{{Short description|none}} {{For|modern definitions and measurements|Earth radius}} {{Use dmy dates|date=November 2019}} {{Use British English|date=February 2023}} {{Geodesy}} '''Earth's circumference''' is the [[circumference|distance]] around [[Earth]]. Measured around the [[equator]], it is {{cvt|40075.017|km|mi}}. Measured passing through the [[geographical pole|poles]], the circumference is {{cvt|40007.863|km|mi}}.<ref>{{cite web |first1=Sigurd |last1=Humerfelt |date=26 October 2010 |title=How WGS 84 defines Earth |url=http://home.online.no/~sigurdhu/WGS84_Eng.html |access-date=29 April 2011 |url-status=dead |archive-url=https://web.archive.org/web/20110424104419/http://home.online.no/~sigurdhu/WGS84_Eng.html |archive-date=24 April 2011 }}</ref>
The first known scientific measurement and calculation was done by [[Eratosthenes]], by comparing altitudes of the mid-day sun at two places a known north–south distance apart.<ref>{{cite book|title=The Illustrated Encyclopedia of the Universe|last=Ridpath|first=Ian|publisher=Watson-Guptill|year=2001|isbn=978-0-8230-2512-1|location=New York, NY|page=31}}</ref> He achieved a great degree of precision in his computation.<ref name="russo273277" /> The Earth's shape deviates from spherical by [[flattening]], but by only about 0.3%.
{{anchor|Earth's circumference in nautical miles}} Measurement of Earth's circumference has been important to [[navigation]] since ancient times. In modern times, Earth's circumference has been used to define fundamental units of measurement of length: the [[nautical mile]] in the seventeenth century and the [[metre]] in the eighteenth. Earth's polar circumference is very near to 21,600 nautical miles because the nautical mile was intended to express one [[minute and second of arc | minute]] of latitude (see [[meridian arc]]), which is 21,600 partitions of the polar circumference (that is 60 minutes × 360 degrees). The polar circumference is also close to 40,000 kilometres because [[History of the metre|the metre was originally defined]] to be one ten millionth (i.e., a kilometre is one ten thousandth) of the arc from pole to equator ([[quarter meridian]]). The accuracy of measuring the circumference has improved since then, but the physical length of each unit of measure has remained close to what it was determined to be at the time, so the Earth's circumference is no longer a [[round number]] in metres or nautical miles.
==History== {{See also|History of geodesy|Spherical Earth#History|Earth radius#History|Meridian arc#History}}
===Eratosthenes=== [[File:Eratosthenes.png|thumb|left|Illustration showing a portion of the globe showing a part of the African continent. The sun beams shown as two rays hitting earth at Syene and Alexandria. Angle of sun beam and the gnomons (vertical sticks) is shown at Alexandria which allowed Eratosthenes's estimate of the circumference of Earth.]]
The measure of Earth's circumference is the most famous among the results obtained by [[Eratosthenes]],<ref>{{cite book |last=Russo |first=Lucio |title=The Forgotten Revolution |page=68}}</ref> who estimated that the meridian has a length of 252,000 [[Stadion (unit)|stadia]], with an error on the real value between −2.4% and +0.8% (assuming a value for the stadion between 155 and 160 metres;<ref name="russo273277" /> the exact value of the stadion remains a subject of debate to this day; see [[Stadion (unit)#Calculations|stadion]]).
Eratosthenes described his technique in a book entitled ''On the measure of the Earth'', which has not been preserved; what has been preserved is the simplified version described by [[Cleomedes]] to popularise the discovery.<ref>Cleomedes, ''Caelestia'', i.7.49–52.</ref> Cleomedes invites his reader to consider two Egyptian cities, [[Alexandria]] and Syene (modern [[Aswan]]): # Cleomedes assumes that the distance between Syene and Alexandria was 5,000 stadia (a figure that was checked yearly by professional [[bematist]]s, ''mensores regii'').<ref>Martianus Capella, ''De nuptiis Philologiae et Mercurii'', VI.598.</ref> # He assumes the simplified (but inaccurate) hypothesis that Syene was precisely on the [[Tropic of Cancer]], saying that at [[Solar noon|local noon]] on the summer [[solstice]] the Sun was directly overhead. Syene was actually north of the tropic by something less than a degree. # He assumes the simplified (but inaccurate) hypothesis that Syene and Alexandria are on the same meridian. Syene was actually about 3 degrees of longitude east of Alexandria.
According to [[Cleomedes]]'s [[Cleomedes#On the Circular Motions of the Celestial Bodies|''On the Circular Motions of the Celestial Bodies'']], around 240 BC, Eratosthenes calculated the [[Earth radius|circumference of the Earth]] in [[Ptolemaic Kingdom|Ptolemaic Egypt]].<ref>{{Cite book |first= Albert |last= Van Helden |title= Measuring the Universe: Cosmic Dimensions from Aristarchus to Halley |publisher= University of Chicago Press |date= 1985 |pages= 4–5 |isbn= 978-0-226-84882-2}}</ref> Using a vertical rod known as a [[gnomon]] and under the previous assumptions, he knew that at local noon on the summer solstice in [[Syene]] (modern [[Aswan]], Egypt), the Sun was directly overhead, as the gnomon cast no shadow. Additionally, the shadow of someone looking down a deep well at that time in Syene blocked the reflection of the Sun on the water. Eratosthenes then measured the Sun's angle of elevation at noon in Alexandria by measuring the length of another gnomon's shadow on the ground.<ref>{{Cite web |url=https://www.eg.bucknell.edu/physics/astronomy/astr101/specials/eratosthenes.html |title=Astronomy 101 Specials: Eratosthenes and the Size of the Earth |website=www.eg.bucknell.edu |access-date=19 December 2017}}</ref> Using the length of the rod and the length of the shadow as the legs of a triangle, he calculated the angle of the sun's rays.<ref name=":6">{{cite web |url=https://anthonybloggeneral.wordpress.com/2012/07/03/eratosthenes-earth-circumference/ |title=How did Eratosthenes measure the circumference of the earth? |date=3 July 2012 |publisher=}}</ref> This angle was about 7°, or 1/50th the circumference of a [[circle]]; assuming the Earth to be perfectly spherical, he concluded that its circumference was 50 times the known distance from Alexandria to Syene (5,000 stadia, a figure that was checked yearly), i.e. 250,000 stadia.<ref name="stade">{{cite web |last=Walkup |first=Newlyn |date=August 2010 |url=https://old.maa.org/press/periodicals/convergence/eratosthenes-and-the-mystery-of-the-stades-how-long-is-a-stade |title=Eratosthenes and the Mystery of the Stades – How Long Is a Stade? |magazine=Convergence}}</ref> Depending on whether he used the "Olympic stade" (176.4 m) or the Italian stade (184.8 m), this would imply a circumference of 44,100 km (an error of 10%) or 46,100 km, an error of 15%.<ref name="stade" /> A value for the stadion of 157.7 metres has even been posited by L.V. Firsov, which would give an even better precision, but is plagued by calculation errors and false assumptions.<ref name=engels>{{cite journal | last1=Engels | first1=Donald | title=The Length of Eratosthenes' Stade | journal=The American Journal of Philology | date=1985 | volume=106 | issue=3 | pages=298–311 | doi=10.2307/295030 | jstor=295030 }}</ref> In 2012, Anthony Abreu Mora repeated Eratosthenes's calculation with more accurate data; the result was 40,074 km, which is 66 km different (0.16%) from the currently accepted polar circumference.<ref name=":6" />
[[File:Eratosthenes_measure_of_Earth_circumference.svg|thumb|upright=1.4|Measure of Earth's circumference according to Cleomedes's simplified version, based on the approximation that [[Aswan|Syene]] is on the [[Tropic of Cancer]] and on the same meridian as [[Alexandria]].]]
Eratosthenes's method was actually more complicated, as stated by the same Cleomedes, whose purpose was to present a simplified version of the one described in Eratosthenes's book. Pliny, for example, has quoted a value of 252,000 stadia.<ref name="Pliny">Pliny, ''Naturalis Historia'', Book 2, Chapter 112.</ref>
The method was based on several [[surveying]] trips conducted by professional [[bematist]]s, whose job was to precisely measure the extent of the territory of Egypt for agricultural and taxation-related purposes.<ref name="russo273277">{{cite book |last=Russo |first=Lucio |author-link=Lucio Russo |date=2004 |title=The Forgotten Revolution |url=https://archive.org/details/forgottenrevolut00russ_217|url-access=limited |location=Berlin |publisher=Springer |page=[https://archive.org/details/forgottenrevolut00russ_217/page/n277 273]–277}}{{Dead link|date=November 2023}}</ref> Furthermore, the fact that Eratosthenes's measure corresponds precisely to 252,000 stadia (according to Pliny) might be intentional, since it is a number that can be divided by all natural numbers from 1 to 10: some historians believe that Eratosthenes changed from the 250,000 value written by Cleomedes to this new value to simplify calculations;<ref>{{cite journal |first=Dennis |last=Rawlins |title=The Eratosthenes-Strabo Nile Map. Is It the Earliest Surviving Instance of Spherical Cartography? Did It Supply the 5000 Stades Arc for Eratosthenes' Experiment? |journal=Archive for History of Exact Sciences |issue=3 |year=1983 |volume=26 |pages=211–219|doi=10.1007/BF00348500 |s2cid=118004246 |url=https://link.springer.com/article/10.1007/BF00348500 |url-access=subscription }}</ref> other historians of science, on the other side, believe that Eratosthenes introduced a new length unit based on the length of the meridian, as stated by Pliny, who writes about the stadion "according to Eratosthenes' ratio".<ref name="russo273277" /><ref name="Pliny" />
===Posidonius=== {{main|Posidonius#Earth's circumference}}
[[Posidonius]] calculated the Earth's circumference by reference to the position of the star [[Canopus (star)|Canopus]]. As explained by [[Cleomedes]], Posidonius observed Canopus on but never above the horizon at [[Rhodes]], while at [[Alexandria]] he saw it ascend as far as {{frac|7|1|2}} degrees above the horizon (the [[meridian arc]] between the latitude of the two locales is actually 5 degrees 14 minutes). Since he thought Rhodes was 5,000 [[stadion (unit of length)|stadia]] due north of Alexandria, and the difference in the star's elevation indicated the distance between the two locales was 1/48 of the circle, he multiplied 5,000 by 48 to arrive at a figure of 240,000 stadia for the circumference of the earth.<ref name="fragment 202">Posidonius, [https://www.attalus.org/translate/poseidonius.html#202.K fragment 202]</ref> It is generally thought{{By whom|date=April 2023}} that the stadion used by Posidonius was almost 1/10 of a modern statute mile.{{Citation needed|date=April 2023}} Thus Posidonius's measure of 240,000 stadia translates to {{cvt|24000|mi|km}}, not much short of the actual circumference of {{cvt|24901|mi|km}}.<ref name="fragment 202"/> [[Strabo]] noted that the distance between Rhodes and Alexandria is 3,750 stadia, and reported Posidonius's estimate of the Earth's circumference to be 180,000 stadia or {{cvt|18000|mi|km}}.<ref>Cleomedes stated that if the distance is measured by some other number the result will be different, and using 3,750 instead of 5,000 produces this estimation: 3,750 x 48 = 180,000; see {{cite journal |last1=Fischer |first1=Irene |title=Another Look at Eratosthenes' and Posidonius' Determinations of the Earth's Circumference |journal=Quarterly Journal of the Royal Astronomical Society |date=1975 |volume=16 |page=152 |bibcode=1975QJRAS..16..152F |bibcode-access=free}}.</ref> [[Pliny the Elder]] mentions Posidonius among his sources and—without naming him—reported his method for estimating the Earth's circumference. He noted, however, that [[Hipparchus]] had added some 26,000 stadia to Eratosthenes's estimate. The smaller value offered by Strabo and the different lengths of Greek and Roman stadia have created a persistent confusion around Posidonius's result. [[Ptolemy]] used Posidonius's lower value of 180,000 stades (about 33% too low) for the earth's circumference in his [[Geography (Ptolemy)|''Geography'']]. This was the number used by [[Christopher Columbus]] in order to underestimate the distance to India as 70,000 stades.<ref>[[John Freely]], [https://books.google.com/books?id=MfhjAAAAQBAJ ''Before Galileo: The Birth of Modern Science in Medieval Europe''] (2012)</ref>
===Aryabhata=== Around AD 525, the Indian mathematician and astronomer wrote ''[[Aryabhatiya]]'', in which he calculated the diameter of earth to be of 1,050 ''[[yojanas]]''. The length of the ''yojana'' intended by Aryabhata is in dispute. One careful reading gives an equivalent of {{convert|14200|km}}, too large by 11%.<ref>{{Cite arXiv|eprint = 1002.3409|last1 = Kak|first1 = Subhash|title = Aryabhata's Mathematics|year = 2010|class = cs.CR}}</ref> Another gives {{convert|15360|km|abbr=on}}, too large by 20%.<ref>{{Cite journal|last1= Fleet|first1= J. F.|url=https://books.google.com/books?id=rtroKSuAQU4C&q=Aryabhata+yojana&pg=RA1-PA655|title= Dimensions of Indian Cities and Countries|journal= Journal of the Royal Asiatic Society of Great Britain and Ireland|year=1907|volume= 39|issue= 3|pages= 641–656|doi= 10.1017/S0035869X00036431|jstor=25210451}}</ref> Yet another gives {{convert|13440|km|abbr=on}}, too large by 5%.<ref>{{cite book | url=https://archive.org/stream/The_Aryabhatiya_of_Aryabhata_Clark_1930#page/n19/mode/2up | title=The Aryabhatiya of Aryabhata |year=1930 |author=W. E. Clarck}}</ref>{{page needed|date=February 2026}}
===Islamic Golden Age=== Around AD 830, [[Caliph]] [[Al-Ma'mun]] commissioned a group of [[Muslim astronomers]] led by [[Muhammad ibn Musa al-Khwarizmi|Al-Khwarizmi]] to measure the distance from Tadmur ([[Palmyra]]) to [[Raqqa]], in modern [[Syria]]. They calculated the Earth's circumference to be within 15% of the modern value, and possibly much closer. How accurate it actually was is not known because of uncertainty in the conversion between the medieval Arabic units and modern units, but in any case, technical limitations of the methods and tools would not permit an accuracy better than about 5%.<ref name="HOC2_1">{{cite encyclopedia|title=Geodesy|last=Mercier|first=Raymond|pages=175–188|encyclopedia=The History of Cartography, Volume 2, Book 1|editor-last1=Harley|editor-first1=J.B.|editor-last2=Woodward|editor-first2=David|publisher=The University of Chicago Press|year=1992|isbn=9780226316352}}</ref>
[[File:Abu Reyhan Biruni-Earth Circumference.svg|thumb|Diagram showing how al-Biruni was able to calculate the Earth's circumference by measuring the dip of the horizon from a point at a known height.]] A more convenient way to estimate was provided in [[Al-Biruni]]'s ''Codex Masudicus'' (1037). In contrast to his predecessors, who measured the Earth's circumference by sighting the Sun simultaneously from two locations, [[al-Biruni]] developed a new method of using [[trigonometry|trigonometric]] calculations, based on the angle between a [[plain]] and [[mountain]] top, which made it possible for it to be measured by a single person from a single location.<ref name="HOC2_1" /> From the top of the mountain, he sighted the [[Horizon#Zenith angle|dip angle]] which, along with the mountain's height (which he determined beforehand), he applied to the [[law of sines]] formula. This was the earliest known use of dip angle and the earliest practical use of the law of sines.<ref name=Savizi>{{cite journal|title=Applicable Problems in History of Mathematics: Practical Examples for the Classroom|author=Behnaz Savizi|journal=Teaching Mathematics and Its Applications|volume=26|issue=1|year=2007|pages=45–50|doi=10.1093/teamat/hrl009}}</ref> However, the method could not provide more accurate results than previous methods, due to technical limitations, and so al-Biruni accepted the value calculated the previous century by the [[al-Ma'mun]] expedition.<ref name="HOC2_1" />
===Columbus's error=== {{main|Christopher Columbus#Quest for Asia}}
1,700 years after Eratosthenes's death, [[Christopher Columbus]] studied what Eratosthenes had written about the size of the Earth. Nevertheless, based on a map by [[Toscanelli]], he chose to believe that the Earth's circumference was 25% smaller. If, instead, Columbus had accepted Eratosthenes's larger value, he would have known that the place where he made landfall was not [[Asia]], but rather a [[New World]].<ref>Gow, Mary. [https://books.google.com/books?id=hWv-WUOHfSIC&pg=PA6&vq=Columbus&dq=Measuring+the+Earth:+Eratosthenes+and+His+Celestial+Geometry.&output=html_text&source=gbs_search_r&cad=1 ''Measuring the Earth: Eratosthenes and His Celestial Geometry''], p. 6 (Berkeley Heights, NJ: Enslow, 2010).</ref>
==Historical use in the definition of units of measurement== {{main|History of the metre#Meridional definition}} {{further|Meridian arc#History of measurement|Earth radius#History|Arc measurement of Delambre and Méchain}}
In 1617 the Dutch scientist [[Willebrord Snellius]] assessed the circumference of the Earth at 24,630 Roman miles (24,024 statute miles). Around that time British mathematician [[Edmund Gunter]] improved navigational tools including a new [[Quadrant (instrument)|quadrant]] to determine latitude at sea. He reasoned that the lines of latitude could be used as the basis for a unit of measurement for [[distance]] and proposed the nautical mile as one minute or one-sixtieth ({{sfrac|1|60}}) of one [[Degree (angle)|degree]] of latitude. As one degree is {{sfrac|1|360}} of a circle, one minute of arc is {{sfrac|1|21600}} of a circle – such that the polar circumference of the Earth would be exactly 21,600 miles. Gunter used Snellius's circumference to define a nautical mile as 6,080 feet, the length of one minute of arc at 48 degrees latitude.<ref>Marine Insight, [https://www.marineinsight.com/guidelines/nautical-mile-knot-units-used-sea/ Why Nautical Mile and Knot Are The Units Used at Sea?]</ref>
In 1793, France defined the metre so as to make the polar circumference of the Earth 40,000 kilometres. To measure this distance accurately, the [[French Academy of Sciences]] commissioned [[Jean Baptiste Joseph Delambre]] and [[Pierre Méchain]] to lead [[Arc measurement of Delambre and Méchain|an expedition]] to attempt to accurately measure the distance between a belfry in [[Dunkirk|Dunkerque]] and [[Montjuïc Castle (Barcelona)|Montjuïc castle]] in [[Barcelona]] to estimate the length of the [[meridian arc]] through Dunkerque. The length of the first [[Metre#International_prototype_metre_bar|prototype metre bar]] was based on these measurements, but it was later determined that its length was short by about 0.2 millimetres because of the miscalculation of the [[flattening]] of the Earth, making the prototype about 0.02% shorter than the original proposed definition of the metre. Regardless, this length became the French standard and was progressively adopted by other countries in Europe.<ref name="Alder2003">{{cite book|last=Alder|first=Ken|title=The Measure of All Things: The Seven-Year Odyssey and Hidden Error That Transformed the World|url=https://books.google.com/books?id=jwsDERPMPhsC|date=October 2003|publisher=Simon and Schuster|isbn=978-0-7432-1676-0}}</ref> This is why the polar circumference of the Earth is actually 40,008 kilometres, instead of 40,000.
==See also== {{portal|Earth|Earth Sciences|Geodesy|History of Science}} *[[Arabic mile]] *[[Arc measurement]] *[[Earth ellipsoid]] *[[Earth's radius]] *[[Geographical mile]] *[[International mile]] *[[Timeline of Earth estimates]] {{clear}}
==References== {{reflist}}
==Bibliography== * {{cite book|last1=Krebs|first1=Robert E.|last2=Krebs|first2=Carolyn A.|title=Groundbreaking Scientific Experiments, Inventions, and Discoveries of the Ancient World|chapter-url=https://books.google.com/books?id=0H0fjBeseVEC&pg=PA52|year=2003|publisher=Greenwood Publishing Group|isbn=978-0-313-31342-4|page=52|chapter=Calculating the Earth's Circumference}} * {{cite book|last=Nicastro|first=Nicholas|title=Circumference: Eratosthenes and the Ancient Quest to Measure the Globe|url=https://archive.org/details/isbn_9780312372477|url-access=registration|date=25 November 2008|publisher=St. Martin's Press|isbn=978-1-4299-5819-6}} * {{cite book|last=Gow|first=Mary|title=Measuring the Earth: Eratosthenes and His Celestial Geometry|url=https://books.google.com/books?id=hWv-WUOHfSIC|date=1 July 2009|publisher=Enslow Publishing, LLC|isbn=978-0-7660-3120-3}} * {{cite book|last=Lowrie|first=William|title=Fundamentals of Geophysics|url=https://books.google.com/books?id=h2-NjUg4RtEC&pg=PA43|date=20 September 2007|publisher=Cambridge University Press|isbn=978-1-139-46595-3}}
==External links== {{sister project links|auto=yes}} * [https://www.youtube.com/watch?v=8hZl3arO7SY Carl Sagan demonstrates how Eratosthenes determined that the Earth was round and the approximate circumference] {{Earth}} {{Earth science}} {{Geodesy navbox}} {{authority control}}
[[Category:Earth|Circumference]] [[Category:Units of length]] [[Category:Geodesy]]