Earth's circumference is the
distance
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
around
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
. Measured around the
Equator, it is . Measured around the
poles
Poles,, ; singular masculine: ''Polak'', singular feminine: ''Polka'' or Polish people, are a West Slavic nation and ethnic group, who share a common history, culture, the Polish language and are identified with the country of Poland in C ...
, the circumference is .
Measurement of Earth's circumference has been important to
navigation
Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation, ...
since ancient times. The first known scientific measurement and calculation was done by
Eratosthenes, who achieved a great degree of precision in his computation.
Treating the Earth as a
sphere
A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is th ...
, its circumference would be its single most important measurement.
Earth deviates from spherical by about 0.3%, as characterized by
flattening
Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution ( spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening i ...
.
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
The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its prefi ...
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 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
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 had remained close to what it was determined to be at the time, so the Earth's circumference is no longer a
round number
A round number is an integer that ends with one or more " 0"s (zero-digit) in a given base. So, 590 is rounder than 592, but 590 is less round than 600. In both technical and informal language, a round number is often interpreted to stand for a ...
in metres or nautical miles.
History
Eratosthenes
The measure of Earth's circumference is the most famous among the results obtained by Eratosthenes, who estimated that the meridian has a length of 252,000
stadia
Stadia may refer to:
* One of the plurals of stadium, along with "stadiums"
* The plural of stadion, an ancient Greek unit of distance, which equals to 600 Greek feet (''podes'').
* Stadia (Caria), a town of ancient Caria, now in Turkey
* Stadi ...
, with an error on the real value between −2.4% and +0.8% (assuming a value for the stadion between 155 and 160 metres).
Eratosthenes described his technique in a book entitled ''On the measure of the Earth'', which has not been preserved.
![Eratosthenes_measure_of_Earth_circumference](https://upload.wikimedia.org/wikipedia/commons/1/1f/Eratosthenes_measure_of_Earth_circumference.svg)
Eratosthenes' method to calculate Earth's circumference has been lost; what has been preserved is the simplified version described by
Cleomedes to popularise the discovery. Cleomedes invites his reader to consider two Egyptian cities,
Alexandria
Alexandria ( or ; ar, ٱلْإِسْكَنْدَرِيَّةُ ; grc-gre, Αλεξάνδρεια, Alexándria) is the second largest city in Egypt, and the largest city on the Mediterranean coast. Founded in by Alexander the Great, Alexandri ...
and
Syene
Aswan (, also ; ar, أسوان, ʾAswān ; cop, Ⲥⲟⲩⲁⲛ ) is a city in Southern Egypt, and is the capital of the Aswan Governorate.
Aswan is a busy market and tourist centre located just north of the Aswan Dam on the east bank of t ...
, modern
Assuan:
# Cleomedes assumes that the distance between Syene and Alexandria was 5,000
stadia
Stadia may refer to:
* One of the plurals of stadium, along with "stadiums"
* The plural of stadion, an ancient Greek unit of distance, which equals to 600 Greek feet (''podes'').
* Stadia (Caria), a town of ancient Caria, now in Turkey
* Stadi ...
(a figure that was checked yearly by professional
bematist
Bematists or bematistae (Ancient Greek βηματισταί (''bēmatistaí'', 'step measurer'), from
βῆμα (''bema'', 'pace')), were specialists in ancient Greece and ancient Egypt who measured distances by pacing.
Measurements of Alexa ...
s, ''mensores regii'').
# He assumes the simplified (but inaccurate) hypothesis that Syene was precisely on the
Tropic of Cancer
The Tropic of Cancer, which is also referred to as the Northern Tropic, is the most northerly circle of latitude on Earth at which the Sun can be directly overhead. This occurs on the June solstice, when the Northern Hemisphere is tilted tow ...
, saying that at
local noon on the summer
solstice
A solstice is an event that occurs when the Sun appears to reach its most northerly or southerly excursion relative to the celestial equator on the celestial sphere. Two solstices occur annually, around June 21 and December 21. In many countr ...
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.
Under the previous assumptions, writes Cleomedes, you can measure the Sun's angle of elevation at noon of the summer solstice in Alexandria, by using a vertical rod (a
gnomon) of known length and measuring the length of its shadow on the ground; it is then possible to calculate the angle of the Sun's rays, which he claims to be about 7°, or 1/50th the circumference of a
circle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is con ...
. Taking the Earth as spherical, the Earth's circumference would be fifty times the distance between Alexandria and Syene, that is 250,000 stadia. Since 1 Egyptian stadion is equal to about 157.7 metres,
[Donald Engels (1985)]
The Length of Eratosthenes' Stade
''American Journal of Philology'' 106 (3): 298–311. . the result is roughly 39,425 km, which is 1.5% less than the real circumference, 40,008 km.
Eratosthenes' 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' book. The method was based on several
surveying trips conducted by professional
bematist
Bematists or bematistae (Ancient Greek βηματισταί (''bēmatistaí'', 'step measurer'), from
βῆμα (''bema'', 'pace')), were specialists in ancient Greece and ancient Egypt who measured distances by pacing.
Measurements of Alexa ...
s, whose job was to precisely measure the extent of the territory of Egypt for agricultural and taxation-related purposes.
Furthermore, the fact that Eratosthenes' measure corresponds precisely to 252,000 stadia 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; 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".
Posidonius
Posidonius
Posidonius (; grc-gre, Ποσειδώνιος , "of Poseidon") "of Apameia" (ὁ Ἀπαμεύς) or "of Rhodes" (ὁ Ῥόδιος) (), was a Greek politician, astronomer, astrologer, geographer, historian, mathematician, and teacher nativ ...
calculated the Earth's circumference by reference to the position of the star
Canopus
Canopus is the brightest star in the southern constellation of Carina and the second-brightest star in the night sky. It is also designated α Carinae, which is Latinised to Alpha Carinae. With a visual apparent magnitude ...
. As explained by
Cleomedes, Posidonius observed
Canopus
Canopus is the brightest star in the southern constellation of Carina and the second-brightest star in the night sky. It is also designated α Carinae, which is Latinised to Alpha Carinae. With a visual apparent magnitude ...
on but never above the horizon at
Rhodes
Rhodes (; el, Ρόδος , translit=Ródos ) is the largest and the historical capital of the Dodecanese islands of Greece. Administratively, the island forms a separate municipality within the Rhodes regional unit, which is part of the S ...
, while at
Alexandria
Alexandria ( or ; ar, ٱلْإِسْكَنْدَرِيَّةُ ; grc-gre, Αλεξάνδρεια, Alexándria) is the second largest city in Egypt, and the largest city on the Mediterranean coast. Founded in by Alexander the Great, Alexandri ...
he saw it ascend as far as 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
stadia
Stadia may refer to:
* One of the plurals of stadium, along with "stadiums"
* The plural of stadion, an ancient Greek unit of distance, which equals to 600 Greek feet (''podes'').
* Stadia (Caria), a town of ancient Caria, now in Turkey
* Stadi ...
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.
[Posidonius]
fragment 202
/ref> It is generally thought that the stadion used by Posidonius was almost exactly 1/10 of a modern statute mile. Thus Posidonius's measure of 240,000 stadia translates to , not much short of the actual circumference of . 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 . Pliny the Elder
Gaius Plinius Secundus (AD 23/2479), called Pliny the Elder (), was a Roman author, naturalist and natural philosopher, and naval and army commander of the early Roman Empire, and a friend of the emperor Vespasian. He wrote the encyclopedic ' ...
mentions Posidonius among his sources and without naming him reported his method for estimating the Earth's circumference. He noted, however, that Hipparchus
Hipparchus (; el, Ἵππαρχος, ''Hipparkhos''; BC) was a Greek astronomer, geographer, and mathematician. He is considered the founder of trigonometry, but is most famous for his incidental discovery of the precession of the equi ...
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
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importance ...
used Posidonius's lower value of 180,000 stades (about 33% too low) for the earth's circumference in his ''Geography''. This was the number used by Christopher Columbus
Christopher Columbus
* lij, Cristoffa C(or)ombo
* es, link=no, Cristóbal Colón
* pt, Cristóvão Colombo
* ca, Cristòfor (or )
* la, Christophorus Columbus. (; born between 25 August and 31 October 1451, died 20 May 1506) was a ...
in order to underestimate the distance to India as 70,000 stades.
Aryabhata
Around AD 525, the Indian mathematician and astronomer Aryabhata wrote '' Aryabhatiya'', in which he calculated the diameter of earth to be of 1,050 ''yojanas
A yojana (Sanskrit: योजन; th, โยชน์; my, ယူဇနာ) is a measure of distance that was used in ancient India, Thailand and Myanmar. A yojana is about 12–15 km.
Edicts of Ashoka (3rd century BCE)
Ashoka, in his Major R ...
''. The length of the ''yojana'' intended by Aryabhata is in dispute. One careful reading gives an equivalent of 14,200 kilometers, too large by 11%. Another gives 15,360 km, too large by 20%. Yet another gives 13,440 km, too large by 5%.
Islamic Golden Age
Around AD 830, Caliph
A caliphate or khilāfah ( ar, خِلَافَة, ) is an institution or public office under the leadership of an Islamic steward with the title of caliph (; ar, خَلِيفَة , ), a person considered a political-religious successor to th ...
Al-Ma'mun commissioned a group of Muslim astronomers led by Al-Khwarizmi
Muḥammad ibn Mūsā al-Khwārizmī ( ar, محمد بن موسى الخوارزمي, Muḥammad ibn Musā al-Khwārazmi; ), or al-Khwarizmi, was a Persian polymath from Khwarazm, who produced vastly influential works in mathematics, astronom ...
to measure the distance from Tadmur (Palmyra
Palmyra (; Palmyrene: () ''Tadmor''; ar, تَدْمُر ''Tadmur'') is an ancient city in present-day Homs Governorate, Syria. Archaeological finds date back to the Neolithic period, and documents first mention the city in the early secon ...
) to Raqqa
Raqqa ( ar, ٱلرَّقَّة, ar-Raqqah, also and ) (Kurdish: Reqa/ ڕەقە) is a city in Syria on the northeast bank of the Euphrates River, about east of Aleppo. It is located east of the Tabqa Dam, Syria's largest dam. The Hellenistic, ...
, 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%.
A more convenient way to estimate was provided in Al-Biruni
Abu Rayhan Muhammad ibn Ahmad al-Biruni (973 – after 1050) commonly known as al-Biruni, was a Khwarazmian Iranian in scholar and polymath during the Islamic Golden Age. He has been called variously the "founder of Indology", "Father of Co ...
'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
Abu Rayhan Muhammad ibn Ahmad al-Biruni (973 – after 1050) commonly known as al-Biruni, was a Khwarazmian Iranian in scholar and polymath during the Islamic Golden Age. He has been called variously the "founder of Indology", "Father of Co ...
developed a new method of using trigonometric
Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. ...
calculations, based on the angle between a plain
In geography, a plain is a flat expanse of land that generally does not change much in elevation, and is primarily treeless. Plains occur as lowlands along valleys or at the base of mountains, as coastal plains, and as plateaus or uplands ...
and mountain
A mountain is an elevated portion of the Earth's crust, generally with steep sides that show significant exposed bedrock. Although definitions vary, a mountain may differ from a plateau in having a limited summit area, and is usually highe ...
top, which made it possible for it to be measured by a single person from a single location. From the top of the mountain, he sighted the dip angle which, along with the mountain's height (which he determined beforehand), he applied to the law of sines
In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles. According to the law,
\frac \,=\, \frac \,=\, \frac \,=\, 2R,
where , and ar ...
formula. This was the earliest known use of dip angle and the earliest practical use of the law of sines. 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.
Columbus's error
1,700 years after Eratosthenes's death, Christopher Columbus
Christopher Columbus
* lij, Cristoffa C(or)ombo
* es, link=no, Cristóbal Colón
* pt, Cristóvão Colombo
* ca, Cristòfor (or )
* la, Christophorus Columbus. (; born between 25 August and 31 October 1451, died 20 May 1506) was a ...
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
The term ''New World'' is often used to mean the majority of Earth's Western Hemisphere, specifically the Americas."America." ''The Oxford Companion to the English Language'' (). McArthur, Tom, ed., 1992. New York: Oxford University Press, p. ...
.
Historical use in the definition of units of measurement
In 1617 the Dutch scientist Willebrord Snellius
Willebrord Snellius (born Willebrord Snel van Royen) (13 June 158030 October 1626) was a Dutch astronomer and mathematician, Snell. His name is usually associated with the law of refraction of light known as Snell's law.
The lunar crater Sn ...
assessed the circumference of the Earth at 24,630 Roman miles (24,024 statute miles). Around that time British mathematician Edmund Gunter
Edmund Gunter (158110 December 1626), was an English clergyman, mathematician, geometer and astronomer of Welsh descent. He is best remembered for his mathematical contributions which include the invention of the Gunter's chain, the Gunter's qu ...
improved navigational tools including a new 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
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
and proposed the nautical mile as one minute or one-sixtieth () of one degree of latitude. As one degree is of a circle, one minute of arc is 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.[Marine Insight]
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. In order to measure this distance accurately, the French Academy of Sciences commissioned Jean Baptiste Joseph Delambre
Jean Baptiste Joseph, chevalier Delambre (19 September 1749 – 19 August 1822) was a French mathematician, astronomer, historian of astronomy, and geodesist. He was also director of the Paris Observatory, and author of well-known books on t ...
and Pierre Méchain
Pierre François André Méchain (; 16 August 1744 – 20 September 1804) was a French astronomer and surveyor who, with Charles Messier, was a major contributor to the early study of deep-sky objects and comets.
Life
Pierre Méchain was born i ...
to lead an expedition to attempt to accurately measure the distance between a belfry in Dunkerque and Montjuïc castle
Montjuïc Castle ( ca, Castell de Montjuïc, es, Castillo de Montjuich) is an old military fortress, with roots dating back from 1640, built on top of Montjuïc hill in Barcelona, Catalonia, Spain. It currently serves as a Barcelona municipal faci ...
in Barcelona
Barcelona ( , , ) is a city on the coast of northeastern Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second most populous municipality of Spain. With a population of 1.6 million within ci ...
to estimate the length of the meridian arc through Dunkerque. The length of the first 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 miscalculation of the flattening
Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution ( spheroid) respectively. Other terms used are ellipticity, or oblateness. The usual notation for flattening i ...
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. This is why the polar circumference of the Earth is actually 40,008 kilometres, instead of 40,000.
See also
* Earth radius
Earth radius (denoted as ''R''🜨 or R_E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly (equatorial radius, deno ...
* Spherical Earth
Spherical Earth or Earth's curvature refers to the approximation of figure of the Earth as a sphere.
The earliest documented mention of the concept dates from around the 5th century BC, when it appears in the writings of Greek philosophers. ...
* Nautical mile
References
Bibliography
*
*
*
* {{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
Carl_Sagan
_demonstrates_how_Eratosthenes_determined_that_the_Earth_was_round_and_the_approximate_circumference.html" ;"title="Carl Sagan">Carl_Sagan">Carl_Sagan_demonstrates_how_Eratosthenes_determined_that_the_Earth_was_round_and_the_approximate_circumference
Earth.html" "title="Carl Sagan
demonstrates how Eratosthenes determined that the Earth was round and the approximate circumference">Carl Sagan">Carl Sagan
demonstrates how Eratosthenes determined that the Earth was round and the approximate circumference
Earth">Circumference
In geometry, the circumference (from Latin ''circumferens'', meaning "carrying around") is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out t ...
Units of length
Geodesy