5"><a href="#Longitude_on_bodies_other_than_Earth"><span class="tocnumber">4</span> <span class="toctext">Longitude on bodies other than Earth</span></a></li>
<li class="toclevel-1 tocsection-6"><a href="#See_also"><span class="tocnumber">5</span> <span class="toctext">See also</span></a></li>
<li class="toclevel-1 tocsection-7"><a href="#References"><span class="tocnumber">6</span> <span class="toctext">References</span></a></li>
<li class="toclevel-1 tocsection-8"><a href="#External_links"><span class="tocnumber">7</span> <span class="toctext">External links</span></a></li>
</ul>
</div>
<h2><span class="mw-headline" id="Noting_and_calculating_longitude">Noting and calculating longitude</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Longitude&action=edit&section=1" title="Edit section: Noting and calculating longitude">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>Longitude is given as an <a href="/enwiki/wiki/Angle" title="Angle">angular measurement</a> ranging from 0° at the Prime Meridian to +180° eastward and −180° westward. The Greek letter λ (lambda),<sup id="cite_ref-32" class="reference"><a href="#cite_note-32">[32]</a></sup><sup id="cite_ref-33" class="reference"><a href="#cite_note-33">[33]</a></sup> is used to denote the location of a place on Earth east or west of the Prime Meridian.
</p><p>Each degree of longitude is sub-divided into 60 <a href="/enwiki/wiki/Minute_of_arc" class="mw-redirect" title="Minute of arc">minutes</a>, each of which is divided into 60 <a href="/enwiki/wiki/Arcsecond" class="mw-redirect" title="Arcsecond">seconds</a>. A longitude is thus specified in <a href="/enwiki/wiki/Sexagesimal" title="Sexagesimal">sexagesimal</a> notation as 23° 27′ 30″ E. For higher precision, the seconds are specified with a <a href="/enwiki/wiki/Decimal#Decimal_fractions" title="Decimal">decimal fraction</a>. An alternative representation uses degrees and minutes, where parts of a minute are expressed in decimal notation with a fraction, thus: 23° 27.5′ E. Degrees may also be expressed as a decimal fraction: 23.45833° E. For calculations, the angular measure may be converted to <a href="/enwiki/wiki/Radian" title="Radian">radians</a>, so longitude may also be expressed in this manner as a signed fraction of <span class="texhtml mvar" style="font-style:italic;">π</span> (<a href="/enwiki/wiki/Pi" title="Pi">pi</a>), or an unsigned fraction of 2<span class="texhtml mvar" style="font-style:italic;">π</span>.
</p><p>For calculations, the West/East suffix is replaced by a negative sign in the <a href="/enwiki/wiki/Western_hemisphere" class="mw-redirect" title="Western hemisphere">western hemisphere</a>. The international standard convention (<a href="/enwiki/wiki/ISO_6709" title="ISO 6709">ISO 6709</a>)—that East is positive—is consistent with a right-handed <a href="/enwiki/wiki/Cartesian_coordinate_system" title="Cartesian coordinate system">Cartesian coordinate system</a>, with the North Pole up. A specific longitude may then be combined with a specific latitude (positive in the <a href="/enwiki/wiki/Northern_hemisphere" class="mw-redirect" title="Northern hemisphere">northern hemisphere</a>) to give a precise position on the Earth's surface. Confusingly, the convention of negative for East is also sometimes seen, most commonly in the <a href="/enwiki/wiki/United_States" title="United States">United States</a>; the <a href="/enwiki/wiki/Earth_System_Research_Laboratory" title="Earth System Research Laboratory">Earth System Research Laboratory</a> used it on an older version of one of their pages, in order "to make coordinate entry less awkward" for applications confined to the <a href="/enwiki/wiki/Western_Hemisphere" title="Western Hemisphere">Western Hemisphere</a>. They have since shifted to the standard approach.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34">[34]</a></sup>
</p><p>There is no other physical principle determining longitude directly but with time. Longitude at a point may be determined by calculating the time difference between that at its location and <a href="/enwiki/wiki/Coordinated_Universal_Time" title="Coordinated Universal Time">Coordinated Universal Time</a> (UTC). Since there are 24 hours in a day and 360 degrees in a circle, the sun moves across the sky at a rate of 15 degrees per hour (360° ÷ 24 hours = 15° per hour). So if the <a href="/enwiki/wiki/Time_zone" title="Time zone">time zone</a> a person is in is three hours ahead of UTC then that person is near 45° longitude (3 hours × 15° per hour = 45°). The word <i>near</i> is used because the point might not be at the center of the time zone; also the time zones are defined politically, so their centers and boundaries often do not lie on meridians at multiples of 15°. In order to perform this calculation, however, a person needs to have a <a href="/enwiki/wiki/Marine_chronometer" title="Marine chronometer">chronometer</a> (watch) set to UTC and needs to determine local time by solar or astronomical observation. The details are more complex than described here: see the articles on <a href="/enwiki/wiki/Universal_Time" title="Universal Time">Universal Time</a> and on the <a href="/enwiki/wiki/Equation_of_time" title="Equation of time">equation of time</a> for more details.
</p>
<h3><span class="mw-headline" id="Singularity_and_discontinuity_of_longitude">Singularity and discontinuity of longitude</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Longitude&action=edit&section=2" title="Edit section: Singularity and discontinuity of longitude">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<p>Note that the longitude is <a href="/enwiki/wiki/Mathematical_singularity" class="mw-redirect" title="Mathematical singularity">singular</a> at the <a href="/enwiki/wiki/Geographical_pole" title="Geographical pole">Poles</a> and calculations that are sufficiently accurate for other positions may be inaccurate at or near the Poles. Also the <a href="/enwiki/wiki/Discontinuity_(mathematics)" class="mw-redirect" title="Discontinuity (mathematics)">discontinuity</a> at the ±<a href="/enwiki/wiki/180th_meridian" title="180th meridian">180° meridian</a> must be handled with care in calculations. An example is a calculation of east displacement by subtracting two longitudes, which gives the wrong answer if the two positions are on either side of this meridian. To avoid these complexities, consider replacing latitude and longitude with another <a href="/enwiki/wiki/Horizontal_position_representation" title="Horizontal position representation">horizontal position representation</a> in calculation.
</p>
<h2><span class="mw-headline" id="Plate_movement_and_longitude">Plate movement and longitude</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Longitude&action=edit&section=3" title="Edit section: Plate movement and longitude">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>The Earth's <a href="/enwiki/wiki/Plate_tectonics" title="Plate tectonics">tectonic plates</a> move relative to one another in different directions at speeds on the order of 50 to 100 mm (2.0 to 3.9 in) per year.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35">[35]</a></sup> So points on the Earth's surface on different plates are always in motion relative to one another. For example, the longitudinal difference between a point on the Equator in Uganda, on the <a href="/enwiki/wiki/African_Plate" title="African Plate">African Plate</a>, and a point on the Equator in Ecuador, on the <a href="/enwiki/wiki/South_American_Plate" title="South American Plate">South American Plate</a>, is increasing by about 0.0014 <a href="/enwiki/wiki/Minute_of_arc#Symbols_and_abbreviations" class="mw-redirect" title="Minute of arc">arcseconds</a> per year. These tectonic movements likewise affect latitude.
</p><p>If a <a href="/enwiki/wiki/Geodetic_datum" title="Geodetic datum">global reference frame</a> (such as <a href="/enwiki/wiki/WGS84" class="mw-redirect" title="WGS84">WGS84</a>, for example) is used, the longitude of a place on the surface will change from year to year. To minimize this change, when dealing just with points on a single plate, a different reference frame can be used, whose coordinates are fixed to a particular plate, such as "<a href="/enwiki/wiki/NAD83" class="mw-redirect" title="NAD83">NAD83</a>" for North America or "<a href="/enwiki/wiki/ETRS89" class="mw-redirect" title="ETRS89">ETRS89</a>" for Europe.
</p>
<h2><span class="mw-headline" id="Length_of_a_degree_of_longitude">Length of a degree of longitude</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Longitude&action=edit&section=4" title="Edit section: Length of a degree of longitude">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>The length of a degree of longitude (east–west distance) depends only on the radius of a circle of latitude. For a sphere of radius <span class="texhtml mvar" style="font-style:italic;">a</span> that radius at latitude <span class="texhtml mvar" style="font-style:italic;">φ</span> is <span class="texhtml"><i>a</i> <a href="/enwiki/wiki/Cosine" class="mw-redirect" title="Cosine">cos</a> <i>φ</i></span>, and the length of a one-degree (or <style data-mw-deduplicate="TemplateStyles:r993651011">.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px;white-space:nowrap}</style><span role="math" class="sfrac nowrap tion" style="display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;"><span class="num" style="display:block; line-height:1em; margin:0 0.1em;"><span class="texhtml mvar" style="font-style:italic;">π</span></span><span class="slash sr-only">/</span><span class="den" style="display:block; line-height:1em; margin:0 0.1em; border-top:1px solid;">180</span></span> <a href="/enwiki/wiki/Radian" title="Radian">radian</a>) arc along a circle of latitude is
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\rm {long}}^{1}={\frac {\pi }{180^{\circ }}}a\cos \phi }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msubsup>
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">l</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">n</mi>
<mi mathvariant="normal">g</mi>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msubsup>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>π<!-- π --></mi>
<msup>
<mn>180</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>∘<!-- ∘ --></mo>
</mrow>
</msup>
</mfrac>
</mrow>
<mi>a</mi>
<mi>cos</mi>
<mo>⁡<!-- --></mo>
<mi>ϕ<!-- ϕ --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Delta _{\rm {long}}^{1}={\frac {\pi }{180^{\circ }}}a\cos \phi }</annotation>
</semantics>
</math></span><img src="https://wikimedia.org/enwiki/api/rest_v1/media/math/render/svg/c958a5e8a1bbfe0a5364b6e6862a9d78a32d3434" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.005ex; width:20.16ex; height:4.843ex;" alt="{\displaystyle \Delta _{\rm {long}}^{1}={\frac {\pi }{180^{\circ }}}a\cos \phi }"/></span></dd></dl>
<table class="wikitable" style="float: right; margin-left:1em; text-align:right;">
<tbody><tr>
<th><span class="texhtml mvar" style="font-style:italic;">φ</span></th>
<th><span class="texhtml">Δ<span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">lat</sub></span></span></th>
<th><span class="texhtml">Δ<span style="display:inline-block;margin-bottom:-0.3em;vertical-align:-0.4em;line-height:1.2em;font-size:80%;text-align:left"><sup style="font-size:inherit;line-height:inherit;vertical-align:baseline">1</sup><br /><sub style="font-size:inherit;line-height:inherit;vertical-align:baseline">long</sub></span></span>
</th></tr>
<tr>
<td>0°</td>
<td>110.574 km</td>
<td>111.320 km
</td></tr>
<tr>
<td>15°</td>
<td>110.649 km</td>
<td>107.551 km
</td></tr>
<tr>
<td>30°</td>
<td>110.852 km</td>
<td>96.486 km
</td></tr>
<tr>
<td>45°</td>
<td>111.133 km</td>
<td>78.847 km
</td></tr>
<tr>
<td>60°</td>
<td>111.412 km</td>
<td>55.800 km
</td></tr>
<tr>
<td>75°</td>
<td>111.618 km</td>
<td>28.902 km
</td></tr>
<tr>
<td>90°</td>
<td>111.694 km</td>
<td>0.000 km
</td></tr></tbody></table>
<div class="thumb tright"><div class="thumbinner" style="width:302px;"><a href="/enwiki/wiki/File:WGS84_angle_to_distance_conversion.svg" class="image"><img alt="" src="/upwiki/wikipedia/commons/thumb/d/d0/WGS84_angle_to_distance_conversion.svg/300px-WGS84_angle_to_distance_conversion.svg.png" decoding="async" width="300" height="240" class="thumbimage" srcset="/upwiki/wikipedia/commons/thumb/d/d0/WGS84_angle_to_distance_conversion.svg/450px-WGS84_angle_to_distance_conversion.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/d/d0/WGS84_angle_to_distance_conversion.svg/600px-WGS84_angle_to_distance_conversion.svg.png 2x" data-file-width="512" data-file-height="410" /></a> <div class="thumbcaption"><div class="magnify"><a href="/enwiki/wiki/File:WGS84_angle_to_distance_conversion.svg" class="internal" title="Enlarge"></a></div>Length of one degree (black), minute (blue) and second (red) of latitude and longitude in metric (upper half) and imperial units (lower half) at a given latitude (vertical axis) in WGS84. For example, the green arrows show that Donetsk (green circle) at 48°N has a Δ<sub>long</sub> of 74.63 km/° (1.244 km/min, 20.73 m/sec etc) and a Δ<sub>lat</sub> of 111.2 km/° (1.853 km/min, 30.89 m/sec etc).</div></div></div>
<p>When the Earth is modelled by an <a href="/enwiki/wiki/Ellipsoid" title="Ellipsoid">ellipsoid</a> this arc length becomes<sup id="cite_ref-osborne_36-0" class="reference"><a href="#cite_note-osborne-36">[36]</a></sup><sup id="cite_ref-rapp_37-0" class="reference"><a href="#cite_note-rapp-37">[37]</a></sup>
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\rm {long}}^{1}={\frac {\pi a\cos \phi }{180^{\circ }{\sqrt {1-e^{2}\sin ^{2}\phi }}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msubsup>
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">l</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">n</mi>
<mi mathvariant="normal">g</mi>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msubsup>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>π<!-- π --></mi>
<mi>a</mi>
<mi>cos</mi>
<mo>⁡<!-- --></mo>
<mi>ϕ<!-- ϕ --></mi>
</mrow>
<mrow>
<msup>
<mn>180</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>∘<!-- ∘ --></mo>
</mrow>
</msup>
<mrow class="MJX-TeXAtom-ORD">
<msqrt>
<mn>1</mn>
<mo>−<!-- − --></mo>
<msup>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<msup>
<mi>sin</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>⁡<!-- --></mo>
<mi>ϕ<!-- ϕ --></mi>
</msqrt>
</mrow>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Delta _{\rm {long}}^{1}={\frac {\pi a\cos \phi }{180^{\circ }{\sqrt {1-e^{2}\sin ^{2}\phi }}}}}</annotation>
</semantics>
</math></span><img src="https://wikimedia.org/enwiki/api/rest_v1/media/math/render/svg/098cb1f25bad1f0c20d0a8e59510b8d2be7f6b8f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -4.671ex; width:28.193ex; height:8.176ex;" alt="{\displaystyle \Delta _{\rm {long}}^{1}={\frac {\pi a\cos \phi }{180^{\circ }{\sqrt {1-e^{2}\sin ^{2}\phi }}}}}"/></span></dd></dl>
<p>where <span class="texhtml mvar" style="font-style:italic;">e</span>, the eccentricity of the ellipsoid, is related to the major and minor axes (the equatorial and polar radii respectively) by
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e^{2}={\frac {a^{2}-b^{2}}{a^{2}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<msup>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo>−<!-- − --></mo>
<msup>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mrow>
<msup>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle e^{2}={\frac {a^{2}-b^{2}}{a^{2}}}}</annotation>
</semantics>
</math></span><img src="https://wikimedia.org/enwiki/api/rest_v1/media/math/render/svg/acc915e4db2a15442229073d080670744d0f1c94" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.171ex; width:13.249ex; height:6.009ex;" alt="e^{2}={\frac {a^{2}-b^{2}}{a^{2}}}"/></span></dd></dl>
<p>An alternative formula is
</p>
<dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta _{\rm {long}}^{1}={\frac {\pi }{180^{\circ }}}a\cos \beta \quad {\mbox{where }}\tan \beta ={\frac {b}{a}}\tan \phi }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msubsup>
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">l</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">n</mi>
<mi mathvariant="normal">g</mi>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msubsup>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>π<!-- π --></mi>
<msup>
<mn>180</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>∘<!-- ∘ --></mo>
</mrow>
</msup>
</mfrac>
</mrow>
<mi>a</mi>
<mi>cos</mi>
<mo>⁡<!-- --></mo>
<mi>β<!-- β --></mi>
<mspace width="1em" />
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="false" scriptlevel="0">
<mtext>where </mtext>
</mstyle>
</mrow>
<mi>tan</mi>
<mo>⁡<!-- --></mo>
<mi>β<!-- β --></mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>b</mi>
<mi>a</mi>
</mfrac>
</mrow>
<mi>tan</mi>
<mo>⁡<!-- --></mo>
<mi>ϕ<!-- ϕ --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \Delta _{\rm {long}}^{1}={\frac {\pi }{180^{\circ }}}a\cos \beta \quad {\mbox{where }}\tan \beta ={\frac {b}{a}}\tan \phi }</annotation>
</semantics>
</math></span><img src="https://wikimedia.org/enwiki/api/rest_v1/media/math/render/svg/5ff2b096b46d41d774c8bdd2e7b44ec821f7f8d6" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.005ex; width:45.106ex; height:5.509ex;" alt="{\displaystyle \Delta _{\rm {long}}^{1}={\frac {\pi }{180^{\circ }}}a\cos \beta \quad {\mbox{where }}\tan \beta ={\frac {b}{a}}\tan \phi }"/></span>; here <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \beta }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>β<!-- β --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \beta }</annotation>
</semantics>
</math></span><img src="https://wikimedia.org/enwiki/api/rest_v1/media/math/render/svg/7ed48a5e36207156fb792fa79d29925d2f7901e8" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:1.332ex; height:2.509ex;" alt="\beta "/></span> is the so-called <a href="/enwiki/wiki/Latitude#Parametric_(or_reduced)_latitude" title="Latitude"><strong>parametric</strong> or <strong>reduced</strong> latitude</a>.</dd></dl>
<p>Cos <span class="texhtml mvar" style="font-style:italic;">φ</span> decreases from 1 at the equator to 0 at the poles, which measures how circles of latitude shrink from the equator to a point at the pole, so the length of a degree of longitude decreases likewise. This contrasts with the small (1%) increase in the <a href="/enwiki/wiki/Length_of_a_degree_of_latitude" class="mw-redirect" title="Length of a degree of latitude">length of a degree of latitude</a> (north–south distance), equator to pole. The table shows both for the <a href="/enwiki/wiki/WGS84" class="mw-redirect" title="WGS84">WGS84</a> ellipsoid with <span class="texhtml mvar" style="font-style:italic;">a</span> = <span class="nowrap"><span data-sort-value="7006637813700000000♠"></span>6<span style="margin-left:.25em;">378</span><span style="margin-left:.25em;">137</span>.0 m</span> and <span class="texhtml mvar" style="font-style:italic;">b</span> = <span class="nowrap"><span data-sort-value="7006635675231420000♠"></span>6<span style="margin-left:.25em;">356</span><span style="margin-left:.25em;">752</span>.3142 m</span>. Note that the distance between two points 1 degree apart on the same circle of latitude, measured along that circle of latitude, is slightly more than the shortest (<a href="/enwiki/wiki/Geodesic" title="Geodesic">geodesic</a>) distance between those points (unless on the equator, where these are equal); the difference is less than 0.6 m (2 ft).
</p><p>A <a href="/enwiki/wiki/Geographical_mile" title="Geographical mile">geographical mile</a> is defined to be the length of one <a href="/enwiki/wiki/Minute_of_arc" class="mw-redirect" title="Minute of arc">minute of arc</a> along the equator (one equatorial minute of longitude), therefore a degree of longitude along the equator is exactly 60 geographical miles or 111.3 kilometers, as there are 60 minutes in a degree. The length of 1 minute of longitude along the equator is 1 geographical mile or 1.855 km or 1.153 miles, while the length of 1 second of it is 0.016 geographical mile or 30.916 m or 101.43 feet.
</p>
<h2><span class="mw-headline" id="Longitude_on_bodies_other_than_Earth">Longitude on bodies other than Earth<span class="anchor" id="Planets"></span></span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Longitude&action=edit&section=5" title="Edit section: Longitude on bodies other than Earth">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<div role="note" class="hatnote navigation-not-searchable">See also: <a href="/enwiki/wiki/Prime_meridian_(planets)" class="mw-redirect" title="Prime meridian (planets)">Prime meridian (planets)</a></div>
<table class="box-More_citations_needed_section plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><a href="/enwiki/wiki/File:Question_book-new.svg" class="image"><img alt="" src="/upwiki/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" srcset="/upwiki/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, /upwiki/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs additional citations for <a href="/enwiki/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a class="external text" href="https://en.wikipedia.org/enwiki/w/index.php?title=Longitude&action=edit">improve this article</a> by <a href="/enwiki/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.</span> <small class="date-container"><i>(<span class="date">January 2020</span>)</i></small><small class="hide-when-compact"><i> (<a href="/enwiki/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this template message</a>)</i></small></div></td></tr></tbody></table>
<p><a href="/enwiki/wiki/Planet" title="Planet">Planetary</a> coordinate systems are defined relative to their mean <a href="/enwiki/wiki/Axis_of_rotation" class="mw-redirect" title="Axis of rotation">axis of rotation</a> and various definitions of longitude depending on the body. The longitude systems of most of those bodies with observable rigid surfaces have been defined by references to a surface feature such as a <a href="/enwiki/wiki/Impact_crater" title="Impact crater">crater</a>. The <a href="/enwiki/wiki/North_pole" class="mw-redirect" title="North pole">north pole</a> is that pole of rotation that lies on the north side of the <a href="/enwiki/wiki/Invariable_plane" title="Invariable plane">invariable plane</a> of the solar system (near the <a href="/enwiki/wiki/Ecliptic" title="Ecliptic">ecliptic</a>). The location of the prime meridian as well as the position of the body's north pole on the celestial sphere may vary with time due to precession of the axis of rotation of the planet (or satellite). If the position angle of the body's prime meridian increases with time, the body has a direct (or <a href="/enwiki/wiki/Direct_motion" class="mw-redirect" title="Direct motion">prograde</a>) rotation; otherwise the rotation is said to be <a href="/enwiki/wiki/Retrograde_motion" class="mw-redirect" title="Retrograde motion">retrograde</a>.
</p><p>In the absence of other information, the axis of rotation is assumed to be normal to the mean <a href="/enwiki/wiki/Orbital_plane_(astronomy)" title="Orbital plane (astronomy)">orbital plane</a>; <a href="/enwiki/wiki/Mercury_(planet)" title="Mercury (planet)">Mercury</a> and most of the satellites are in this category. For many of the satellites, it is assumed that the rotation rate is equal to the mean <a href="/enwiki/wiki/Orbital_period" title="Orbital period">orbital period</a>. In the case of the <a href="/enwiki/wiki/Gas_giant" title="Gas giant">giant planets</a>, since their surface features are constantly changing and moving at various rates, the rotation of their <a href="/enwiki/wiki/Magnetic_field" title="Magnetic field">magnetic fields</a> is used as a reference instead. In the case of the <a href="/enwiki/wiki/Sun" title="Sun">Sun</a>, even this criterion fails (because its magnetosphere is very complex and does not really rotate in a steady fashion), and an agreed-upon value for the rotation of its equator is used instead.
</p><p>For <i>planetographic longitude</i>, west longitudes (i.e., longitudes measured positively to the west) are used when the rotation is prograde, and east longitudes (i.e., longitudes measured positively to the east) when the rotation is retrograde. In simpler terms, imagine a distant, non-orbiting observer viewing a planet as it rotates. Also suppose that this observer is within the plane of the planet's equator. A point on the Equator that passes directly in front of this observer later in time has a higher planetographic longitude than a point that did so earlier in time.
</p><p>However, <i>planetocentric longitude</i> is always measured positively to the east, regardless of which way the planet rotates. <i>East</i> is defined as the counter-clockwise direction around the planet, as seen from above its north pole, and the north pole is whichever pole more closely aligns with the Earth's north pole. Longitudes traditionally have been written using "E" or "W" instead of "+" or "−" to indicate this polarity. For example, −91°, 91°W, +269° and 269°E all mean the same thing.
</p><p>The reference surfaces for some planets (such as Earth and <a href="/enwiki/wiki/Mars" title="Mars">Mars</a>) are <a href="/enwiki/wiki/Ellipsoid" title="Ellipsoid">ellipsoids</a> of revolution for which the equatorial radius is larger than the polar radius, such that they are <a href="/enwiki/wiki/Oblate_spheroid" class="mw-redirect" title="Oblate spheroid">oblate spheroids</a>. Smaller bodies (<a href="/enwiki/wiki/Io_(moon)" title="Io (moon)">Io</a>, <a href="/enwiki/wiki/Mimas_(moon)" title="Mimas (moon)">Mimas</a>, etc.) tend to be better approximated by <a href="/enwiki/wiki/Triaxial_ellipsoid" class="mw-redirect" title="Triaxial ellipsoid">triaxial ellipsoids</a>; however, triaxial ellipsoids would render many computations more complicated, especially those related to <a href="/enwiki/wiki/Map_projection" title="Map projection">map projections</a>. Many projections would lose their elegant and popular properties. For this reason spherical reference surfaces are frequently used in mapping programs.
</p><p>The modern standard for maps of Mars (since about 2002) is to use planetocentric coordinates. Guided by the works of historical astronomers, <a href="/enwiki/wiki/Merton_E._Davies" title="Merton E. Davies">Merton E. Davies</a> established the meridian of Mars at <a href="/enwiki/wiki/Airy-0" title="Airy-0">Airy-0</a> crater.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38">[38]</a></sup><sup id="cite_ref-39" class="reference"><a href="#cite_note-39">[39]</a></sup> For <a href="/enwiki/wiki/Mercury_(planet)" title="Mercury (planet)">Mercury</a>, the only other planet with a solid surface visible from Earth, a thermocentric coordinate is used: the prime meridian runs through the point on the equator where the planet is hottest (due to the planet's rotation and orbit, the sun briefly <a href="/enwiki/wiki/Apparent_retrograde_motion" title="Apparent retrograde motion">retrogrades</a> at noon at this point during <a href="/enwiki/wiki/Perihelion" class="mw-redirect" title="Perihelion">perihelion</a>, giving it more sun). By convention, this meridian is defined as exactly twenty degrees of longitude east of <a href="/enwiki/wiki/Hun_Kal_(crater)" title="Hun Kal (crater)">Hun Kal</a>.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40">[40]</a></sup><sup id="cite_ref-ArchinalA’Hearn2010_41-0" class="reference"><a href="#cite_note-ArchinalA’Hearn2010-41">[41]</a></sup><sup id="cite_ref-usgs_42-0" class="reference"><a href="#cite_note-usgs-42">[42]</a></sup>
</p><p><a href="/enwiki/wiki/Tidal_lock" class="mw-redirect" title="Tidal lock">Tidally-locked</a> bodies have a natural reference longitude passing through the point nearest to their parent body: 0° the center of the primary-facing hemisphere, 90° the center of the leading hemisphere, 180° the center of the anti-primary hemisphere, and 270° the center of the trailing hemisphere.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43">[43]</a></sup> However, <a href="/enwiki/wiki/Libration" title="Libration">libration</a> due to non-circular orbits or axial tilts causes this point to move around any fixed point on the celestial body like an <a href="/enwiki/wiki/Analemma" title="Analemma">analemma</a>.
</p>
<h2><span class="mw-headline" id="See_also">See also</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Longitude&action=edit&section=6" title="Edit section: See also">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<style data-mw-deduplicate="TemplateStyles:r998391716">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 20em;">
<ul><li><a href="/enwiki/wiki/American_Practical_Navigator" class="mw-redirect" title="American Practical Navigator">American Practical Navigator</a></li>
<li><a href="/enwiki/wiki/Cardinal_direction" title="Cardinal direction">Cardinal direction</a></li>
<li><a href="/enwiki/wiki/Ecliptic_longitude" class="mw-redirect" title="Ecliptic longitude">Ecliptic longitude</a></li>
<li><a href="/enwiki/wiki/Geodesy" title="Geodesy">Geodesy</a></li>
<li><a href="/enwiki/wiki/Geodetic_system" class="mw-redirect" title="Geodetic system">Geodetic system</a></li>
<li><a href="/enwiki/wiki/Geographic_coordinate_system" title="Geographic coordinate system">Geographic coordinate system</a></li>
<li><a href="/enwiki/wiki/Geographical_distance" title="Geographical distance">Geographical distance</a></li>
<li><a href="/enwiki/wiki/Geotagging" title="Geotagging">Geotagging</a></li>
<li><a href="/enwiki/wiki/Great-circle_distance" title="Great-circle distance">Great-circle distance</a></li>
<li><a href="/enwiki/wiki/History_of_longitude" title="History of longitude">History of longitude</a></li>
<li><i><a href="/enwiki/wiki/The_Island_of_the_Day_Before" title="The Island of the Day Before">The Island of the Day Before</a></i></li>
<li><a href="/enwiki/wiki/Latitude" title="Latitude">Latitude</a></li>
<li><a href="/enwiki/wiki/Meridian_arc" title="Meridian arc">Meridian arc</a></li>
<li><a href="/enwiki/wiki/Natural_Area_Code" title="Natural Area Code">Natural Area Code</a></li>
<li><a href="/enwiki/wiki/Navigation" title="Navigation">Navigation</a></li>
<li><a href="/enwiki/wiki/Orders_of_magnitude_(length)" title="Orders of magnitude (length)">Orders of magnitude</a></li>
<li><a href="/enwiki/wiki/Right_ascension" title="Right ascension">Right ascension</a> on <a href="/enwiki/wiki/Celestial_sphere" title="Celestial sphere">celestial sphere</a></li>
<li><a href="/enwiki/wiki/World_Geodetic_System" title="World Geodetic System">World Geodetic System</a></li></ul>
</div>
<h2><span class="mw-headline" id="References">References</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Longitude&action=edit&section=7" title="Edit section: References">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<div class="reflist" style="list-style-type: decimal;">
<div class="mw-references-wrap mw-references-columns"><ol class="references">
<li id="cite_note-Dicks-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Dicks_1-0">^</a></b></span> <span class="error mw-ext-cite-error" lang="en" dir="ltr">Cite error: The named reference <code>Dicks</code> was invoked but never defined (see the <a href="/enwiki/wiki/Help:Cite_errors/Cite_error_references_no_text" title="Help:Cite errors/Cite error references no text">help page</a>).
</span></li>
<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r999302996">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url("/upwiki/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),url("/upwiki/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url("/upwiki/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url("/upwiki/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFHoffman2016" class="citation book cs1">Hoffman, Susanne M. (2016). "How time served to measure the geographical position since Hellenism". In Arias, Elisa Felicitas; Combrinck, Ludwig; Gabor, Pavel; Hohenkerk, Catherine; Seidelmann, P.Kenneth (eds.). <i>The Science of Time</i>. Astrophysics and Space Science Proceedings. <b>50</b>. Springer International. pp. 25–36. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-319-59909-0_4">10.1007/978-3-319-59909-0_4</a>. <a href="/enwiki/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/enwiki/wiki/Special:BookSources/978-3-319-59908-3" title="Special:BookSources/978-3-319-59908-3"><bdi>978-3-319-59908-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=How+time+served+to+measure+the+geographical+position+since+Hellenism&rft.btitle=The+Science+of+Time&rft.series=Astrophysics+and+Space+Science+Proceedings&rft.pages=25-36&rft.pub=Springer+International&rft.date=2016&rft_id=info%3Adoi%2F10.1007%2F978-3-319-59909-0_4&rft.isbn=978-3-319-59908-3&rft.aulast=Hoffman&rft.aufirst=Susanne+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
</li>
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<li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFBlumenthalNosonovsky2020" class="citation journal cs1">Blumenthal, Aaron S.; Nosonovsky, Michael (2020). <a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fapplmech1020008">"Friction and Dynamics of Verge and Foliot: How the Invention of the Pendulum Made Clocks Much More Accurate"</a>. <i>Applied Mechanics</i>. <b>1</b> (2): 111–122. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="cs1-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3390%2Fapplmech1020008">10.3390/applmech1020008</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Applied+Mechanics&rft.atitle=Friction+and+Dynamics+of+Verge+and+Foliot%3A+How+the+Invention+of+the+Pendulum+Made+Clocks+Much+More+Accurate&rft.volume=1&rft.issue=2&rft.pages=111-122&rft.date=2020&rft_id=info%3Adoi%2F10.3390%2Fapplmech1020008&rft.aulast=Blumenthal&rft.aufirst=Aaron+S.&rft.au=Nosonovsky%2C+Michael&rft_id=%2F%2Fdoi.org%2F10.3390%252Fapplmech1020008&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
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<li id="cite_note-Olmsted-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-Olmsted_18-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFOlmsted1960" class="citation journal cs1">Olmsted, J.W. (1960). "The Voyage of Jean Richer to Acadia in 1670: A Study in the Relations of Science and Navigation under Colbert". <i>Proceedings of the American Philosophical Society</i>. <b>104</b> (6): 612–634. <a href="/enwiki/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="/enwiki//www.jstor.org/stable/985537">985537</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+American+Philosophical+Society&rft.atitle=The+Voyage+of+Jean+Richer+to+Acadia+in+1670%3A+A+Study+in+the+Relations+of+Science+and+Navigation+under+Colbert&rft.volume=104&rft.issue=6&rft.pages=612-634&rft.date=1960&rft_id=%2F%2Fwww.jstor.org%2Fstable%2F985537%23id-name%3DJSTOR&rft.aulast=Olmsted&rft.aufirst=J.W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
</li>
<li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text">See, for example, Port Royal, Jamaica: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFHalley1722" class="citation journal cs1">Halley, Edmond (1722). <a rel="nofollow" class="external text" href="https://archive.org/details/jstor-103607">"Observations on the Eclipse of the Moon, June 18, 1722. and the Longitude of Port Royal in Jamaica"</a>. <i>Philosophical Transactions</i>. <b>32</b> (370–380): 235–236.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions&rft.atitle=Observations+on+the+Eclipse+of+the+Moon%2C+June+18%2C+1722.+and+the+Longitude+of+Port+Royal+in+Jamaica&rft.volume=32&rft.issue=370%E2%80%93380&rft.pages=235-236&rft.date=1722&rft.aulast=Halley&rft.aufirst=Edmond&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fjstor-103607&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span>; Buenos Aires: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFHalley1722" class="citation journal cs1">Halley, Edm. (1722). <a rel="nofollow" class="external text" href="https://archive.org/details/jstor-103565">"The Longitude of Buenos Aires, Determin'd from an Observation Made There by Père Feuillée"</a>. <i>Philosophical Transactions</i>. <b>32</b> (370–380): 2–4.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions&rft.atitle=The+Longitude+of+Buenos+Aires%2C+Determin%27d+from+an+Observation+Made+There+by+P%C3%A8re+Feuill%C3%A9e&rft.volume=32&rft.issue=370%E2%80%93380&rft.pages=2-4&rft.date=1722&rft.aulast=Halley&rft.aufirst=Edm.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fjstor-103565&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span>Santa Catarina, Brazil: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFLeggeAtwell1743" class="citation journal cs1">Legge, Edward; Atwell, Joseph (1743). <a rel="nofollow" class="external text" href="https://archive.org/details/jstor-104132">"Extract of a letter from the Honble Edward Legge, Esq; F. R. S. Captain of his Majesty's ship the Severn, containing an observation of the eclipse of the moon, Dec. 21. 1740. at the Island of St. Catharine on the Coast of Brasil"</a>. <i>Philosophical Transactions</i>. <b>42</b> (462): 18–19.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions&rft.atitle=Extract+of+a+letter+from+the+Honble+Edward+Legge%2C+Esq%3B+F.+R.+S.+Captain+of+his+Majesty%27s+ship+the+Severn%2C+containing+an+observation+of+the+eclipse+of+the+moon%2C+Dec.+21.+1740.+at+the+Island+of+St.+Catharine+on+the+Coast+of+Brasil&rft.volume=42&rft.issue=462&rft.pages=18-19&rft.date=1743&rft.aulast=Legge&rft.aufirst=Edward&rft.au=Atwell%2C+Joseph&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fjstor-104132&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
</li>
<li id="cite_note-Siegel-20"><span class="mw-cite-backlink">^ <a href="#cite_ref-Siegel_20-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Siegel_20-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFSiegel2009" class="citation journal cs1">Siegel, Jonathan R. (2009). "Law and Longitude". <i>Tulane Law Review</i>. <b>84</b>: 1–66.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Tulane+Law+Review&rft.atitle=Law+and+Longitude&rft.volume=84&rft.pages=1-66&rft.date=2009&rft.aulast=Siegel&rft.aufirst=Jonathan+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
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<li id="cite_note-Forbes2006-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-Forbes2006_21-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFForbes2006" class="citation journal cs1">Forbes, Eric Gray (2006). "Tobias Mayer's lunar tables". <i>Annals of Science</i>. <b>22</b> (2): 105–116. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F00033796600203075">10.1080/00033796600203075</a>. <a href="/enwiki/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="/enwiki//www.worldcat.org/issn/0003-3790">0003-3790</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+Science&rft.atitle=Tobias+Mayer%27s+lunar+tables&rft.volume=22&rft.issue=2&rft.pages=105-116&rft.date=2006&rft_id=info%3Adoi%2F10.1080%2F00033796600203075&rft.issn=0003-3790&rft.aulast=Forbes&rft.aufirst=Eric+Gray&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
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<li id="cite_note-Wess2015-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-Wess2015_22-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFWess2015" class="citation book cs1">Wess, Jane (2015). "Navigation and Mathematics: A Match Made in the Heavens?". In Dunn, Richard; Higgitt, Rebekah (eds.). <i>Navigational Enterprises in Europe and its Empires, 1730-1850</i>. London: Palgrave Macmillan UK. pp. 201–222. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1057%2F9781137520647_11">10.1057/9781137520647_11</a>. <a href="/enwiki/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/enwiki/wiki/Special:BookSources/978-1-349-56744-7" title="Special:BookSources/978-1-349-56744-7"><bdi>978-1-349-56744-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Navigation+and+Mathematics%3A+A+Match+Made+in+the+Heavens%3F&rft.btitle=Navigational+Enterprises+in+Europe+and+its+Empires%2C+1730-1850&rft.place=London&rft.pages=201-222&rft.pub=Palgrave+Macmillan+UK&rft.date=2015&rft_id=info%3Adoi%2F10.1057%2F9781137520647_11&rft.isbn=978-1-349-56744-7&rft.aulast=Wess&rft.aufirst=Jane&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
</li>
<li id="cite_note-Littlehales-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-Littlehales_23-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFLittlehales1909" class="citation journal cs1">Littlehales, G.W. (1909). <a rel="nofollow" class="external text" href="https://archive.org/details/jstor-200792">"The Decline of the Lunar Distance for the Determination of the Time and Longitude at"</a>. <i>Bulletin of the American Geographical Society</i>. <b>41</b> (2): 83–86. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F200792">10.2307/200792</a>. <a href="/enwiki/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="/enwiki//www.jstor.org/stable/200792">200792</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+of+the+American+Geographical+Society&rft.atitle=The+Decline+of+the+Lunar+Distance+for+the+Determination+of+the+Time+and+Longitude+at&rft.volume=41&rft.issue=2&rft.pages=83-86&rft.date=1909&rft_id=info%3Adoi%2F10.2307%2F200792&rft_id=%2F%2Fwww.jstor.org%2Fstable%2F200792%23id-name%3DJSTOR&rft.aulast=Littlehales&rft.aufirst=G.W.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fjstor-200792&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
</li>
<li id="cite_note-Walker_1850-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-Walker_1850_24-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFWalker1850" class="citation journal cs1">Walker, Sears C (1850). <a rel="nofollow" class="external text" href="https://archive.org/details/appendix-telegraphic-longitude-the-american-journal-of-science-and-arts">"Report on the experience of the Coast Survey in regard to telegraph operations, for determination of longitude &c"</a>. <i>American Journal of Science and Arts</i>. <b>10</b> (28): 151–160.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Science+and+Arts&rft.atitle=Report+on+the+experience+of+the+Coast+Survey+in+regard+to+telegraph+operations%2C+for+determination+of+longitude+%26c.&rft.volume=10&rft.issue=28&rft.pages=151-160&rft.date=1850&rft.aulast=Walker&rft.aufirst=Sears+C&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fappendix-telegraphic-longitude-the-american-journal-of-science-and-arts&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
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<li id="cite_note-Knox-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-Knox_25-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFKnox1957" class="citation journal cs1">Knox, Robert W. (1957). "Precise Determination of Longitude in the United States". <i>Geographical Review</i>. <b>47</b>: 555–563. <a href="/enwiki/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="/enwiki//www.jstor.org/stable/211865">211865</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Geographical+Review&rft.atitle=Precise+Determination+of+Longitude+in+the+United+States&rft.volume=47&rft.pages=555-563&rft.date=1957&rft_id=%2F%2Fwww.jstor.org%2Fstable%2F211865%23id-name%3DJSTOR&rft.aulast=Knox&rft.aufirst=Robert+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
</li>
<li id="cite_note-Green1883-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-Green1883_26-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFGreenDavisNorris1883" class="citation book cs1">Green, Francis Mathews; Davis, Charles Henry; Norris, John Alexander (1883). <a rel="nofollow" class="external text" href="https://archive.org/details/in.ernet.dli.2015.177254"><i>Telegraphic Determination of Longitudes in Japan, China, and the East Indies: Embracing the Meridians of Yokohama, Nagasaki, Wladiwostok, Shanghai, Amoy, Hong-Kong, Manila, Cape St. James, Singapore, Batavia, and Madras, with the Latitude of the Several Stations</i></a>. Washington: US Hydrographic Office.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Telegraphic+Determination+of+Longitudes+in+Japan%2C+China%2C+and+the+East+Indies%3A+Embracing+the+Meridians+of+Yokohama%2C+Nagasaki%2C+Wladiwostok%2C+Shanghai%2C+Amoy%2C+Hong-Kong%2C+Manila%2C+Cape+St.+James%2C+Singapore%2C+Batavia%2C+and+Madras%2C+with+the+Latitude+of+the+Several+Stations&rft.place=Washington&rft.pub=US+Hydrographic+Office&rft.date=1883&rft.aulast=Green&rft.aufirst=Francis+Mathews&rft.au=Davis%2C+Charles+Henry&rft.au=Norris%2C+John+Alexander&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fin.ernet.dli.2015.177254&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
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<li id="cite_note-Munro1902-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-Munro1902_27-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFMunro1902" class="citation journal cs1">Munro, John (1902). <a rel="nofollow" class="external text" href="https://zenodo.org/record/2080631">"Time-Signals by Wireless Telegraphy"</a>. <i>Nature</i>. <b>66</b> (1713): 416. <a href="/enwiki/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1902Natur..66..416M">1902Natur..66..416M</a>. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F066416d0">10.1038/066416d0</a>. <a href="/enwiki/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="/enwiki//www.worldcat.org/issn/0028-0836">0028-0836</a>. <a href="/enwiki/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4021629">4021629</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Time-Signals+by+Wireless+Telegraphy&rft.volume=66&rft.issue=1713&rft.pages=416&rft.date=1902&rft_id=info%3Adoi%2F10.1038%2F066416d0&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4021629%23id-name%3DS2CID&rft.issn=0028-0836&rft_id=info%3Abibcode%2F1902Natur..66..416M&rft.aulast=Munro&rft.aufirst=John&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F2080631&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
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<li id="cite_note-Hutchnson-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hutchnson_28-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFHutchinson1908" class="citation journal cs1">Hutchinson, D.L. (1908). <a rel="nofollow" class="external text" href="https://archive.org/details/hutchinson-1908-proceedingstrans-32roya">"Wireless Time Signals from the St. John Observatory of the Canadian Meteorological Service"</a>. <i>Proceedings and Transactions of the Royal Society of Canada</i>. Ser. 3 Vol. 2: 153–154.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+and+Transactions+of+the+Royal+Society+of+Canada&rft.atitle=Wireless+Time+Signals+from+the+St.+John+Observatory+of+the+Canadian+Meteorological+Service.&rft.volume=Ser.+3+Vol.+2&rft.pages=153-154&rft.date=1908&rft.aulast=Hutchinson&rft.aufirst=D.L.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhutchinson-1908-proceedingstrans-32roya&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
</li>
<li id="cite_note-Lockyer1913-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-Lockyer1913_29-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFLockyer1913" class="citation journal cs1">Lockyer, William J. S. (1913). <a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F091033b0">"International Time and Weather Radio-Telegraphic Signals"</a>. <i>Nature</i>. <b>91</b> (2263): 33–36. <a href="/enwiki/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1913Natur..91...33L">1913Natur..91...33L</a>. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="cs1-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F091033b0">10.1038/091033b0</a></span>. <a href="/enwiki/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="/enwiki//www.worldcat.org/issn/0028-0836">0028-0836</a>. <a href="/enwiki/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:3977506">3977506</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=International+Time+and+Weather+Radio-Telegraphic+Signals&rft.volume=91&rft.issue=2263&rft.pages=33-36&rft.date=1913&rft_id=info%3Adoi%2F10.1038%2F091033b0&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A3977506%23id-name%3DS2CID&rft.issn=0028-0836&rft_id=info%3Abibcode%2F1913Natur..91...33L&rft.aulast=Lockyer&rft.aufirst=William+J.+S.&rft_id=%2F%2Fdoi.org%2F10.1038%252F091033b0&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
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<li id="cite_note-Zimmerman-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-Zimmerman_30-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFZimmerman" class="citation web cs1">Zimmerman, Arthur E. <a rel="nofollow" class="external text" href="https://www.antiquewireless.org/wp-content/uploads/50-the_first_wireless_time_signals_to_ships_at_sea.pdf">"The first wireless time signals to ships at sea"</a> <span class="cs1-format">(PDF)</span>. <i>antiquewireless.org</i>. Antique Wireless Association<span class="reference-accessdate">. Retrieved <span class="nowrap">9 July</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=antiquewireless.org&rft.atitle=The+first+wireless+time+signals+to+ships+at+sea&rft.aulast=Zimmerman&rft.aufirst=Arthur+E.&rft_id=https%3A%2F%2Fwww.antiquewireless.org%2Fwp-content%2Fuploads%2F50-the_first_wireless_time_signals_to_ships_at_sea.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
</li>
<li id="cite_note-Pierce-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-Pierce_31-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFPierce1946" class="citation journal cs1">Pierce, J.A. (1946). "An introduction to Loran". <i>Proceedings of the IRE</i>. <b>34</b> (5): 216–234. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2FJRPROC.1946.234564">10.1109/JRPROC.1946.234564</a>. <a href="/enwiki/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:20739091">20739091</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+IRE&rft.atitle=An+introduction+to+Loran&rft.volume=34&rft.issue=5&rft.pages=216-234&rft.date=1946&rft_id=info%3Adoi%2F10.1109%2FJRPROC.1946.234564&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A20739091%23id-name%3DS2CID&rft.aulast=Pierce&rft.aufirst=J.A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
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<li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090929121405/http://www.colorado.edu/geography/gcraft/notes/datum/gif/llhxyz.gif">"Coordinate Conversion"</a>. <i>colorado.edu</i>. Archived from <a rel="nofollow" class="external text" href="http://www.colorado.edu/geography/gcraft/notes/datum/gif/llhxyz.gif">the original</a> on 29 September 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">14 March</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=colorado.edu&rft.atitle=Coordinate+Conversion&rft_id=http%3A%2F%2Fwww.colorado.edu%2Fgeography%2Fgcraft%2Fnotes%2Fdatum%2Fgif%2Fllhxyz.gif&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
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<li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text">"λ = Longitude east of Greenwich (for longitude west of Greenwich, use a minus sign)."<br />John P. Snyder, <i><a rel="nofollow" class="external text" href="https://pubs.er.usgs.gov/usgspubs/pp/pp1395">Map Projections, A Working Manual</a></i>, <a href="/enwiki/wiki/USGS" class="mw-redirect" title="USGS">USGS</a> Professional Paper 1395, page ix</span>
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<li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.esrl.noaa.gov/gmd/grad/solcalc/sunrise.html">NOAA ESRL Sunrise/Sunset Calculator</a> (deprecated). <i><a href="/enwiki/wiki/Earth_System_Research_Laboratory" title="Earth System Research Laboratory">Earth System Research Laboratory</a></i>. Retrieved October 18, 2019.</span>
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<li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFRead_HH,_Watson_Janet1975" class="citation book cs1">Read HH, Watson Janet (1975). <i>Introduction to Geology</i>. New York: Halsted. pp. 13–15.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Geology&rft.place=New+York&rft.pages=13-15&rft.pub=Halsted&rft.date=1975&rft.au=Read+HH%2C+Watson+Janet&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
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<li id="cite_note-osborne-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-osborne_36-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFOsborne2013" class="citation book cs1">Osborne, Peter (2013). "Chapter 5: The geometry of the ellipsoid". <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160509180529/http://www.mercator99.webspace.virginmedia.com/mercator.pdf"><i>The Mercator Projections: The Normal and Transverse Mercator Projections on the Sphere and the Ellipsoid with Full Derivations of all Formulae</i></a> <span class="cs1-format">(PDF)</span>. Edinburgh. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.5281%2Fzenodo.35392">10.5281/zenodo.35392</a>. Archived from <a rel="nofollow" class="external text" href="http://www.mercator99.webspace.virginmedia.com/mercator.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2016-05-09<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-01-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+5%3A+The+geometry+of+the+ellipsoid&rft.btitle=The+Mercator+Projections%3A+The+Normal+and+Transverse+Mercator+Projections+on+the+Sphere+and+the+Ellipsoid+with+Full+Derivations+of+all+Formulae&rft.place=Edinburgh&rft.date=2013&rft_id=info%3Adoi%2F10.5281%2Fzenodo.35392&rft.aulast=Osborne&rft.aufirst=Peter&rft_id=http%3A%2F%2Fwww.mercator99.webspace.virginmedia.com%2Fmercator.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
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<li id="cite_note-rapp-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-rapp_37-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFRapp1991" class="citation book cs1">Rapp, Richard H. (April 1991). "Chapter 3: Properties of the Ellipsoid". <i>Geometric Geodesy Part I</i>. Columbus, Ohio.: Department of Geodetic Science and Surveying, Ohio State University. <a href="/enwiki/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<a rel="nofollow" class="external text" href="/enwiki//hdl.handle.net/1811%2F24333">1811/24333</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Chapter+3%3A+Properties+of+the+Ellipsoid&rft.btitle=Geometric+Geodesy+Part+I&rft.place=Columbus%2C+Ohio.&rft.pub=Department+of+Geodetic+Science+and+Surveying%2C+Ohio+State+University&rft.date=1991-04&rft_id=info%3Ahdl%2F1811%2F24333&rft.aulast=Rapp&rft.aufirst=Richard+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
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<li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.esa.int/SPECIALS/Mars_Express/SEM0VQV4QWD_0.html">Where is zero degrees longitude on Mars?</a> – Copyright 2000 – 2010 © European Space Agency. All rights reserved.</span>
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<li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text">Davies, M. E., and R. A. Berg, "Preliminary Control Net of Mars,"Journal of Geophysical Research, Vol. 76, No. 2, pps. 373-393, January 10, 1971.</span>
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<li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text">Davies, M. E., "Surface Coordinates and Cartography of Mercury," Journal of Geophysical Research, Vol. 80, No. 17, June 10, 1975.</span>
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<li id="cite_note-ArchinalA’Hearn2010-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-ArchinalA’Hearn2010_41-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFArchinalA'HearnBowellConrad2010" class="citation journal cs1">Archinal, Brent A.; A'Hearn, Michael F.; Bowell, Edward L.; Conrad, Albert R.; et al. (2010). "Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2009". <i>Celestial Mechanics and Dynamical Astronomy</i>. <b>109</b> (2): 101–135. <a href="/enwiki/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011CeMDA.109..101A">2011CeMDA.109..101A</a>. <a href="/enwiki/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs10569-010-9320-4">10.1007/s10569-010-9320-4</a>. <a href="/enwiki/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="/enwiki//www.worldcat.org/issn/0923-2958">0923-2958</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Celestial+Mechanics+and+Dynamical+Astronomy&rft.atitle=Report+of+the+IAU+Working+Group+on+Cartographic+Coordinates+and+Rotational+Elements%3A+2009&rft.volume=109&rft.issue=2&rft.pages=101-135&rft.date=2010&rft.issn=0923-2958&rft_id=info%3Adoi%2F10.1007%2Fs10569-010-9320-4&rft_id=info%3Abibcode%2F2011CeMDA.109..101A&rft.aulast=Archinal&rft.aufirst=Brent+A.&rft.au=A%27Hearn%2C+Michael+F.&rft.au=Bowell%2C+Edward+L.&rft.au=Conrad%2C+Albert+R.&rft.au=Consolmagno%2C+Guy+J.&rft.au=Courtin%2C+R%C3%A9gis&rft.au=Fukushima%2C+Toshio&rft.au=Hestroffer%2C+Daniel&rft.au=Hilton%2C+James+L.&rft.au=Krasinsky%2C+George+A.&rft.au=Neumann%2C+Gregory+A.&rft.au=Oberst%2C+J%C3%BCrgen&rft.au=Seidelmann%2C+P.+Kenneth&rft.au=Stooke%2C+Philip+J.&rft.au=Tholen%2C+David+J.&rft.au=Thomas%2C+Peter+C.&rft.au=Williams%2C+Iwan+P.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
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<li id="cite_note-usgs-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-usgs_42-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20111024101856/http://astrogeology.usgs.gov/Projects/WGCCRE/constants/iau2000_table1.html">"USGS Astrogeology: Rotation and pole position for the Sun and planets (IAU WGCCRE)"</a>. Archived from <a rel="nofollow" class="external text" href="https://astrogeology.usgs.gov/Projects/WGCCRE/constants/iau2000_table1.html">the original</a> on October 24, 2011<span class="reference-accessdate">. Retrieved <span class="nowrap">October 22,</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=USGS+Astrogeology%3A+Rotation+and+pole+position+for+the+Sun+and+planets+%28IAU+WGCCRE%29&rft_id=https%3A%2F%2Fastrogeology.usgs.gov%2FProjects%2FWGCCRE%2Fconstants%2Fiau2000_table1.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALongitude" class="Z3988"></span></span>
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<li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.cfa.harvard.edu/image_archive/2007/31/lores.jpg">First map of extraterrestrial planet</a> – Center of Astrophysics.</span>
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</ol></div></div>
<h2><span class="mw-headline" id="External_links">External links</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/enwiki/w/index.php?title=Longitude&action=edit&section=8" title="Edit section: External links">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<div role="navigation" aria-labelledby="sister-projects" class="metadata plainlinks sistersitebox plainlist mbox-small" style="border:1px solid #aaa;padding:0;background:#f9f9f9"><div style="padding:0.75em 0;text-align:center"><b style="display:block">Longitude</b>at Wikipedia's <a href="/enwiki/wiki/Wikipedia:Wikimedia_sister_projects" title="Wikipedia:Wikimedia sister projects"><span id="sister-projects">sister projects</span></a></div><ul style="border-top:1px solid #aaa;padding:0.75em 0;width:217px;margin:0 auto"><li style="min-height:31px"><span style="display:inline-block;width:31px;line-height:31px;vertical-align:middle;text-align:center"><img alt="" src="/upwiki/wikipedia/en/thumb/0/06/Wiktionary-logo-v2.svg/27px-Wiktionary-logo-v2.svg.png" decoding="async" width="27" height="27" style="vertical-align: middle" srcset="/upwiki/wikipedia/en/thumb/0/06/Wiktionary-logo-v2.svg/41px-Wiktionary-logo-v2.svg.png 1.5x, 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href="https://commons.wikimedia.org/wiki/Category:Longitudes" class="extiw" title="c:Category:Longitudes">Media</a> from Wikimedia Commons</span></li><li style="min-height:31px"><span style="display:inline-block;width:31px;line-height:31px;vertical-align:middle;text-align:center"><img alt="" src="/upwiki/wikipedia/commons/thumb/2/24/Wikinews-logo.svg/27px-Wikinews-logo.svg.png" decoding="async" width="27" height="15" style="vertical-align: middle" srcset="/upwiki/wikipedia/commons/thumb/2/24/Wikinews-logo.svg/41px-Wikinews-logo.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/2/24/Wikinews-logo.svg/54px-Wikinews-logo.svg.png 2x" data-file-width="759" data-file-height="415" /></span><span style="display:inline-block;margin-left:4px;width:182px;vertical-align:middle"><a href="https://en.wikinews.org/wiki/Special:Search/Longitude" class="extiw" title="n:Special:Search/Longitude">News</a> from Wikinews</span></li><li style="min-height:31px"><span style="display:inline-block;width:31px;line-height:31px;vertical-align:middle;text-align:center"><img alt="" src="/upwiki/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/23px-Wikiquote-logo.svg.png" decoding="async" width="23" height="27" style="vertical-align: middle" srcset="/upwiki/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/35px-Wikiquote-logo.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/46px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></span><span style="display:inline-block;margin-left:4px;width:182px;vertical-align:middle"><a href="https://en.wikiquote.org/wiki/Special:Search/Longitude" class="extiw" title="q:Special:Search/Longitude">Quotations</a> from Wikiquote</span></li><li style="min-height:31px"><span style="display:inline-block;width:31px;line-height:31px;vertical-align:middle;text-align:center"><img alt="" src="/upwiki/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/26px-Wikisource-logo.svg.png" decoding="async" width="26" height="27" style="vertical-align: middle" srcset="/upwiki/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/39px-Wikisource-logo.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/51px-Wikisource-logo.svg.png 2x" data-file-width="410" data-file-height="430" /></span><span style="display:inline-block;margin-left:4px;width:182px;vertical-align:middle"><a href="https://en.wikisource.org/wiki/Special:Search/Longitude" class="extiw" title="s:Special:Search/Longitude">Texts</a> from Wikisource</span></li><li style="min-height:31px"><span style="display:inline-block;width:31px;line-height:31px;vertical-align:middle;text-align:center"><img alt="" src="/upwiki/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/27px-Wikibooks-logo.svg.png" decoding="async" width="27" height="27" style="vertical-align: middle" srcset="/upwiki/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/41px-Wikibooks-logo.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/54px-Wikibooks-logo.svg.png 2x" data-file-width="300" data-file-height="300" /></span><span style="display:inline-block;margin-left:4px;width:182px;vertical-align:middle"><a href="https://en.wikibooks.org/wiki/Special:Search/Longitude" class="extiw" title="b:Special:Search/Longitude">Textbooks</a> from Wikibooks</span></li><li style="min-height:31px"><span style="display:inline-block;width:31px;line-height:31px;vertical-align:middle;text-align:center"><img alt="" src="/upwiki/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/27px-Wikiversity_logo_2017.svg.png" decoding="async" width="27" height="22" style="vertical-align: middle" srcset="/upwiki/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/41px-Wikiversity_logo_2017.svg.png 1.5x, /upwiki/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/54px-Wikiversity_logo_2017.svg.png 2x" data-file-width="626" data-file-height="512" /></span><span style="display:inline-block;margin-left:4px;width:182px;vertical-align:middle"><a href="https://en.wikiversity.org/wiki/Special:Search/Longitude" class="extiw" title="v:Special:Search/Longitude">Resources</a> from Wikiversity</span></li></ul></div>
<ul><li><a rel="nofollow" class="external text" href="http://jan.ucc.nau.edu/~cvm/latlon_find_location.html">Resources for determining your latitude and longitude</a></li>
<li><a rel="nofollow" class="external text" href="http://www.hnsky.org/iau-iag.htm">IAU/IAG Working Group On Cartographic Coordinates and Rotational Elements of the Planets and Satellites</a></li>
<li><a rel="nofollow" class="external text" href="http://entertainment.timesonline.co.uk/tol/arts_and_entertainment/the_tls/article5136819.ece">"Longitude forged"</a>: an essay exposing a hoax solution to the problem of calculating longitude, undetected in Dava Sobel's Longitude, from <a rel="nofollow" class="external text" href="http://www.the-tls.co.uk">TLS</a>, November 12, 2008.</li>
<li><a rel="nofollow" class="external text" href="http://cudl.lib.cam.ac.uk/collections/longitude">Board of Longitude Collection, Cambridge Digital Library</a> – complete digital version of the Board's archive</li>
<li><a rel="nofollow" class="external text" href="http://www.thegpscoordinates.com">Longitude And Latitude Of Points of Interest</a></li>
<li><a rel="nofollow" class="external text" href="http://www.csgnetwork.com/degreelenllavcalc.html">Length Of A Degree Of Latitude And Longitude Calculator</a></li>
<li><a rel="nofollow" class="external text" href="http://articles.adsabs.harvard.edu/full/seri/RA.../0002//0000185.000.html">Esame critico intorno alla scoperta di Vespucci ...</a></li>
<li><a rel="nofollow" class="external text" href="https://exhibits.museogalileo.it/waldseemuller/ewal.php?c%5B%5D=54117">A land beyond the stars - Museo Galileo</a></li></ul>
<div role="navigation" class="navbox" aria-labelledby="Map_projection" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r992953826"/><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/enwiki/wiki/Template:Map_projections" title="Template:Map projections"><abbr title="View this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">v</abbr></a></li><li class="nv-talk"><a href="/enwiki/wiki/Template_talk:Map_projections" title="Template talk:Map projections"><abbr title="Discuss this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">t</abbr></a></li><li class="nv-edit"><a class="external text" href="https://en.wikipedia.org/enwiki/w/index.php?title=Template:Map_projections&action=edit"><abbr title="Edit this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">e</abbr></a></li></ul></div><div id="Map_projection" style="font-size:114%;margin:0 4em"><a href="/enwiki/wiki/Map_projection" title="Map projection">Map projection</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div id="*_History_*_List_*_Portal">
<ul><li><a href="/enwiki/wiki/History_of_cartography" title="History of cartography">History</a></li>
<li><a href="/enwiki/wiki/List_of_map_projections" title="List of map projections">List</a></li>
<li><a href="/enwiki/wiki/Portal:Maps" title="Portal:Maps">Portal</a></li></ul>
</div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="By_surface" style="font-size:114%;margin:0 4em"><a href="/enwiki/wiki/Map_projection#Projections_by_surface" title="Map projection">By surface</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Cylindrical" title="Map projection">Cylindrical</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="/enwiki/wiki/Mercator_projection" title="Mercator projection">Mercator</a>-conformal</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Gauss%E2%80%93Kr%C3%BCger_coordinate_system" title="Gauss–Krüger coordinate system">Gauss–Krüger</a></li>
<li><a href="/enwiki/wiki/Transverse_Mercator_projection" title="Transverse Mercator projection">Transverse Mercator</a></li>
<li><a href="/enwiki/wiki/Oblique_Mercator_projection" title="Oblique Mercator projection">Oblique Mercator</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="/enwiki/wiki/Cylindrical_equal-area_projection" title="Cylindrical equal-area projection">Equal-area</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Balthasart</a></li>
<li><a href="/enwiki/wiki/Behrmann_projection" title="Behrmann projection">Behrmann</a></li>
<li><a href="/enwiki/wiki/Gall%E2%80%93Peters_projection" title="Gall–Peters projection">Gall–Peters</a></li>
<li><a href="/enwiki/wiki/Hobo%E2%80%93Dyer_projection" title="Hobo–Dyer projection">Hobo–Dyer</a></li>
<li><a href="/enwiki/wiki/Lambert_cylindrical_equal-area_projection" title="Lambert cylindrical equal-area projection">Lambert</a></li>
<li><a href="/enwiki/wiki/Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Smyth equal-surface</a></li>
<li><a href="/enwiki/wiki/Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Trystan Edwards</a></li></ul>
</div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Cassini_projection" title="Cassini projection">Cassini</a></li>
<li><a href="/enwiki/wiki/Central_cylindrical_projection" title="Central cylindrical projection">Central</a></li>
<li><a href="/enwiki/wiki/Equirectangular_projection" title="Equirectangular projection">Equirectangular</a></li>
<li><a href="/enwiki/wiki/Gall_stereographic_projection" title="Gall stereographic projection">Gall stereographic</a></li>
<li><a href="/enwiki/wiki/Gall_isographic_projection" title="Gall isographic projection">Gall isographic</a></li>
<li><a href="/enwiki/wiki/Miller_cylindrical_projection" title="Miller cylindrical projection">Miller</a></li>
<li><a href="/enwiki/wiki/Space-oblique_Mercator_projection" title="Space-oblique Mercator projection">Space-oblique Mercator</a></li>
<li><a href="/enwiki/wiki/Web_Mercator_projection" title="Web Mercator projection">Web Mercator</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Pseudocylindrical" title="Map projection">Pseudocylindrical</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Eckert_II_projection" title="Eckert II projection">Eckert II</a></li>
<li><a href="/enwiki/wiki/Eckert_IV_projection" title="Eckert IV projection">Eckert IV</a></li>
<li><a href="/enwiki/wiki/Eckert_VI_projection" title="Eckert VI projection">Eckert VI</a></li>
<li><a href="/enwiki/wiki/Equal_Earth_projection" title="Equal Earth projection">Equal Earth</a></li>
<li><a href="/enwiki/wiki/Goode_homolosine_projection" title="Goode homolosine projection">Goode homolosine</a></li>
<li><a href="/enwiki/wiki/Kavrayskiy_VII_projection" title="Kavrayskiy VII projection">Kavrayskiy VII</a></li>
<li><a href="/enwiki/wiki/Mollweide_projection" title="Mollweide projection">Mollweide</a></li>
<li><a href="/enwiki/wiki/Sinusoidal_projection" title="Sinusoidal projection">Sinusoidal</a></li>
<li><a href="/enwiki/wiki/Tobler_hyperelliptical_projection" title="Tobler hyperelliptical projection">Tobler hyperelliptical</a></li>
<li><a href="/enwiki/wiki/Wagner_VI_projection" title="Wagner VI projection">Wagner VI</a></li>
<li><a href="/enwiki/wiki/Winkel_projection" title="Winkel projection">Winkel I and II</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Conical" title="Map projection">Conical</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Albers_projection" title="Albers projection">Albers</a></li>
<li><a href="/enwiki/wiki/Equidistant_conic_projection" title="Equidistant conic projection">Equidistant</a></li>
<li><a href="/enwiki/wiki/Lambert_conformal_conic_projection" title="Lambert conformal conic projection">Lambert conformal</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Pseudoconical" title="Map projection">Pseudoconical</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Bonne_projection" title="Bonne projection">Bonne</a></li>
<li><a href="/enwiki/wiki/Bottomley_projection" title="Bottomley projection">Bottomley</a></li>
<li><a href="/enwiki/wiki/Polyconic_projection_class" title="Polyconic projection class">Polyconic</a>
<ul><li><a href="/enwiki/wiki/American_polyconic_projection" title="American polyconic projection">American</a></li>
<li><a href="/enwiki/wiki/Latitudinally_equal-differential_polyconic_projection" title="Latitudinally equal-differential polyconic projection">Chinese</a></li></ul></li>
<li><a href="/enwiki/wiki/Werner_projection" title="Werner projection">Werner</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Azimuthal" title="Map projection">Azimuthal<br /><style data-mw-deduplicate="TemplateStyles:r886047488">'"`UNIQ--templatestyles-000000A2-QINU`"'</style><span class="nobold">(planar)</span></a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="General_perspective" scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="/enwiki/wiki/General_Perspective_projection" title="General Perspective projection">General perspective</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Gnomonic_projection" title="Gnomonic projection">Gnomonic</a></li>
<li><a href="/enwiki/wiki/Orthographic_map_projection" title="Orthographic map projection">Orthographic</a></li>
<li><a href="/enwiki/wiki/Stereographic_projection_in_cartography" title="Stereographic projection in cartography">Stereographic</a></li></ul>
</div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Azimuthal_equidistant_projection" title="Azimuthal equidistant projection">Equidistant</a></li>
<li><a href="/enwiki/wiki/Lambert_azimuthal_equal-area_projection" title="Lambert azimuthal equal-area projection">Lambert equal-area</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Pseudoazimuthal" title="Map projection">Pseudoazimuthal</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Aitoff_projection" title="Aitoff projection">Aitoff</a></li>
<li><a href="/enwiki/wiki/Hammer_projection" title="Hammer projection">Hammer</a></li>
<li><a href="/enwiki/wiki/Wiechel_projection" title="Wiechel projection">Wiechel</a></li>
<li><a href="/enwiki/wiki/Winkel_tripel_projection" title="Winkel tripel projection">Winkel tripel</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="By_metric" style="font-size:114%;margin:0 4em"><a href="/enwiki/wiki/Map_projection#Projections_by_preservation_of_a_metric_property" title="Map projection">By metric</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Conformal" title="Map projection">Conformal</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Adams_hemisphere-in-a-square_projection" title="Adams hemisphere-in-a-square projection">Adams hemisphere-in-a-square</a></li>
<li><a href="/enwiki/wiki/Gauss%E2%80%93Kr%C3%BCger_coordinate_system" title="Gauss–Krüger coordinate system">Gauss–Krüger</a></li>
<li><a href="/enwiki/wiki/Guyou_hemisphere-in-a-square_projection" title="Guyou hemisphere-in-a-square projection">Guyou hemisphere-in-a-square</a></li>
<li><a href="/enwiki/wiki/Lambert_conformal_conic_projection" title="Lambert conformal conic projection">Lambert conformal conic</a></li>
<li><a href="/enwiki/wiki/Mercator_projection" title="Mercator projection">Mercator</a></li>
<li><a href="/enwiki/wiki/Peirce_quincuncial_projection" title="Peirce quincuncial projection">Peirce quincuncial</a></li>
<li><a href="/enwiki/wiki/Stereographic_projection" title="Stereographic projection">Stereographic</a></li>
<li><a href="/enwiki/wiki/Transverse_Mercator_projection" title="Transverse Mercator projection">Transverse Mercator</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Equal-area" title="Map projection">Equal-area</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="/enwiki/wiki/Bonne_projection" title="Bonne projection">Bonne</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Sinusoidal_projection" title="Sinusoidal projection">Sinusoidal</a></li>
<li><a href="/enwiki/wiki/Werner_projection" title="Werner projection">Werner</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="/enwiki/wiki/Bottomley_projection" title="Bottomley projection">Bottomley</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Sinusoidal_projection" title="Sinusoidal projection">Sinusoidal</a></li>
<li><a href="/enwiki/wiki/Werner_projection" title="Werner projection">Werner</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="/enwiki/wiki/Cylindrical_equal-area_projection" title="Cylindrical equal-area projection">Cylindrical</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Balthasart</a></li>
<li><a href="/enwiki/wiki/Behrmann_projection" title="Behrmann projection">Behrmann</a></li>
<li><a href="/enwiki/wiki/Gall%E2%80%93Peters_projection" title="Gall–Peters projection">Gall–Peters</a></li>
<li><a href="/enwiki/wiki/Hobo%E2%80%93Dyer_projection" title="Hobo–Dyer projection">Hobo–Dyer</a></li>
<li><a href="/enwiki/wiki/Lambert_cylindrical_equal-area_projection" title="Lambert cylindrical equal-area projection">Lambert cylindrical equal-area</a></li>
<li><a href="/enwiki/wiki/Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Smyth equal-surface</a></li>
<li><a href="/enwiki/wiki/Cylindrical_equal-area_projection#Discussion" title="Cylindrical equal-area projection">Trystan Edwards</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="/enwiki/wiki/Tobler_hyperelliptical_projection" title="Tobler hyperelliptical projection">Tobler hyperelliptical</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Collignon_projection" title="Collignon projection">Collignon</a></li>
<li><a href="/enwiki/wiki/Mollweide_projection" title="Mollweide projection">Mollweide</a></li></ul>
</div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Albers_projection" title="Albers projection">Albers</a></li>
<li><a href="/enwiki/wiki/Hammer_projection#Briesemeister" title="Hammer projection">Briesemeister</a></li>
<li><a href="/enwiki/wiki/Eckert_II_projection" title="Eckert II projection">Eckert II</a></li>
<li><a href="/enwiki/wiki/Eckert_IV_projection" title="Eckert IV projection">Eckert IV</a></li>
<li><a href="/enwiki/wiki/Eckert_VI_projection" title="Eckert VI projection">Eckert VI</a></li>
<li><a href="/enwiki/wiki/Equal_Earth_projection" title="Equal Earth projection">Equal Earth</a></li>
<li><a href="/enwiki/wiki/Goode_homolosine_projection" title="Goode homolosine projection">Goode homolosine</a></li>
<li><a href="/enwiki/wiki/Hammer_projection" title="Hammer projection">Hammer</a></li>
<li><a href="/enwiki/wiki/Lambert_azimuthal_equal-area_projection" title="Lambert azimuthal equal-area projection">Lambert azimuthal equal-area</a></li>
<li><a href="/enwiki/wiki/Quadrilateralized_spherical_cube" title="Quadrilateralized spherical cube">Quadrilateralized spherical cube</a></li>
<li><a href="/enwiki/wiki/Strebe_1995_projection" title="Strebe 1995 projection">Strebe 1995</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Equidistant" title="Map projection">Equidistant in<br />some aspect</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Equidistant_conic_projection" title="Equidistant conic projection">Conic</a></li>
<li><a href="/enwiki/wiki/Equirectangular_projection" title="Equirectangular projection">Equirectangular</a></li>
<li><a href="/enwiki/wiki/Sinusoidal_projection" title="Sinusoidal projection">Sinusoidal</a></li>
<li><a href="/enwiki/wiki/Two-point_equidistant_projection" title="Two-point equidistant projection">Two-point</a></li>
<li><a href="/enwiki/wiki/Werner_projection" title="Werner projection">Werner</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Gnomonic" title="Map projection">Gnomonic</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Gnomonic_projection" title="Gnomonic projection">Gnomonic</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Rhumb_line" title="Map projection">Loxodromic</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Loximuthal_projection" title="Loximuthal projection">Loximuthal</a></li>
<li><a href="/enwiki/wiki/Mercator_projection" title="Mercator projection">Mercator</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Retroazimuthal" title="Map projection">Retroazimuthal</a><br /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r886047488"/><span class="nobold">(Mecca or Qibla)</span></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Craig_retroazimuthal_projection" title="Craig retroazimuthal projection">Craig</a></li>
<li><a href="/enwiki/wiki/Hammer_retroazimuthal_projection" title="Hammer retroazimuthal projection">Hammer</a></li>
<li><a href="/enwiki/wiki/Littrow_projection" title="Littrow projection">Littrow</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="By_construction" style="font-size:114%;margin:0 4em"><a href="/enwiki/wiki/Map_projection#Classification" title="Map projection">By construction</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Compromise_projections" title="Map projection">Compromise</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Chamberlin_trimetric_projection" title="Chamberlin trimetric projection">Chamberlin trimetric</a></li>
<li><a href="/enwiki/wiki/Kavrayskiy_VII_projection" title="Kavrayskiy VII projection">Kavrayskiy VII</a></li>
<li><a href="/enwiki/wiki/Miller_cylindrical_projection" title="Miller cylindrical projection">Miller cylindrical</a></li>
<li><a href="/enwiki/wiki/Natural_Earth_projection" title="Natural Earth projection">Natural Earth</a></li>
<li><a href="/enwiki/wiki/Robinson_projection" title="Robinson projection">Robinson</a></li>
<li><a href="/enwiki/wiki/Van_der_Grinten_projection" title="Van der Grinten projection">Van der Grinten</a></li>
<li><a href="/enwiki/wiki/Wagner_VI_projection" title="Wagner VI projection">Wagner VI</a></li>
<li><a href="/enwiki/wiki/Winkel_tripel_projection" title="Winkel tripel projection">Winkel tripel</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Hybrid" title="Map projection">Hybrid</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Goode_homolosine_projection" title="Goode homolosine projection">Goode homolosine</a></li>
<li><a href="/enwiki/wiki/HEALPix" title="HEALPix">HEALPix</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Perspective_projections" title="Map projection">Perspective</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Planar" scope="row" class="navbox-group" style="width:1%;font-weight: normal;"><a href="/enwiki/wiki/General_Perspective_projection" title="General Perspective projection">Planar</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Gnomonic_projection" title="Gnomonic projection">Gnomonic</a></li>
<li><a href="/enwiki/wiki/Orthographic_map_projection" title="Orthographic map projection">Orthographic</a></li>
<li><a href="/enwiki/wiki/Stereographic_projection" title="Stereographic projection">Stereographic</a></li></ul>
</div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Central_cylindrical_projection" title="Central cylindrical projection">Central cylindrical</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Map_projection#Polyhedral" title="Map projection">Polyhedral</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/AuthaGraph_projection" title="AuthaGraph projection">AuthaGraph</a></li>
<li><a href="/enwiki/wiki/Bernard_J._S._Cahill" title="Bernard J. S. Cahill">Cahill Butterfly</a></li>
<li><a href="/enwiki/wiki/Cahill%E2%80%93Keyes_projection" title="Cahill–Keyes projection">Cahill–Keyes M-shape</a></li>
<li><a href="/enwiki/wiki/Dymaxion_map" title="Dymaxion map">Dymaxion</a></li>
<li><a href="/enwiki/wiki/Snyder_equal-area_projection" title="Snyder equal-area projection">ISEA</a></li>
<li><a href="/enwiki/wiki/Quadrilateralized_spherical_cube" title="Quadrilateralized spherical cube">Quadrilateralized spherical cube</a></li>
<li><a href="/enwiki/wiki/Waterman_butterfly_projection" title="Waterman butterfly projection">Waterman butterfly</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks mw-collapsible mw-collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="See_also" style="font-size:114%;margin:0 4em">See also</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Interruption_(map_projection)" title="Interruption (map projection)">Interruption (map projection)</a></li>
<li><a href="/enwiki/wiki/Latitude" title="Latitude">Latitude</a></li>
<li><a class="mw-selflink selflink">Longitude</a></li>
<li><a href="/enwiki/wiki/Tissot%27s_indicatrix" title="Tissot's indicatrix">Tissot's indicatrix</a></li>
<li><a href="/enwiki/wiki/Map_projection_of_the_tri-axial_ellipsoid" title="Map projection of the tri-axial ellipsoid">Map projection of the tri-axial ellipsoid</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr></tbody></table></div>
<div role="navigation" class="navbox" aria-labelledby="Time_signal_stations" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r992953826"/><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/enwiki/wiki/Template:Time_signal_stations" title="Template:Time signal stations"><abbr title="View this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">v</abbr></a></li><li class="nv-talk"><a href="/enwiki/wiki/Template_talk:Time_signal_stations" title="Template talk:Time signal stations"><abbr title="Discuss this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">t</abbr></a></li><li class="nv-edit"><a class="external text" href="https://en.wikipedia.org/enwiki/w/index.php?title=Template:Time_signal_stations&action=edit"><abbr title="Edit this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">e</abbr></a></li></ul></div><div id="Time_signal_stations" style="font-size:114%;margin:0 4em"><a href="/enwiki/wiki/Radio_clock" title="Radio clock">Time signal stations</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Longwave" title="Longwave">Longwave</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/BPC_(time_signal)" title="BPC (time signal)">BPC</a></li>
<li><a href="/enwiki/wiki/BPL_(time_service)" title="BPL (time service)">BPL</a></li>
<li><a href="/enwiki/wiki/BSF_(time_service)" title="BSF (time service)">BSF</a></li>
<li><a href="/enwiki/wiki/DCF77" title="DCF77">DCF77</a></li>
<li><a href="/enwiki/wiki/JJY" title="JJY">JJY</a></li>
<li><a href="/enwiki/wiki/RBU_(radio_station)" title="RBU (radio station)">RBU</a></li>
<li><a href="/enwiki/wiki/Beta_(time_signal)" title="Beta (time signal)">RJH (Beta)</a></li>
<li>RNS (CHAYKA)</li>
<li><a href="/enwiki/wiki/RTZ_(radio_station)" title="RTZ (radio station)">RTZ</a></li>
<li><a href="/enwiki/wiki/Time_from_NPL_(MSF)" title="Time from NPL (MSF)">MSF</a></li>
<li><a href="/enwiki/wiki/TDF_time_signal" title="TDF time signal">TDF</a></li>
<li><a href="/enwiki/wiki/WWVB" title="WWVB">WWVB</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/High_frequency" title="High frequency">Shortwave</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/BPM_(time_service)" title="BPM (time service)">BPM</a></li>
<li><a href="/enwiki/wiki/CHU_(radio_station)" title="CHU (radio station)">CHU</a></li>
<li><a href="/enwiki/wiki/ROA_Time" title="ROA Time">EBC</a></li>
<li><a href="/enwiki/wiki/HD2IOA" title="HD2IOA">HD2IOA</a></li>
<li><a href="/enwiki/wiki/HLA_(radio_station)" title="HLA (radio station)">HLA</a></li>
<li><a href="/enwiki/wiki/JN53DV" title="JN53DV">JN53DV</a></li>
<li><a href="/enwiki/w/index.php?title=LOL_(radio_station)&action=edit&redlink=1" class="new" title="LOL (radio station) (page does not exist)">LOL</a></li>
<li><a href="/enwiki/wiki/RWM" title="RWM">RWM</a></li>
<li><a href="/enwiki/wiki/WWV_(radio_station)" title="WWV (radio station)">WWV</a></li>
<li><a href="/enwiki/wiki/WWVH" title="WWVH">WWVH (Hawaii, USA)</a></li>
<li><a href="/enwiki/wiki/YVTO" title="YVTO">YVTO</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Very-high_frequency" class="mw-redirect" title="Very-high frequency">VHF</a>/<a href="/enwiki/wiki/FM_band" class="mw-redirect" title="FM band">FM</a>/<a href="/enwiki/wiki/Ultra-high_frequency" class="mw-redirect" title="Ultra-high frequency">UHF</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/RDS_CT" class="mw-redirect" title="RDS CT">RDS CT</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Satellite_navigation" title="Satellite navigation">Satellite</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Global_Positioning_System" title="Global Positioning System">GPS</a></li>
<li><a href="/enwiki/wiki/BeiDou" title="BeiDou">BeiDou</a></li>
<li><a href="/enwiki/wiki/Galileo_(satellite_navigation)" title="Galileo (satellite navigation)">Galileo</a></li>
<li><a href="/enwiki/wiki/GLONASS" title="GLONASS">GLONASS</a></li>
<li><a href="/enwiki/wiki/Indian_Regional_Navigation_Satellite_System" title="Indian Regional Navigation Satellite System">IRNSS</a></li>
<li><a href="/enwiki/wiki/Quasi-Zenith_Satellite_System" title="Quasi-Zenith Satellite System">QZSS</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Defunct</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/w/index.php?title=ATA_(radio_station)&action=edit&redlink=1" class="new" title="ATA (radio station) (page does not exist)">ATA</a></li>
<li><a href="/enwiki/wiki/BSF_(time_service)" title="BSF (time service)">BSF (Shortwave)</a></li>
<li><a href="/enwiki/wiki/HBG_(time_signal)" title="HBG (time signal)">HBG</a></li>
<li><a href="/enwiki/wiki/NAA_(Arlington,_Virginia)" title="NAA (Arlington, Virginia)">NAA</a></li>
<li><a href="/enwiki/wiki/WWVB#History" title="WWVB">WWVL</a></li>
<li><a href="/enwiki/wiki/OMA_(time_signal)" title="OMA (time signal)">OMA</a></li>
<li><a href="/enwiki/wiki/OLB5" title="OLB5">OLB5</a></li>
<li><a href="/enwiki/wiki/Radio_VNG" title="Radio VNG">VNG</a></li>
<li><a href="/enwiki/wiki/Y3S" title="Y3S">Y3S</a></li></ul>
</div></td></tr></tbody></table></div>
<div role="navigation" class="navbox" aria-labelledby="Time" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r992953826"/><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/enwiki/wiki/Template:Time_topics" title="Template:Time topics"><abbr title="View this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">v</abbr></a></li><li class="nv-talk"><a href="/enwiki/wiki/Template_talk:Time_topics" title="Template talk:Time topics"><abbr title="Discuss this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">t</abbr></a></li><li class="nv-edit"><a class="external text" href="https://en.wikipedia.org/enwiki/w/index.php?title=Template:Time_topics&action=edit"><abbr title="Edit this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">e</abbr></a></li></ul></div><div id="Time" style="font-size:114%;margin:0 4em"><a href="/enwiki/wiki/Time" title="Time">Time</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Key concepts</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Past" title="Past">Past</a>
<ul><li><a href="/enwiki/wiki/History" title="History">history</a></li>
<li><a href="/enwiki/wiki/Deep_time" title="Deep time">deep time</a></li></ul></li>
<li><a href="/enwiki/wiki/Present" title="Present">Present</a></li>
<li><a href="/enwiki/wiki/Future" title="Future">Future</a></li>
<li><a href="/enwiki/wiki/Futures_studies" title="Futures studies">Futures studies</a></li>
<li><a href="/enwiki/wiki/Far_future_in_religion" title="Far future in religion">Far future in religion</a></li>
<li><a href="/enwiki/wiki/Timeline_of_the_far_future" title="Timeline of the far future">Timeline of the far future</a></li>
<li><a href="/enwiki/wiki/Eternity" title="Eternity">Eternity</a></li>
<li><a href="/enwiki/wiki/Eternity_of_the_world" title="Eternity of the world">Eternity of the world</a></li></ul>
</div></td><td class="noviewer navbox-image" rowspan="9" style="width:1px;padding:0px 0px 0px 2px"><div><a href="/enwiki/wiki/File:Wooden_hourglass_3.jpg" class="image"><img alt="Wooden hourglass 3.jpg" src="/upwiki/wikipedia/commons/thumb/7/70/Wooden_hourglass_3.jpg/50px-Wooden_hourglass_3.jpg" decoding="async" width="50" height="101" srcset="/upwiki/wikipedia/commons/thumb/7/70/Wooden_hourglass_3.jpg/75px-Wooden_hourglass_3.jpg 1.5x, /upwiki/wikipedia/commons/thumb/7/70/Wooden_hourglass_3.jpg/100px-Wooden_hourglass_3.jpg 2x" data-file-width="967" data-file-height="1959" /></a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Measurement<br />and <a href="/enwiki/wiki/Time_standard" title="Time standard">standards</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6.5em;font-weight:normal; text-align:center;"><a href="/enwiki/wiki/Chronometry" title="Chronometry">Chronometry</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Coordinated_Universal_Time" title="Coordinated Universal Time">UTC</a></li>
<li><a href="/enwiki/wiki/Universal_Time" title="Universal Time">UT</a></li>
<li><a href="/enwiki/wiki/International_Atomic_Time" title="International Atomic Time">TAI</a></li>
<li><a href="/enwiki/wiki/Unit_of_time" title="Unit of time">Unit of time</a></li>
<li><a href="/enwiki/wiki/Planck_time" class="mw-redirect" title="Planck time">Planck time</a></li>
<li><a href="/enwiki/wiki/New_Earth_Time" title="New Earth Time">New Earth Time</a></li>
<li><a href="/enwiki/wiki/Second" title="Second">Second</a></li>
<li><a href="/enwiki/wiki/Minute" title="Minute">Minute</a></li>
<li><a href="/enwiki/wiki/Hour" title="Hour">Hour</a></li>
<li><a href="/enwiki/wiki/Day" title="Day">Day</a></li>
<li><a href="/enwiki/wiki/Week" title="Week">Week</a></li>
<li><a href="/enwiki/wiki/Month" title="Month">Month</a></li>
<li><a href="/enwiki/wiki/Season" title="Season">Season</a></li>
<li><a href="/enwiki/wiki/Year" title="Year">Year</a></li>
<li><a href="/enwiki/wiki/Decade" title="Decade">Decade</a></li>
<li><a href="/enwiki/wiki/Century" title="Century">Century</a></li>
<li><a href="/enwiki/wiki/Millennium" title="Millennium">Millennium</a></li>
<li><a href="/enwiki/wiki/Tropical_year" title="Tropical year">Tropical year</a></li>
<li><a href="/enwiki/wiki/Sidereal_year" title="Sidereal year">Sidereal year</a></li>
<li><a href="/enwiki/wiki/Samvatsara" title="Samvatsara">Samvatsara</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:6.5em;font-weight:normal; text-align:center;"><a href="/enwiki/wiki/System_of_measurement" title="System of measurement">Measurement systems</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Italian_six-hour_clock" title="Italian six-hour clock">6-hour clock (Italian)</a></li>
<li><a href="/enwiki/wiki/Thai_six-hour_clock" title="Thai six-hour clock">6-hour clock (Thai)</a></li>
<li><a href="/enwiki/wiki/12-hour_clock" title="12-hour clock">12-hour clock</a></li>
<li><a href="/enwiki/wiki/24-hour_clock" title="24-hour clock">24-hour clock</a></li>
<li><a href="/enwiki/wiki/Daylight_saving_time" title="Daylight saving time">Daylight saving time</a></li>
<li><a href="/enwiki/wiki/Decimal_time" title="Decimal time">Decimal</a></li>
<li><a href="/enwiki/wiki/Hexadecimal_time" title="Hexadecimal time">Hexadecimal</a></li>
<li><a href="/enwiki/wiki/Metric_time" title="Metric time">Metric</a></li>
<li><a href="/enwiki/wiki/Sidereal_time" title="Sidereal time">Sidereal</a></li>
<li><a href="/enwiki/wiki/Solar_time" title="Solar time">Solar</a></li>
<li><a href="/enwiki/wiki/Time_zone" title="Time zone">Time zone</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:6.5em;font-weight:normal; text-align:center;"><a href="/enwiki/wiki/Calendar" title="Calendar">Calendars</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Gregorian_calendar" title="Gregorian calendar">Gregorian</a></li>
<li><a href="/enwiki/wiki/Julian_calendar" title="Julian calendar">Julian</a></li>
<li><a href="/enwiki/wiki/Hebrew_calendar" title="Hebrew calendar">Hebrew</a></li>
<li><a href="/enwiki/wiki/Islamic_calendar" title="Islamic calendar">Islamic</a></li>
<li><a href="/enwiki/wiki/Lunar_calendar" title="Lunar calendar">Lunar</a></li>
<li><a href="/enwiki/wiki/Solar_Hijri_calendar" title="Solar Hijri calendar">Solar Hijri</a></li>
<li><a href="/enwiki/wiki/Maya_calendar" title="Maya calendar">Mayan</a></li>
<li><a href="/enwiki/wiki/Intercalation_(timekeeping)" title="Intercalation (timekeeping)">Intercalation</a></li>
<li><a href="/enwiki/wiki/Leap_second" title="Leap second">Leap second</a></li>
<li><a href="/enwiki/wiki/Leap_year" title="Leap year">Leap year</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Clock" title="Clock">Clocks</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Horology" title="Horology">Horology</a></li>
<li><a href="/enwiki/wiki/History_of_timekeeping_devices" title="History of timekeeping devices">History of timekeeping devices</a></li>
<li><a href="/enwiki/wiki/Clock#Time-measuring_devices" title="Clock">Main types</a>
<ul><li><a href="/enwiki/wiki/Astrarium" title="Astrarium">astrarium</a></li>
<li><a href="/enwiki/wiki/Atomic_clock" title="Atomic clock">atomic</a>
<ul><li><a href="/enwiki/wiki/Quantum_clock" title="Quantum clock">quantum</a></li></ul></li>
<li><a href="/enwiki/wiki/Hourglass" title="Hourglass">hourglass</a></li>
<li><a href="/enwiki/wiki/Marine_chronometer" title="Marine chronometer">marine</a></li>
<li><a href="/enwiki/wiki/Sundial" title="Sundial">sundial</a></li>
<li><a href="/enwiki/wiki/Schema_for_horizontal_dials" title="Schema for horizontal dials">sundial markup schema</a></li>
<li><a href="/enwiki/wiki/Watch" title="Watch">watch</a>
<ul><li><a href="/enwiki/wiki/Mechanical_watch" title="Mechanical watch">mechanical</a></li>
<li><a href="/enwiki/wiki/Stopwatch" title="Stopwatch">stopwatch</a></li></ul></li>
<li><a href="/enwiki/wiki/Water_clock" title="Water clock">water-based</a></li></ul></li>
<li><a href="/enwiki/wiki/Cuckoo_clock" title="Cuckoo clock">Cuckoo clock</a></li>
<li><a href="/enwiki/wiki/Digital_clock" title="Digital clock">Digital clock</a></li>
<li><a href="/enwiki/wiki/Grandfather_clock" title="Grandfather clock">Grandfather clock</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div class="hlist hlist-separated"><ul><li><a href="/enwiki/wiki/Chronology" title="Chronology">Chronology</a></li><li>History</li></ul></div></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Astronomical_chronology" title="Astronomical chronology">Astronomical chronology</a></li>
<li><a href="/enwiki/wiki/Big_History" title="Big History">Big History</a></li>
<li><a href="/enwiki/wiki/Calendar_era" title="Calendar era">Calendar era</a></li>
<li><a href="/enwiki/wiki/Chronicle" title="Chronicle">Chronicle</a></li>
<li><a href="/enwiki/wiki/Deep_time" title="Deep time">Deep time</a></li>
<li><a href="/enwiki/wiki/Periodization" title="Periodization">Periodization</a></li>
<li><a href="/enwiki/wiki/Regnal_year" title="Regnal year">Regnal year</a></li>
<li><a href="/enwiki/wiki/Timeline" title="Timeline">Timeline</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div class="hlist hlist-separated"><ul><li><a href="/enwiki/wiki/Category:Time_in_religion" title="Category:Time in religion">Religion</a></li><li>Mythology</li></ul></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Dreamtime" class="mw-redirect" title="Dreamtime">Dreamtime</a></li>
<li><a href="/enwiki/wiki/Kaal" title="Kaal">Kaal</a></li>
<li><a href="/enwiki/wiki/Kalachakra" title="Kalachakra">Kalachakra</a></li>
<li><a href="/enwiki/wiki/Prophecy" title="Prophecy">Prophecy</a></li>
<li><a href="/enwiki/wiki/Time_and_fate_deities" title="Time and fate deities">Time and fate deities</a></li>
<li><a href="/enwiki/wiki/Wheel_of_time" title="Wheel of time">Wheel of time</a></li>
<li><a href="/enwiki/wiki/Immortality" title="Immortality">Immortality</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Philosophy_of_space_and_time" title="Philosophy of space and time">Philosophy of time</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/A_series_and_B_series" title="A series and B series">A series and B series</a></li>
<li><a href="/enwiki/wiki/B-theory_of_time" title="B-theory of time">B-theory of time</a></li>
<li><a href="/enwiki/wiki/Causality" title="Causality">Causality</a></li>
<li><a href="/enwiki/wiki/Duration_(philosophy)" title="Duration (philosophy)">Duration</a></li>
<li><a href="/enwiki/wiki/Endurantism" title="Endurantism">Endurantism</a></li>
<li><a href="/enwiki/wiki/Eternal_return" title="Eternal return">Eternal return</a></li>
<li><a href="/enwiki/wiki/Eternalism_(philosophy_of_time)" title="Eternalism (philosophy of time)">Eternalism</a></li>
<li><a href="/enwiki/wiki/Event_(philosophy)" title="Event (philosophy)">Event</a></li>
<li><a href="/enwiki/wiki/Multiple_time_dimensions" title="Multiple time dimensions">Multiple time dimensions</a></li>
<li><a href="/enwiki/wiki/Perdurantism" title="Perdurantism">Perdurantism</a></li>
<li><a href="/enwiki/wiki/Philosophical_presentism" title="Philosophical presentism">Presentism</a></li>
<li><a href="/enwiki/wiki/Static_interpretation_of_time" title="Static interpretation of time">Static interpretation of time</a></li>
<li><a href="/enwiki/wiki/Temporal_finitism" title="Temporal finitism">Temporal finitism</a></li>
<li><a href="/enwiki/wiki/Temporal_parts" title="Temporal parts">Temporal parts</a></li>
<li>"<a href="/enwiki/wiki/The_Unreality_of_Time" title="The Unreality of Time">The Unreality of Time</a>"</li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Human experience<br />and use of time</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Accounting_period" title="Accounting period">Accounting period</a></li>
<li><a href="/enwiki/wiki/Chronemics" title="Chronemics">Chronemics</a></li>
<li><a href="/enwiki/wiki/Fiscal_year" title="Fiscal year">Fiscal year</a></li>
<li><a href="/enwiki/wiki/Generation_time" title="Generation time">Generation time</a></li>
<li><a href="/enwiki/wiki/Mental_chronometry" title="Mental chronometry">Mental chronometry</a></li>
<li><a href="/enwiki/wiki/Duration_(music)" title="Duration (music)">Music</a></li>
<li><a href="/enwiki/wiki/Procrastination" title="Procrastination">Procrastination</a></li>
<li><a href="/enwiki/wiki/Punctuality" title="Punctuality">Punctuality</a></li>
<li><a href="/enwiki/wiki/Temporal_database" title="Temporal database">Temporal database</a></li>
<li><a href="/enwiki/wiki/Term_(time)" title="Term (time)">Term</a></li>
<li><a href="/enwiki/wiki/Time_discipline" title="Time discipline">Time discipline</a></li>
<li><a href="/enwiki/wiki/Time_management" title="Time management">Time management</a></li>
<li><a href="/enwiki/wiki/Time_perception" title="Time perception">Time perception</a>
<ul><li><a href="/enwiki/wiki/Specious_present" title="Specious present">Specious present</a></li></ul></li>
<li><a href="/enwiki/wiki/Time-tracking_software" title="Time-tracking software">Time-tracking software</a></li>
<li><a href="/enwiki/wiki/Time-use_research" title="Time-use research">Time-use research</a></li>
<li><a href="/enwiki/wiki/Time-based_currency" title="Time-based currency">Time-based currency</a></li>
<li><a href="/enwiki/wiki/Time_value_of_money" title="Time value of money">Time value of money</a></li>
<li><a href="/enwiki/wiki/Time_clock" title="Time clock">Time clock</a></li>
<li><a href="/enwiki/wiki/Timesheet" title="Timesheet">Timesheet</a></li>
<li><a href="/enwiki/wiki/Yesterday_(time)" title="Yesterday (time)">Yesterday</a> – <a href="/enwiki/wiki/Present" title="Present">Today</a> – <a href="/enwiki/wiki/Tomorrow_(time)" title="Tomorrow (time)">Tomorrow</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Time in</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6.5em;font-weight:normal; text-align:center;"><a href="/enwiki/wiki/Geology" title="Geology">Geology</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Geologic_time_scale" title="Geologic time scale">Geological time</a>
<ul><li><a href="/enwiki/wiki/Age_(geology)" title="Age (geology)">age</a></li>
<li><a href="/enwiki/wiki/Chronozone" title="Chronozone">chron</a></li>
<li><a href="/enwiki/wiki/Eon_(geology)" class="mw-redirect" title="Eon (geology)">eon</a></li>
<li><a href="/enwiki/wiki/Epoch_(geology)" title="Epoch (geology)">epoch</a></li>
<li><a href="/enwiki/wiki/Era_(geology)" title="Era (geology)">era</a></li>
<li><a href="/enwiki/wiki/Geological_period" title="Geological period">period</a></li></ul></li>
<li><a href="/enwiki/wiki/Geochronology" title="Geochronology">Geochronology</a></li>
<li><a href="/enwiki/wiki/Geological_history_of_Earth" title="Geological history of Earth">Geological history of Earth</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:6.5em;font-weight:normal; text-align:center;"><a href="/enwiki/wiki/Time_in_physics" title="Time in physics">Physics</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Absolute_space_and_time" title="Absolute space and time">Absolute space and time</a></li>
<li><a href="/enwiki/wiki/Arrow_of_time" title="Arrow of time">Arrow of time</a></li>
<li><a href="/enwiki/wiki/Chronon" title="Chronon">Chronon</a></li>
<li><a href="/enwiki/wiki/Coordinate_time" title="Coordinate time">Coordinate time</a></li>
<li><a href="/enwiki/wiki/Imaginary_time" title="Imaginary time">Imaginary time</a></li>
<li><a href="/enwiki/wiki/Planck_epoch" class="mw-redirect" title="Planck epoch">Planck epoch</a></li>
<li><a href="/enwiki/wiki/Planck_time" class="mw-redirect" title="Planck time">Planck time</a></li>
<li><a href="/enwiki/wiki/Proper_time" title="Proper time">Proper time</a></li>
<li><a href="/enwiki/wiki/Rate_(mathematics)" title="Rate (mathematics)">Rate</a></li>
<li><a href="/enwiki/wiki/Spacetime" title="Spacetime">Spacetime</a></li>
<li><a href="/enwiki/wiki/Theory_of_relativity" title="Theory of relativity">Theory of relativity</a></li>
<li><a href="/enwiki/wiki/Time_dilation" title="Time dilation">Time dilation</a>
<ul><li><a href="/enwiki/wiki/Gravitational_time_dilation" title="Gravitational time dilation">gravitational</a></li></ul></li>
<li><a href="/enwiki/wiki/Time_domain" title="Time domain">Time domain</a></li>
<li><a href="/enwiki/wiki/Time_translation_symmetry" title="Time translation symmetry">Time translation symmetry</a></li>
<li><a href="/enwiki/wiki/T-symmetry" title="T-symmetry">Time reversal symmetry</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:6.5em;font-weight:normal; text-align:center;">Other subject areas</th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Chronological_dating" title="Chronological dating">Chronological dating</a></li>
<li><a href="/enwiki/wiki/Chronobiology" title="Chronobiology">Chronobiology</a></li>
<li><a href="/enwiki/wiki/Circadian_rhythm" title="Circadian rhythm">Circadian rhythms</a></li>
<li><a href="/enwiki/wiki/Dating_methodologies_in_archaeology" class="mw-redirect" title="Dating methodologies in archaeology">Dating methodologies in archaeology</a></li>
<li><a href="/enwiki/wiki/Time_geography" title="Time geography">Time geography</a></li></ul>
</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><i><a href="/enwiki/wiki/Carpe_diem" title="Carpe diem">Carpe diem</a></i></li>
<li><a href="/enwiki/wiki/Clock_position" title="Clock position">Clock position</a></li>
<li><a href="/enwiki/wiki/Space" title="Space">Space</a></li>
<li><a href="/enwiki/wiki/System_time" title="System time">System time</a></li>
<li><i><a href="/enwiki/wiki/Tempus_fugit" title="Tempus fugit">Tempus fugit</a></i></li>
<li><a href="/enwiki/wiki/Time_capsule" title="Time capsule">Time capsule</a></li>
<li><a href="/enwiki/wiki/Time_complexity" title="Time complexity">Time complexity</a></li>
<li><a href="/enwiki/wiki/Time_signature" title="Time signature">Time signature</a></li>
<li><a href="/enwiki/wiki/Time_travel" title="Time travel">Time travel</a></li></ul>
</div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div>
<ul><li><img alt="Category" src="/upwiki/wikipedia/en/thumb/4/48/Folder_Hexagonal_Icon.svg/16px-Folder_Hexagonal_Icon.svg.png" decoding="async" title="Category" width="16" height="14" srcset="/upwiki/wikipedia/en/thumb/4/48/Folder_Hexagonal_Icon.svg/24px-Folder_Hexagonal_Icon.svg.png 1.5x, /upwiki/wikipedia/en/thumb/4/48/Folder_Hexagonal_Icon.svg/32px-Folder_Hexagonal_Icon.svg.png 2x" data-file-width="36" data-file-height="31" /> <b><a href="/enwiki/wiki/Category:Time" title="Category:Time">Category</a></b></li>
<li><img alt="Commons page" src="/upwiki/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" title="Commons page" width="12" height="16" srcset="/upwiki/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, /upwiki/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /> <b><a href="https://commons.wikimedia.org/wiki/Category:Time" class="extiw" title="commons:Category:Time">Commons</a></b></li></ul>
</div></td></tr></tbody></table></div>
<div role="navigation" class="navbox" aria-labelledby="Time_measurement_and_standards" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r992953826"/><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/enwiki/wiki/Template:Time_measurement_and_standards" title="Template:Time measurement and standards"><abbr title="View this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">v</abbr></a></li><li class="nv-talk"><a href="/enwiki/wiki/Template_talk:Time_measurement_and_standards" title="Template talk:Time measurement and standards"><abbr title="Discuss this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">t</abbr></a></li><li class="nv-edit"><a class="external text" href="https://en.wikipedia.org/enwiki/w/index.php?title=Template:Time_measurement_and_standards&action=edit"><abbr title="Edit this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">e</abbr></a></li></ul></div><div id="Time_measurement_and_standards" style="font-size:114%;margin:0 4em"><a href="/enwiki/wiki/Time" title="Time">Time measurement</a> and <a href="/enwiki/wiki/Time_standard" title="Time standard">standards</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="3"><div id="*_Chronometry_*_Orders_of_magnitude_*_Metrology">
<ul><li><a href="/enwiki/wiki/Chronometry" title="Chronometry">Chronometry</a></li>
<li><a href="/enwiki/wiki/Orders_of_magnitude_(time)" title="Orders of magnitude (time)">Orders of magnitude</a></li>
<li><a href="/enwiki/wiki/Metrology" title="Metrology">Metrology</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">International standards</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Coordinated_Universal_Time" title="Coordinated Universal Time">Coordinated Universal Time</a>
<ul><li><a href="/enwiki/wiki/UTC_offset" title="UTC offset">offset</a></li></ul></li>
<li><a href="/enwiki/wiki/Universal_Time" title="Universal Time">UT</a></li>
<li><a href="/enwiki/wiki/%CE%94T_(timekeeping)" title="ΔT (timekeeping)">ΔT</a></li>
<li><a href="/enwiki/wiki/DUT1" title="DUT1">DUT1</a></li>
<li><a href="/enwiki/wiki/International_Earth_Rotation_and_Reference_Systems_Service" title="International Earth Rotation and Reference Systems Service">International Earth Rotation and Reference Systems Service</a></li>
<li><a href="/enwiki/wiki/ISO_31-1" title="ISO 31-1">ISO 31-1</a></li>
<li><a href="/enwiki/wiki/ISO_8601" title="ISO 8601">ISO 8601</a></li>
<li><a href="/enwiki/wiki/International_Atomic_Time" title="International Atomic Time">International Atomic Time</a></li>
<li><a href="/enwiki/wiki/12-hour_clock" title="12-hour clock">12-hour clock</a></li>
<li><a href="/enwiki/wiki/24-hour_clock" title="24-hour clock">24-hour clock</a></li>
<li><a href="/enwiki/wiki/Barycentric_Coordinate_Time" title="Barycentric Coordinate Time">Barycentric Coordinate Time</a></li>
<li><a href="/enwiki/wiki/Barycentric_Dynamical_Time" title="Barycentric Dynamical Time">Barycentric Dynamical Time</a></li>
<li><a href="/enwiki/wiki/Civil_time" title="Civil time">Civil time</a></li>
<li><a href="/enwiki/wiki/Daylight_saving_time" title="Daylight saving time">Daylight saving time</a></li>
<li><a href="/enwiki/wiki/Geocentric_Coordinate_Time" title="Geocentric Coordinate Time">Geocentric Coordinate Time</a></li>
<li><a href="/enwiki/wiki/International_Date_Line" title="International Date Line">International Date Line</a></li>
<li><a href="/enwiki/wiki/Leap_second" title="Leap second">Leap second</a></li>
<li><a href="/enwiki/wiki/Solar_time" title="Solar time">Solar time</a></li>
<li><a href="/enwiki/wiki/Terrestrial_Time" title="Terrestrial Time">Terrestrial Time</a></li>
<li><a href="/enwiki/wiki/Time_zone" title="Time zone">Time zone</a></li>
<li><a href="/enwiki/wiki/180th_meridian" title="180th meridian">180th meridian</a></li></ul>
</div></td><td class="noviewer navbox-image" rowspan="9" style="width:1px;padding:0px 0px 0px 2px"><div><img alt="WPtimetracer.png" src="/upwiki/wikipedia/commons/thumb/5/54/WPtimetracer.png/75px-WPtimetracer.png" decoding="async" width="75" height="56" srcset="/upwiki/wikipedia/commons/5/54/WPtimetracer.png 1.5x" data-file-width="100" data-file-height="75" /><br /></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Obsolete standards</th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Ephemeris_time" title="Ephemeris time">Ephemeris time</a></li>
<li><a href="/enwiki/wiki/Greenwich_Mean_Time" title="Greenwich Mean Time">Greenwich Mean Time</a></li>
<li><a href="/enwiki/wiki/Prime_meridian" title="Prime meridian">Prime meridian</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Time_in_physics" title="Time in physics">Time in physics</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Absolute_space_and_time" title="Absolute space and time">Absolute space and time</a></li>
<li><a href="/enwiki/wiki/Spacetime" title="Spacetime">Spacetime</a></li>
<li><a href="/enwiki/wiki/Chronon" title="Chronon">Chronon</a></li>
<li><a href="/enwiki/wiki/Continuous_signal" class="mw-redirect" title="Continuous signal">Continuous signal</a></li>
<li><a href="/enwiki/wiki/Coordinate_time" title="Coordinate time">Coordinate time</a></li>
<li><a href="/enwiki/wiki/Cosmological_decade" title="Cosmological decade">Cosmological decade</a></li>
<li><a href="/enwiki/wiki/Discrete_time_and_continuous_time" title="Discrete time and continuous time">Discrete time and continuous time</a></li>
<li><a href="/enwiki/wiki/Planck_units" title="Planck units">Planck time</a></li>
<li><a href="/enwiki/wiki/Proper_time" title="Proper time">Proper time</a></li>
<li><a href="/enwiki/wiki/Theory_of_relativity" title="Theory of relativity">Theory of relativity</a></li>
<li><a href="/enwiki/wiki/Time_dilation" title="Time dilation">Time dilation</a></li>
<li><a href="/enwiki/wiki/Gravitational_time_dilation" title="Gravitational time dilation">Gravitational time dilation</a></li>
<li><a href="/enwiki/wiki/Time_domain" title="Time domain">Time domain</a></li>
<li><a href="/enwiki/wiki/Time_translation_symmetry" title="Time translation symmetry">Time translation symmetry</a></li>
<li><a href="/enwiki/wiki/T-symmetry" title="T-symmetry">T-symmetry</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Horology" title="Horology">Horology</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Clock" title="Clock">Clock</a></li>
<li><a href="/enwiki/wiki/Astrarium" title="Astrarium">Astrarium</a></li>
<li><a href="/enwiki/wiki/Atomic_clock" title="Atomic clock">Atomic clock</a></li>
<li><a href="/enwiki/wiki/Complication_(horology)" title="Complication (horology)">Complication</a></li>
<li><a href="/enwiki/wiki/History_of_timekeeping_devices" title="History of timekeeping devices">History of timekeeping devices</a></li>
<li><a href="/enwiki/wiki/Hourglass" title="Hourglass">Hourglass</a></li>
<li><a href="/enwiki/wiki/Marine_chronometer" title="Marine chronometer">Marine chronometer</a></li>
<li><a href="/enwiki/wiki/Marine_sandglass" title="Marine sandglass">Marine sandglass</a></li>
<li><a href="/enwiki/wiki/Radio_clock" title="Radio clock">Radio clock</a></li>
<li><a href="/enwiki/wiki/Watch" title="Watch">Watch</a>
<ul><li><a href="/enwiki/wiki/Stopwatch" title="Stopwatch">stopwatch</a></li></ul></li>
<li><a href="/enwiki/wiki/Water_clock" title="Water clock">Water clock</a></li>
<li><a href="/enwiki/wiki/Sundial" title="Sundial">Sundial</a></li>
<li><a href="/enwiki/wiki/Dialing_scales" title="Dialing scales">Dialing scales</a></li>
<li><a href="/enwiki/wiki/Equation_of_time" title="Equation of time">Equation of time</a></li>
<li><a href="/enwiki/wiki/History_of_sundials" title="History of sundials">History of sundials</a></li>
<li><a href="/enwiki/wiki/Schema_for_horizontal_dials" title="Schema for horizontal dials">Sundial markup schema</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Calendar" title="Calendar">Calendar</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Astronomical_year_numbering" title="Astronomical year numbering">Astronomical</a></li>
<li><a href="/enwiki/wiki/Dominical_letter" title="Dominical letter">Dominical letter</a></li>
<li><a href="/enwiki/wiki/Epact" title="Epact">Epact</a></li>
<li><a href="/enwiki/wiki/Equinox" title="Equinox">Equinox</a></li>
<li><a href="/enwiki/wiki/Gregorian_calendar" title="Gregorian calendar">Gregorian</a></li>
<li><a href="/enwiki/wiki/Hebrew_calendar" title="Hebrew calendar">Hebrew</a></li>
<li><a href="/enwiki/wiki/Hindu_calendar" title="Hindu calendar">Hindu</a></li>
<li><a href="/enwiki/wiki/Holocene_calendar" title="Holocene calendar">Holocene</a></li>
<li><a href="/enwiki/wiki/Intercalation_(timekeeping)" title="Intercalation (timekeeping)">Intercalation</a></li>
<li><a href="/enwiki/wiki/Islamic_calendar" title="Islamic calendar">Islamic</a></li>
<li><a href="/enwiki/wiki/Julian_calendar" title="Julian calendar">Julian</a></li>
<li><a href="/enwiki/wiki/Leap_year" title="Leap year">Leap year</a></li>
<li><a href="/enwiki/wiki/Lunar_calendar" title="Lunar calendar">Lunar</a></li>
<li><a href="/enwiki/wiki/Lunisolar_calendar" title="Lunisolar calendar">Lunisolar</a></li>
<li><a href="/enwiki/wiki/Solar_calendar" title="Solar calendar">Solar</a></li>
<li><a href="/enwiki/wiki/Solstice" title="Solstice">Solstice</a></li>
<li><a href="/enwiki/wiki/Tropical_year" title="Tropical year">Tropical year</a></li>
<li><a href="/enwiki/wiki/Determination_of_the_day_of_the_week" title="Determination of the day of the week">Weekday determination</a></li>
<li><a href="/enwiki/wiki/Names_of_the_days_of_the_week" title="Names of the days of the week">Weekday names</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Archaeology and geology</th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Chronological_dating" title="Chronological dating">Chronological dating</a></li>
<li><a href="/enwiki/wiki/Geologic_time_scale" title="Geologic time scale">Geologic time scale</a></li>
<li><a href="/enwiki/wiki/International_Commission_on_Stratigraphy" title="International Commission on Stratigraphy">International Commission on Stratigraphy</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Astronomical_chronology" title="Astronomical chronology">Astronomical chronology</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Galactic_year" title="Galactic year">Galactic year</a></li>
<li><a href="/enwiki/wiki/Nuclear_timescale" title="Nuclear timescale">Nuclear timescale</a></li>
<li><a href="/enwiki/wiki/Precession" title="Precession">Precession</a></li>
<li><a href="/enwiki/wiki/Sidereal_time" title="Sidereal time">Sidereal time</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other <a href="/enwiki/wiki/Unit_of_time" title="Unit of time">units of time</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Flick_(time)" title="Flick (time)">Flick</a></li>
<li><a href="/enwiki/wiki/Shake_(unit)" title="Shake (unit)">Shake</a></li>
<li><a href="/enwiki/wiki/Jiffy_(time)" title="Jiffy (time)">Jiffy</a></li>
<li><a href="/enwiki/wiki/Second" title="Second">Second</a></li>
<li><a href="/enwiki/wiki/Minute" title="Minute">Minute</a></li>
<li><a href="/enwiki/wiki/Moment_(time)" title="Moment (time)">Moment</a></li>
<li><a href="/enwiki/wiki/Hour" title="Hour">Hour</a></li>
<li><a href="/enwiki/wiki/Day" title="Day">Day</a></li>
<li><a href="/enwiki/wiki/Week" title="Week">Week</a></li>
<li><a href="/enwiki/wiki/Fortnight" title="Fortnight">Fortnight</a></li>
<li><a href="/enwiki/wiki/Month" title="Month">Month</a></li>
<li><a href="/enwiki/wiki/Year" title="Year">Year</a></li>
<li><a href="/enwiki/wiki/Olympiad" title="Olympiad">Olympiad</a></li>
<li><a href="/enwiki/wiki/Lustrum" title="Lustrum">Lustrum</a></li>
<li><a href="/enwiki/wiki/Decade" title="Decade">Decade</a></li>
<li><a href="/enwiki/wiki/Century" title="Century">Century</a></li>
<li><a href="/enwiki/wiki/Saeculum" title="Saeculum">Saeculum</a></li>
<li><a href="/enwiki/wiki/Millennium" title="Millennium">Millennium</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/enwiki/wiki/Chronology" title="Chronology">Chronology</a></li>
<li><a href="/enwiki/wiki/Duration_(philosophy)" title="Duration (philosophy)">Duration</a>
<ul><li><a href="/enwiki/wiki/Duration_(music)" title="Duration (music)">music</a></li></ul></li>
<li><a href="/enwiki/wiki/Mental_chronometry" title="Mental chronometry">Mental chronometry</a></li>
<li><a href="/enwiki/wiki/Decimal_time" title="Decimal time">Decimal time</a></li>
<li><a href="/enwiki/wiki/Metric_time" title="Metric time">Metric time</a></li>
<li><a href="/enwiki/wiki/System_time" title="System time">System time</a></li>
<li><a href="/enwiki/wiki/Time_value_of_money" title="Time value of money">Time value of money</a></li>
<li><a href="/enwiki/wiki/Timekeeper" title="Timekeeper">Timekeeper</a></li></ul>
</div></td></tr></tbody></table></div>
<div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_frameless_&#124;text-top_&#124;10px_&#124;alt=Edit_this_at_Wikidata_&#124;link=https&#58;//www.wikidata.org/wiki/Q36477#identifiers&#124;Edit_this_at_Wikidata" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Authority_control_frameless_&#124;text-top_&#124;10px_&#124;alt=Edit_this_at_Wikidata_&#124;link=https&#58;//www.wikidata.org/wiki/Q36477#identifiers&#124;Edit_this_at_Wikidata" scope="row" class="navbox-group" style="width:1%"><a href="/enwiki/wiki/Help:Authority_control" title="Help:Authority control">Authority control</a> <a href="https://www.wikidata.org/wiki/Q36477#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="/upwiki/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" style="vertical-align: text-top" srcset="/upwiki/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, /upwiki/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><span class="nowrap"><a href="/enwiki/wiki/GND_(identifier)" class="mw-redirect" title="GND (identifier)">GND</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4020221-5">4020221-5</a></span></span></li></ul>
</div></td></tr></tbody></table></div>
' |
Whether or not the change was made through a Tor exit node (tor_exit_node) | false |
Unix timestamp of change (timestamp) | 1610978892 |
