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Spherical Earth or Earth's curvature refers to the approximation of the figure of the Earth to a sphere. The concept of a spherical Earth gradually displaced earlier beliefs in a flat Earth during classical antiquity and the Middle Ages. The figure of the Earth is more accurately described as an ellipsoid, which was realized in the early modern period.

Cause

Earth is massive enough that the pull of gravity maintains its roughly spherical shape. Most of its deviation from spherical stems from the centrifugal force caused by rotation around its north-south axis. This force deforms the sphere into an oblate ellipsoid.^[1]

Formation

The Solar System formed from a dust cloud that was at least partially the remnant of one or more supernovas that produced heavy elements by nucleosynthesis. Grains of matter accreted through electrostatic interaction. As they grew in mass, gravity took over in gathering yet more mass, releasing the potential energy of their collisions and in-falling as heat. The protoplanetary disk also had a greater proportion of radioactive elements than Earth today because, over time, those elements decayed. Their decay heated the early Earth even further, and continue to contribute to Earth's internal heat budget. The early Earth was thus mostly liquid.

A sphere is the only stable shape for a non-rotating, gravitationally self-attracting liquid. The outward acceleration caused by Earth's rotation is greater at the equator than at the poles (where is it zero), so the sphere gets deformed into an ellipsoid, which represents the shape having the lowest potential energy for a rotating, fluid body. This ellipsoid is slightly fatter around the equator than a perfect sphere would be. Earth's shape is also slightly lumpy because it is composed of different materials of different densities that exert slightly different amounts of gravitational force per volume.

The liquidity of a hot, newly formed planet allows heavier elements to sink down to the middle and forces lighter elements closer to the surface, a process known as planetary differentiation. This event is known as the iron catastrophe; the most abundant heavier elements were iron and nickel, which now form the Earth's core.

Later shape changes and effects

Though the surface rocks of Earth have cooled enough to solidify, the outer core of the planet is still hot enough to remain liquid. Energy is still being released; volcanic and tectonic activity has pushed rocks into hills and mountains and blown them out of calderas. Meteors also cause impact craters and surrounding ridges. However, if the energy release from these processes halts, then they tend to erode away over time and return toward the lowest potential-energy curve of the ellipsoid. Weather powered by solar energy can also move water, rock, and soil to make Earth slightly out of round.

Earth undulates as the shape of its lowest potential energy changes daily due to the gravity of the Sun and Moon as they move around with respect to Earth. This is what causes tides in the oceans' water, which can flow freely along the changing potential.

History of concept and measurement

The spherical shape of the Earth was known and measured by astronomers, mathematicians, and navigators from a variety of literate ancient cultures, including the Hellenic World, and Ancient India. Greek ethnographer Megasthenes, c. 300 BC, has been interpreted as stating that the contemporary Brahmans of India believed in a spherical Earth as the center of the universe.^[2] The knowledge of the Greeks was inherited by Ancient Rome, and Christian and Islamic realms in the Middle Ages. Circumnavigation of the world in the Age of Discovery provided direct evidence. Improvements in transportation and other technologies refined estimations of the size of the Earth, and helped spread knowledge of it.

The earliest documented mention of the concept dates from around the 5th century BC, when it appears in the writings of Greek philosophers.^[3]^[4] In the 3rd century BC, Hellenistic astronomy established the roughly spherical shape of Earth as a physical fact and calculated the Earth's circumference. This knowledge was gradually adopted throughout the Old World during Late Antiquity and the Middle Ages.^[5]^[6]^[7]^[8] A practical demonstration of Earth's sphericity was achieved by Ferdinand Magellan and Juan Sebastián Elcano's circumnavigation (1519–1522).^[9]

The concept of a spherical Earth displaced earlier beliefs in a flat Earth: In early Mesopotamian mythology, the world was portrayed as a disk floating in the ocean with a hemispherical sky-dome above,^[10] and this forms the premise for early world maps like those of Anaximander and Hecataeus of Miletus. Other speculations on the shape of Earth include a seven-layered ziggurat or cosmic mountain, alluded to in the Avesta and ancient Persian writings (see seven climes).

The realization that the figure of the Earth is more accurately described as an ellipsoid dates to the 17th century, as described by Isaac Newton in Principia. In the early 19th century, the flattening of the earth ellipsoid was determined to be of the order of 1/300 (Delambre, Everest). The modern value as determined by the US DoD World Geodetic System since the 1960s is close to 1/298.25.^[11]

Measurement and representation

Geodesy, also called geodetics, is the scientific discipline that deals with the measurement and representation of Earth, its gravitational field and geodynamic phenomena (polar motion, Earth tides, and crustal motion) in three-dimensional time-varying space.

Geodesy is primarily concerned with positioning and the gravity field and geometrical aspects of their temporal variations, although it can also include the study of Earth's magnetic field. Especially in the German speaking world, geodesy is divided into geomensuration ("Erdmessung" or "höhere Geodäsie"), which is concerned with measuring Earth on a global scale, and surveying ("Ingenieurgeodäsie"), which is concerned with measuring parts of the surface.

Earth's shape can be thought of in at least two ways:

as the shape of the geoid, the mean sea level of the world ocean; or
as the shape of Earth's land surface as it rises above and falls below the sea.

As the science of geodesy measured Earth more accurately, the shape of the geoid was first found not to be a perfect sphere but to approximate an oblate spheroid, a specific type of ellipsoid. More recent^[when?] measurements have measured the geoid to unprecedented accuracy, revealing mass concentrations beneath Earth's surface.

Evidence

The roughly spherical shape of Earth can be empirically evidenced by many different types of observation, ranging from ground level, flight, or orbit. The spherical shape causes a number of effects and phenomena that when combined disprove flat Earth beliefs.

These include the visibility of distant objects on Earth's surface; lunar hi eclipses; appearance of the Moon; observation of the sky from a certain altitude; observation of certain fixed stars from different locations; observing the Sun; surface navigation; grid distortion on a spherical surface; weather systems; gravity; and modern technology.

References

^ "Why Are Planets Round?". NASA Space Place. June 27, 2019. Retrieved 2019-08-31.
^ E. At. Schwanbeck (1877). Ancient India as described by Megasthenês and Arrian; being a translation of the fragments of the Indika of Megasthenês collected by Dr. Schwanbeck, and of the first part of the Indika of Arrian. p. 101.
^ Dicks, D.R. (1970). Early Greek Astronomy to Aristotle. Ithaca, N.Y.: Cornell University Press. pp. 72–198. ISBN 978-0-8014-0561-7.
^ Cormack, Lesley B. (2015), "That before Columbus, geographers and other educated people knew the Earth was flat", in Numbers, Ronald L.; Kampourakis, Kostas (eds.), Newton's Apple and Other Myths about Science, Harvard University Press, pp. 16–24, ISBN 9780674915473
^ Continuation into Roman and medieval thought: Reinhard Krüger: "Materialien und Dokumente zur mittelalterlichen Erdkugeltheorie von der Spätantike bis zur Kolumbusfahrt (1492)"
^ Jamil, Jamil (2009). "Astronomy". In Fleet, Kate; Krämer, Gudrun; Matringe, Denis; Nawas, John; Rowson, Everett (eds.). Encyclopaedia of Islam. doi:10.1163/1573-3912_ei3_COM_22652. ISBN 978-90-04-17852-6.
^ Direct adoption by India: D. Pingree: "History of Mathematical Astronomy in India", Dictionary of Scientific Biography, Vol. 15 (1978), pp. 533–633 (554f.); Glick, Thomas F., Livesey, Steven John, Wallis, Faith (eds.): "Medieval Science, Technology, and Medicine: An Encyclopedia", Routledge, New York 2005, ISBN 0-415-96930-1, p. 463
^ Adoption by China via European science: Martzloff, Jean-Claude (1993). "Space and Time in Chinese Texts of Astronomy and of Mathematical Astronomy in the Seventeenth and Eighteenth Centuries". Chinese Science. 11 (11): 66–92. doi:10.1163/26669323-01101005. JSTOR 43290474. Archived from the original on 2021-10-26. Retrieved 2021-10-12. and Cullen, C. (1976). "A Chinese Eratosthenes of the Flat Earth: A Study of a Fragment of Cosmology in Huai Nan tzu 淮南子". Bulletin of the School of Oriental and African Studies, University of London. 39 (1): 106–127. doi:10.1017/S0041977X00052137. JSTOR 616189. S2CID 171017315.
^ Pigafetta, Antonio (1906). Magellan's Voyage around the World. Arthur A. Clark. [1]
^ Neugebauer, Otto E. (1975). A History of Ancient Mathematical Astronomy. Birkhäuser. p. 577. ISBN 978-3-540-06995-9.
^ See Figure of the Earth and Earth radius § Global radii for details. Recent measurements from satellites suggest that Earth is actually slightly pear-shaped. Hugh Thurston, Early Astronomy, (New York: Springer-Verlag), p. 119. ISBN 0-387-94107-X.

Works cited

Needham, Joseph; Wang, Ling (1995) [1959]. Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth. Vol. 3 (reprint ed.). Cambridge: Cambridge University Press. ISBN 0-521-05801-5.

External links

You say the earth is round? Prove it (from The Straight Dope)
NASA – Most Changes in Earth's Shape Are Due to Changes in Climate
The Round Earth and Christopher Columbus, educational web site
Top 10 Ways to Know the Earth is Not Flat, science education site

[1] "Why Are Planets Round?". NASA Space Place. June 27, 2019. Retrieved 2019-08-31.

[2] E. At. Schwanbeck (1877). Ancient India as described by Megasthenês and Arrian; being a translation of the fragments of the Indika of Megasthenês collected by Dr. Schwanbeck, and of the first part of the Indika of Arrian. p. 101.

[Dicks-3] Dicks, D.R. (1970). Early Greek Astronomy to Aristotle. Ithaca, N.Y.: Cornell University Press. pp. 72–198. ISBN 978-0-8014-0561-7.

[4] Cormack, Lesley B. (2015), "That before Columbus, geographers and other educated people knew the Earth was flat", in Numbers, Ronald L.; Kampourakis, Kostas (eds.), Newton's Apple and Other Myths about Science, Harvard University Press, pp. 16–24, ISBN 9780674915473

[Krüger:_Roman_and_medieval_continuation-5] Continuation into Roman and medieval thought: Reinhard Krüger: "Materialien und Dokumente zur mittelalterlichen Erdkugeltheorie von der Spätantike bis zur Kolumbusfahrt (1492)"

[Encyclopaedia_of_Islam:_Astronomy-6] Jamil, Jamil (2009). "Astronomy". In Fleet, Kate; Krämer, Gudrun; Matringe, Denis; Nawas, John; Rowson, Everett (eds.). Encyclopaedia of Islam. doi:10.1163/1573-3912_ei3_COM_22652. ISBN 978-90-04-17852-6.

[Pingree:_Indian_adoption-7] Direct adoption by India: D. Pingree: "History of Mathematical Astronomy in India", Dictionary of Scientific Biography, Vol. 15 (1978), pp. 533–633 (554f.); Glick, Thomas F., Livesey, Steven John, Wallis, Faith (eds.): "Medieval Science, Technology, and Medicine: An Encyclopedia", Routledge, New York 2005, ISBN 0-415-96930-1, p. 463

[Martzloff,_Cullen:_Chinese_adoption-8] Adoption by China via European science: Martzloff, Jean-Claude (1993). "Space and Time in Chinese Texts of Astronomy and of Mathematical Astronomy in the Seventeenth and Eighteenth Centuries". Chinese Science. 11 (11): 66–92. doi:10.1163/26669323-01101005. JSTOR 43290474. Archived from the original on 2021-10-26. Retrieved 2021-10-12. and Cullen, C. (1976). "A Chinese Eratosthenes of the Flat Earth: A Study of a Fragment of Cosmology in Huai Nan tzu 淮南子". Bulletin of the School of Oriental and African Studies, University of London. 39 (1): 106–127. doi:10.1017/S0041977X00052137. JSTOR 616189. S2CID 171017315.

[9] Pigafetta, Antonio (1906). Magellan's Voyage around the World. Arthur A. Clark. [1]

[Neugebauer-10] Neugebauer, Otto E. (1975). A History of Ancient Mathematical Astronomy. Birkhäuser. p. 577. ISBN 978-3-540-06995-9.

[11] See Figure of the Earth and Earth radius § Global radii for details. Recent measurements from satellites suggest that Earth is actually slightly pear-shaped. Hugh Thurston, Early Astronomy, (New York: Springer-Verlag), p. 119. ISBN 0-387-94107-X.

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@@ Line 1: / Line 1: @@
+{{Short description|Approximation of the figure of Earth as a sphere}}
-[[Image:John Gower world Vox Clamantis detail.jpg|thumb|right|[[Medieval]] artistic representation of a spherical Earth - with compartments representing [[earth]], [[air]], and [[water]] (c.1400).]]
+{{Redirect|Round world|other uses|The World is Round (disambiguation){{!}}The World is Round}}{{Distinguish|Scleroderma (fungus){{!}}Earth ball}}
-The concept of a '''[[Sphere|spherical]] [[Earth]]''' dates back to around the 6th century BCE in ancient [[Greek philosophy]].<ref name="dicks">{{cite book |last=Dicks |first=D.R. |title=Early Greek Astronomy to Aristotle |pages=72–198 |year=1970 |isbn=9780801405617 |publisher=Cornell University Press |location=Ithaca, N.Y.}}</ref> It remained a matter of philosophical speculation until the 3rd century BCE when [[Hellenistic astronomy]] established the spherical shape of the earth as a physical given.
+[[File:ISS-40 Sicily and Italy.jpg|thumb|Image from space: The curved surface of the spherical planet Earth]]'''Spherical Earth''' or '''Earth's curvature''' refers to the [[approximation]] of the [[figure of the Earth]] to a [[sphere]]. The concept of a spherical Earth gradually displaced earlier beliefs in a [[flat Earth]] during [[classical antiquity]] and the [[Middle Ages]]. The [[figure of the Earth]] is more accurately described as an [[Earth ellipsoid|ellipsoid]], which was realized in the [[early modern period]].
-The concept of a spherical Earth displaced earlier beliefs in a [[flat Earth]]: In early [[Mesopotamia]]n thought, the world was portrayed as a flat disk floating in the ocean, and this forms the premise for early Greek maps like those of [[Anaximander]] and [[Hecataeus of Miletus]]. Other speculations on the shape of Earth include a seven-layered [[ziggurat]] or [[cosmic mountain]], alluded to in the [[Avesta]] and ancient [[Persian Empire|Persian]] writings (see [[seven climes]]).
+==Cause==
-As determined by modern instruments, a sphere approximates the Earth's shape to within one part in 300. An oblate ellipsoid with a flattening of 1/300 approximates the Earth exceedingly well. See [[Figure of the Earth]].
+{{main|Equatorial bulge}}
+{{see also|Hydrostatic equilibrium#Planetary geology}}
+Earth is massive enough that the pull of [[gravity]] maintains its roughly spherical shape. Most of its deviation from spherical stems from the [[centrifugal force]] caused by [[Earth's rotation|rotation]] around its north-south axis. This force deforms the sphere into an [[oblate ellipsoid]].<ref>{{cite web |url=https://spaceplace.nasa.gov/planets-round/en/ |date=June 27, 2019 |title=Why Are Planets Round? |website=NASA Space Place |access-date=2019-08-31}}</ref>
-==History==
-===Early development===
-;Pythagoras
-Early Greek philosophers alluded to a spherical Earth, though with some ambiguity.<ref name="dicks1">{{cite book |last=Dicks |first=D.R. |title=Early Greek Astronomy to Aristotle |pages=68 |year=1970 |isbn=9780801405617 |publisher=Cornell University Press |location=Ithaca, N.Y.}}</ref> This idea influenced [[Pythagoras]] (b. 570 BCE), who saw [[harmony]] in the universe and sought to explain it. He reasoned that Earth and the other planets must be spheres, since the most harmonious [[geometric]] solid form is a [[sphere]].<ref name="dicks" /> After the fifth century BCE, no Greek writer of repute thought the world was anything but round.<ref name="dicks1" />
+===Formation===
+{{Further|History of Earth}}
+The [[formation and evolution of the Solar System|Solar System formed]] from a dust cloud that was at least partially the remnant of one or more [[supernova]]s that produced heavy elements by [[nucleosynthesis]]. Grains of matter accreted through electrostatic interaction. As they grew in mass, gravity took over in gathering yet more mass, releasing the [[potential energy]] of their collisions and in-falling as [[heat]]. The [[protoplanetary disk]] also had a greater proportion of radioactive elements than Earth today because, over time, those elements [[Radioactive decay|decayed]]. Their decay heated the early Earth even further, and continue to contribute to [[Earth's internal heat budget]]. The early Earth was thus mostly liquid.
+A sphere is the only stable shape for a non-rotating, gravitationally self-attracting liquid. The outward acceleration caused by Earth's rotation is greater at the equator than at the poles (where is it zero), so the sphere gets deformed into an [[ellipsoid]], which represents the shape having the lowest potential energy for a rotating, fluid body. This ellipsoid is slightly fatter around the equator than a perfect sphere would be. Earth's shape is also slightly lumpy because it is composed of different materials of different densities that exert slightly different amounts of gravitational force per volume.
-;Yomomma
+The liquidity of a hot, newly formed planet allows heavier elements to sink down to the middle and forces lighter elements closer to the surface, a process known as [[planetary differentiation]]. This event is known as the [[iron catastrophe]]; the most abundant heavier elements were [[iron]] and [[nickel]], which now form the [[Earth's core]].
+===Later shape changes and effects===
+Though the surface rocks of Earth have cooled enough to solidify, the [[outer core]] of the planet is still hot enough to remain liquid. Energy is still being released; [[volcano|volcanic]] and [[tectonic]] activity has pushed rocks into hills and mountains and blown them out of [[caldera]]s. [[Meteor]]s also cause [[impact crater]]s and surrounding ridges. However, if the energy release from these processes halts, then they tend to [[Erosion|erode]] away over time and return toward the lowest potential-energy curve of the ellipsoid. [[Weather]] powered by [[solar energy]] can also move water, rock, and soil to make Earth slightly out of round.
+Earth undulates as the shape of its lowest potential energy changes daily due to the gravity of the Sun and Moon as they move around with respect to Earth. This is what causes [[tides]] in the [[ocean]]s' water, which can flow freely along the changing potential.
+==History of concept and measurement{{anchor|History}}==
+{{see|History of geodesy}}
+[[File:John Gower world Vox Clamantis detail.jpg|thumb|[[Middle Ages|Medieval]] artistic representation of a spherical Earth{{snd}}with compartments representing [[earth]], [[air]], and [[water]] ({{circa|1400}})]][[File:Behaims Erdapfel.jpg|thumb|upright|The ''[[Erdapfel]]'', the oldest surviving terrestrial globe (1492/1493)]]
+The spherical shape of the Earth was known and measured by astronomers, mathematicians, and navigators from a variety of literate ancient cultures, including the Hellenic World, and Ancient India. Greek ethnographer [[Megasthenes]], {{circa|300&nbsp;BC}}, has been interpreted as stating that the contemporary Brahmans of India believed in a spherical Earth as the center of the universe.<ref>{{cite book|title=Ancient India as described by Megasthenês and Arrian; being a translation of the fragments of the Indika of Megasthenês collected by Dr. Schwanbeck, and of the first part of the Indika of Arrian|url=https://archive.org/details/b29352290|author=E. At. Schwanbeck|date=1877|page=[https://archive.org/details/b29352290/page/101 101]}}</ref> The knowledge of the Greeks was inherited by Ancient Rome, and Christian and Islamic realms in the Middle Ages.  [[Circumnavigation]] of the world in the [[Age of Discovery]] provided direct evidence. Improvements in transportation and other technologies refined estimations of the size of the Earth, and helped spread knowledge of it.
+The earliest documented mention of the concept dates from around the 5th century BC, when it appears in the writings of [[Ancient Greek philosophy|Greek philosophers]].<ref name="Dicks">{{cite book |last=Dicks |first=D.R. |url=https://archive.org/details/earlygreekastron0000dick |title=Early Greek Astronomy to Aristotle |date=1970 |publisher=Cornell University Press |isbn=978-0-8014-0561-7 |location=Ithaca, N.Y. |pages=72–198}}</ref><ref>{{citation |last=Cormack |first=Lesley B. |title=Newton's Apple and Other Myths about Science |date=2015 |pages=16–24 |editor-last1=Numbers |editor-first1=Ronald L. |editor-last2=Kampourakis |editor-first2=Kostas |url=https://books.google.com/books?id=pWouCwAAQBAJ |article=That before Columbus, geographers and other educated people knew the Earth was flat |publisher=Harvard University Press |isbn=9780674915473 |author-link=Lesley Cormack}}</ref> In the 3rd century&nbsp;BC, [[History of geodesy#Hellenic world|Hellenistic astronomy]] established the [[figure of the Earth|roughly spherical shape of Earth]] as a physical fact and calculated the [[Earth's circumference]]. This knowledge was gradually adopted throughout the [[Old World]] during [[late antiquity|Late Antiquity]] and the [[Middle Ages]].<ref name="Krüger: Roman and medieval continuation">Continuation into Roman and medieval thought: Reinhard Krüger: "[http://www.uni-stuttgart.de/lettres/krueger/forschungsvorhaben_erdkugeltheorie_biblio.html Materialien und Dokumente zur mittelalterlichen Erdkugeltheorie von der Spätantike bis zur Kolumbusfahrt (1492)]"</ref><ref name="Encyclopaedia of Islam: Astronomy">{{cite book |last1=Jamil |first1=Jamil |url=https://archive.org/details/encyclopaediaofi0000unse_u8d8 |title=Encyclopaedia of Islam |year=2009 |isbn=978-90-04-17852-6 |editor1-last=Fleet |editor1-first=Kate |chapter=Astronomy |doi=10.1163/1573-3912_ei3_COM_22652 |editor2-last=Krämer |editor2-first=Gudrun |editor3-last=Matringe |editor3-first=Denis |editor4-last=Nawas |editor4-first=John |editor5-last=Rowson |editor5-first=Everett |url-access=registration}}</ref><ref name="Pingree: Indian adoption">Direct adoption by India: [[David Pingree|D. Pingree]]: "History of Mathematical Astronomy in India", ''Dictionary of Scientific Biography'', Vol. 15 (1978), pp. 533–633 (554f.); Glick, Thomas F., Livesey, Steven John, Wallis, Faith (eds.): "Medieval Science, Technology, and Medicine: An Encyclopedia", Routledge, New York 2005, {{ISBN|0-415-96930-1}}, p. 463</ref><ref name="Martzloff, Cullen: Chinese adoption">Adoption by China via European science: {{cite journal |last1=Martzloff |first1=Jean-Claude |date=1993 |title=Space and Time in Chinese Texts of Astronomy and of Mathematical Astronomy in the Seventeenth and Eighteenth Centuries |url=http://www.eastm.org/index.php/journal/article/view/526/457 |url-status=dead |journal=Chinese Science |volume=11 |issue=11 |pages=66–92 |doi=10.1163/26669323-01101005 |jstor=43290474 |archive-url=https://web.archive.org/web/20211026212951/http://www.eastm.org/index.php/journal/article/view/526/457 |archive-date=2021-10-26 |access-date=2021-10-12}} and {{cite journal |last1=Cullen |first1=C. |date=1976 |title=A Chinese Eratosthenes of the Flat Earth: A Study of a Fragment of Cosmology in Huai Nan tzu 淮 南 子 |journal=Bulletin of the School of Oriental and African Studies, University of London |volume=39 |issue=1 |pages=106–127 |doi=10.1017/S0041977X00052137 |jstor=616189 |s2cid=171017315}}</ref> A practical demonstration of Earth's [[sphericity]] was achieved by [[Ferdinand Magellan]] and [[Juan Sebastián Elcano]]'s [[circumnavigation]] (1519–1522).<ref>Pigafetta, Antonio (1906). Magellan's Voyage around the World. Arthur A. Clark. [https://archive.org/details/primerviajeentor00piga]</ref>
+The concept of a spherical Earth displaced earlier beliefs in a [[flat Earth]]: In early [[Mesopotamian myths|Mesopotamian mythology]], the world was portrayed as a disk floating in the ocean with a hemispherical sky-dome above,<ref name="Neugebauer">{{cite book |last=Neugebauer |first=Otto E. |author-link=Otto E. Neugebauer |title=A History of Ancient Mathematical Astronomy |date=1975 |publisher=Birkhäuser |isbn=978-3-540-06995-9 |page=577}}</ref> and this forms the premise for [[early world maps]] like those of [[Anaximander]] and [[Hecataeus of Miletus]]. Other speculations on the shape of Earth include a seven-layered [[ziggurat]] or [[cosmic mountain]], alluded to in the [[Avesta]] and ancient [[Achaemenid Empire|Persian]] writings (see [[clime|seven climes]]).
+The realization that the [[figure of the Earth]] is more accurately described as an [[Earth ellipsoid|ellipsoid]] dates to the 17th century, as described by [[Isaac Newton]] in ''[[Philosophiæ Naturalis Principia Mathematica|Principia]]''. In the early 19th century, the flattening of the earth ellipsoid was determined to be of the order of 1/300 ([[Jean Baptiste Joseph Delambre|Delambre]], [[George Everest|Everest]]). The modern value as determined by the [[United States Department of Defense|US DoD]] [[World Geodetic System]] since the 1960s is close to 1/298.25.<ref>See [[Figure of the Earth]] and {{slink|Earth radius#Global radii}} for details. Recent measurements from [[Satellite|satellites]] suggest that Earth is actually slightly [[pear]]-shaped. Hugh Thurston, ''[https://books.google.com/books?id=5SPeevvl4oEC&pg=PA119 Early Astronomy]'', (New York: Springer-Verlag), p. 119. {{ISBN|0-387-94107-X}}.</ref>
+==Measurement and representation==
-===Hellenistic era===
+{{Main|Geodesy}}
-;Eratosthenes
-[[Eratosthenes]] (276 BCE - 194 BCE) estimated [[Earth]]'s circumference around 240 BCE. He had heard that in [[Syene]] the [[Sun]] was directly overhead at the summer solstice whereas in [[Alexandria]] it still cast a shadow.  Using the differing angles the shadows made as the basis of his trigonometric calculations he estimated a circumference of around 250,000 ''[[Ancient Greek units of measurement|stades]]''. The length of a 'stade' is not precisely known, but Eratosthenes' figure only has an error of around five to ten percent.<ref>{{cite web|url=http://www.nasa.gov/lb/audience/forstudents/5-8/features/F_JSC_NES_School_Measures_Up.html|title=JSC NES School Measures Up|publisher=NASA|date=11 April 2006|accessdate=24 January 2008}}</ref><ref>{{cite web|url=http://www-istp.gsfc.nasa.gov/stargaze/Scolumb.htm|title=The Round Earth|publisher=NASA|date=12 December 2004|accessdate=24 January 2008}}</ref>
+[[Geodesy]], also called geodetics, is the scientific discipline that deals with the measurement and representation of Earth, its [[gravitation]]al field and geodynamic phenomena ([[polar motion]], Earth [[tide]]s, and crustal motion) in three-dimensional time-varying space.
-;Seleucus of Seleucia
-[[Seleucus of Seleucia]] (c. 190 BC), who lived in the [[Seleucia]] region of [[Mesopotamia]], stated that the Earth is spherical (and actually orbits the [[Sun]], influenced by the [[heliocentrism|heliocentric theory]] of [[Aristarchus of Samos]]).
+Geodesy is primarily concerned with positioning and the gravity field and geometrical aspects of their temporal variations, although it can also include the study of Earth's [[magnetic field]]. Especially in the [[German language|German]] speaking world, geodesy is divided into [[geomensuration]] ("Erdmessung" or "höhere Geodäsie"), which is concerned with measuring Earth on a global scale, and [[Geophysical survey|surveying]] ("Ingenieurgeodäsie"), which is concerned with measuring parts of the surface.
-;Claudius Ptolemy
-[[Claudius Ptolemy]] ([[Anno Domini|CE]] 90 - 168) lived in [[Alexandria]], the centre of scholarship in the second century.  Around 150, he produced his eight-volume [[Geographia (Ptolemy)|Geographia]].
+Earth's shape can be thought of in at least two ways:
-The first part of the ''Geographia'' is a discussion of the data and of the methods he used. As with the model of the solar system in the ''Almagest'', Ptolemy put all this information into a grand scheme. He assigned [[coordinate]]s to all the places and geographic features he knew, in a [[Grid (spatial index)|grid]] that spanned the globe. [[Latitude]] was measured from the [[equator]], as it is today, but Ptolemy preferred to express it as the length of the longest day rather than [[degree (angle)|degrees of arc]] (the length of the [[midsummer]] day increases from 12h to 24h as you go from the equator to the [[polar circle]]). He put the [[meridian (geography)|meridian]] of 0 [[longitude]] at the most western land he knew, the [[Canary Islands]].
+* as the shape of the [[geoid]], the mean sea level of the world ocean; or
-Geographia indicated the countries of "[[Seres|Serica]]" and "Sinae" ([[China]]) at the extreme right, beyond the island of "Taprobane" ([[Sri Lanka]], oversized) and the "Aurea Chersonesus" ([[Southeast Asia|Southeast Asian peninsula]]).
-Ptolemy also devised and provided instructions on how to create maps both of the whole inhabited world (''oikoumenè'') and of the Roman provinces. In the second part of the ''Geographia'' he provided the necessary [[topographic]] lists, and captions for the maps. His ''oikoumenè'' spanned 180 degrees of longitude from the Canary Islands in the [[Atlantic Ocean]] to [[China]], and about 81 degrees of latitude from the Arctic to the [[East Indies]] and deep into [[Africa]].  Ptolemy was well aware that he knew about only a quarter of the globe.
-===Late Antiquity===
-;Aryabhata
-The works of the classical [[Indian astronomy|Indian astronomer]] and [[Indian mathematics|mathematician]], [[Aryabhata]] (476-550 AD), deal with the sphericity of the Earth and the motion of the planets. The final two parts of his [[Sanskrit]] magnum opus, the ''[[Aryabhatiya]]'', which were named the ''Kalakriya'' ("reckoning of time") and the ''Gola'' ("sphere"), state that the Earth is spherical and that its circumference is 4,967 [[yojana]]s, which in modern units is 39,968&nbsp;km, which is only 62&nbsp;km less than the current value of 40,030&nbsp;km.<ref>[http://www-history.mcs.st-andrews.ac.uk/Biographies/Aryabhata_I.html Aryabhata_I biography<!-- Bot generated title -->]</ref><ref>http://www.gongol.com/research/math/aryabhatiya ''The Aryabhatiya: Foundations of Indian Mathematics''</ref> He also stated that the apparent rotation of the celestial objects was due to the actual [[Earth's rotation|rotation of the Earth]], calculating the length of the [[sidereal day]] to be 23 hours, 56 minutes and 4.1 seconds, which is also surprisingly accurate. It is likely that Aryabhata's results influenced European astronomy, because the 8th century [[Arabic]] version of the Aryabhatiya was translated into Latin in the 13th century.
-===Middle Ages===
-[[Anania Shirakatsi]] ({{lang-hy|Անանիա Շիրակացի}}), also known as Ananias of Sirak, (610&ndash;685) was an [[Armenians|Armenian]] [[scholar]], [[mathematician]], and [[geographer]]. His most famous works are ''Geography Guide'' (‘Ashharatsuyts’ in [[Armenian language|Armenian]]), and ''Cosmography'' (Tiezeragitutiun).  He described the world as "being like an egg with a spherical yolk (the globe)  surrounded by a layer of white (the atmosphere) and covered with a hard shell (the sky)." <ref>Hewson, Robert H. "Science in Seventh-Century Armenia: Ananias of Sirak, ''Isis'', Vol. 59, No. 1, (Spring, 1968), pp. 32-45</ref>
-Shirakatsi's work ‘Ashharatsuyts’ reports details and mapping of the ancient homeland of [[Bulgars]] in the [[Mount Imeon]] area of [[Central Asia]].
-====Islamic World====
-Early Islamic scholars recognized earth's sphericity<ref>[[Muhammad Hamidullah]]. '''L'Islam et son impulsion scientifique originelle''', ''Tiers-Monde'', 1982, vol. 23, n° 92, p. 789.</ref>, leading [[Islamic mathematics|Muslim mathematicians]] to develop [[spherical trigonometry]]<ref>David A. King, ''Astronomy in the Service of Islam'', (Aldershot (U.K.): Variorum), 1993.</ref> in order to further mensuration and to calculate the distance and direction from any given point on the Earth to [[Mecca]]. This determined the [[Qibla]], or Muslim direction of prayer.
-;Al-Ma'mun
-Around 830 CE, Caliph [[al-Ma'mun]] commissioned a group of [[Islamic astronomy|Muslim astronomers]] and [[Islamic geography|geographers]] to measure the distance from Tadmur ([[Palmyra]]) to [[Ar Raqqah|al-Raqqah]], in modern Syria. They found the cities to be separated by one degree of latitude and the distance between them to be 66 2/3&nbsp;miles and thus calculated the Earth's circumference to be 24,000&nbsp;miles.<ref>''Gharā'ib al-funūn wa-mulah al-`uyūn'' (The Book of Curiosities of the Sciences and Marvels for the Eyes), 2.1 "On the mensuration of the Earth and its division into seven climes, as related by Ptolemy and others," (ff. 22b-23a)[http://www.bodley.ox.ac.uk/bookofcuriosities]</ref>
-Another estimate given by his astronomers was 56 2/3 Arabic miles per degree, which corresponds to 111.8&nbsp;km per degree and a circumference of 40,248&nbsp;km, very close to the currently modern values of 111.3&nbsp;km per degree and 40,068&nbsp;km circumference, respectively.<ref>Edward S. Kennedy, ''Mathematical Geography'', pp=187-8, in {{Harv|Rashed|Morelon|1996|pp=185-201}}</ref>
-;Al-Farghānī
-[[Al-Farghānī]] (Latinized as Alfraganus) was a Persian astronomer of the 9th century involved in measuring the diameter of the Earth, and commissioned by Al-Ma'mun. His estimate given above for a degree (56 2/3 Arabic miles) was much more accurate than the 60 2/3 Roman miles (89.7&nbsp;km) given by Ptolemy. [[Christopher Columbus]] uncritically used Alfraganus's figure as if it were in Roman miles instead of in Arabic miles, in order to prove a smaller size of the Earth than that propounded by Ptolemy.<ref>Felipe Fernández-Armesto, ''Columbus and the conquest of the impossible'', pp. 20-1, Phoenix Press, 1974.</ref>
-;Al-Biruni
-[[Abū Rayhān al-Bīrūnī]] (973-1048) solved a complex [[Geodesy|geodesic]] equation in order to accurately compute the Earth's [[circumference]], which was close to modern values of the Earth's circumference.<ref name=Khwarizm>[http://muslimheritage.com/topics/default.cfm?ArticleID=482 Khwarizm], Foundation for Science Technology and Civilisation.</ref><ref>James S. Aber (2003). Alberuni calculated the Earth's circumference at a small town of Pind Dadan Khan, District Jhelum, Punjab, Pakistan.[http://academic.emporia.edu/aberjame/histgeol/biruni/biruni.htm Abu Rayhan al-Biruni], [[Emporia State University]].</ref> His estimate of 6,339.9&nbsp;km for the [[Earth radius]] was only 16.8&nbsp;km less than the modern value of 6,356.7&nbsp;km. In contrast to his predecessors who measured the Earth's circumference by sighting the Sun simultaneously from two different locations, al-Biruni developed a new method of using [[Trigonometry|trigonometric]] calculations based on the angle between a [[plain]] and [[mountain]] top which yielded more accurate measurements of the Earth's circumference and made it possible for it to be measured by a single person from a single location.<ref>Lenn Evan Goodman (1992), ''Avicenna'', p. 31, [[Routledge]], ISBN 041501929X.</ref>
-John J. O'Connor and Edmund F. Robertson write in the ''[[MacTutor History of Mathematics archive]]'':
-{{quote|"Important contributions to [[geodesy]] and [[Islamic geography|geography]] were also made by Biruni. He introduced techniques to measure the earth and distances on it using [[triangulation]]. He found the [[Earth radius|radius of the earth]] to be 6339.6 km, a value not obtained in the West until the 16th century. His ''Masudic canon'' contains a table giving the coordinates of six hundred places, almost all of which he had direct knowledge."<ref name=MacTutor>{{MacTutor|id=Al-Biruni|title=Al-Biruni}}</ref>}}
-==Geodesy==
-[[Geodesy]], also called '''geodetics''', is the scientific discipline that deals with the measurement and representation of the Earth, its [[gravitation]]al field and geodynamic phenomena ([[polar motion]], Earth [[tide]]s, and crustal motion) in three-dimensional time-varying space.
-Geodesy is primarily concerned with positioning and the gravity field and geometrical aspects of their temporal variations, although it can also include the study of Earth's [[magnetic field]]. Especially in the [[German language|German]] speaking world, geodesy is divided into [[geomensuration]] ("Erdmessung" or "höhere Geodäsie"), which is concerned with measuring the Earth on a global scale, and  [[Geophysical survey|surveying]] ("Ingenieurgeodäsie"), which is concerned with measuring parts of the surface.
-The Earth's shape can be thought of in at least two ways;
-* as the shape of the [[geoid]], the mean sea level of the world ocean; or
 * as the shape of Earth's land surface as it rises above and falls below the sea.
-As the science of [[geodesy]] measured Earth more accurately, the shape of the geoid was first found not to be a perfect sphere but to approximate an [[spheroid|oblate spheroid]], a specific type of [[ellipsoid]]. More recent measurements have measured the geoid to unprecedented accuracy, revealing [[mass concentration]]s beneath Earth's surface.
+As the science of [[geodesy]] measured Earth more accurately, the shape of the geoid was first found not to be a perfect sphere but to approximate an [[spheroid|oblate spheroid]], a specific type of [[ellipsoid]]. More recent{{when|date=November 2021}} measurements have measured the geoid to unprecedented accuracy, revealing [[Mass concentration (astronomy)|mass concentration]]s beneath Earth's surface.
+==Evidence==
-==Spherical models==
+{{excerpt|Empirical evidence for the spherical shape of Earth}}
-{{Main|Earth radius}}
-[[Image:The Earth seen from Apollo 17.jpg|thumb|right|The Earth as seen from the [[Apollo 17]] mission.]]
-There are several reasonable ways to approximate Earth's shape as a sphere. Most preserve a different feature of an ellipsoid that closely models the real Earth in order to compute the [[radius]] of the spherical model. All examples in this section assume the [[World Geodetic System|WGS 84]] datum, with an equatorial radius ''a'' of 6,378.137&nbsp;km and a polar radius ''b'' of 6,356.752&nbsp;km. A sphere being a gross approximation of the spheroid, which itself is an approximation of the geoid, units are given here in kilometers rather than the millimeter resolution appropriate for geodesy.
-*Preserve the equatorial circumference. This is simplest, being a sphere with circumference identical to the equatorial circumference of the ellipsoidal model. Since the circumference is the same, so is the radius, at 6,378.137&nbsp;km.
-*Preserve the lengths of meridians. This requires an [[Circumference#Ellipse|elliptic integral]] to find, given the polar and equatorial radii: <math>\frac{2a}{\pi}\int_{0}^{\frac{\pi}{2}}\sqrt{\cos^2\phi + \frac{b^2}{a^2}\sin^2 \phi}\,d\phi</math>. A sphere preserving the lengths of meridians has a ''rectifying'' radius of 6,367.449&nbsp;km. This can be approximated using the ''elliptical'' quadratic mean:  <math>\sqrt{\frac{a^2+b^2}{2}}\,\!</math>, about  6,367.454&nbsp;km; or even just the mean of the two axes: <math>\frac{a+b}{2}\,\!</math>, about 6,367.445&nbsp;km.
-*Preserve the surface area of the ellipsoidal model. This gives the ''[[Earth radius#Authalic mean radius: Ar|authalic radius]]'' (denoted <math>R_2</math> by the [[International Union of Geodesy and Geophysics]]):  <math>\sqrt{\frac{a^2+\frac{ab^2}{\sqrt{a^2-b^2}}\ln{(\frac{a+\sqrt{a^2-b^2}}b)}}{2}}\,\!</math>, or 6,371.007&nbsp;km.
-*Preserve the volume of the ellipsoidal model. This ''[[Earth radius#Volumetric radius: Vr|volumetric radius]]'' (denoted <math>R_3</math> by the [[International Union of Geodesy and Geophysics|IUGG]]) is computed as:   <math>\sqrt[3]{a^2b}</math>, or 6,371.001&nbsp;km.
-*Synthesize some mean radius. The [[International Union of Geodesy and Geophysics|IUGG]] defines the mean radius (denoted <math>R_1</math>) to be <math>\frac{2a+b}{3}\,\!</math>, giving 6,371.009&nbsp;km. There are other ways to define the mean.
 ==See also==
+*[[Astronomical body#Shapes|Shapes of other astronomical bodies]]
+*[[Celestial sphere]]
+*[[Celestial spheres]]
 *[[Earth radius]]
+*{{section link|Earth's rotation|Empirical tests}}
-*[[Figure of the Earth]]
-*[[Flat Earth]]
 *[[Geographical distance]]
+*[[Myth of the flat Earth]]
-*[[Celestial sphere]]
 *[[Physical geodesy]]
 *[[Terra Australis]]
@@ Line 97: / Line 64: @@
 ==References==
-{{reflist}}
+{{Reflist|30em}}
+===Works cited===
+{{refbegin}}
+*{{cite book|last1=Needham|first1=Joseph|last2=Wang|first2=Ling|title=Science and Civilization in China: Mathematics and the Sciences of the Heavens and the Earth|date=1995|orig-date=1959|volume=3|edition=reprint|location=Cambridge|publisher=Cambridge University Press|isbn=0-521-05801-5|ref={{harvid|Needham|1959}}}}
+{{refend}}
+==Further reading==
+*{{cite book|title=Janice VanCleave's Science Through the Ages|author=Janice VanCleave|publisher=John Wiley & Sons|date=2002|url=https://books.google.com/books?id=RFp4KeYt9s8C|isbn=9780471208303}}
+*{{cite book|title=Early Astronomy and Cosmology: A Reconstruction of the Earliest Cosmic System, Etc.|author=Menon, CPS|location=Whitegishm MT, US.|publisher=Kessinger Publishing|url=https://books.google.com/books?id=qnz2vGVaPjsC|isbn=9780766131040|date=2003}}
+*{{cite book|title=How Did We Find Out the Earth is Round?|author=Isaac Asimov|date=1972|publisher=New York, Walker|isbn=978-0802761217|url-access=registration|url=https://archive.org/details/earthisround00asim}}
 ==External links==
+{{Commons|Spherical Earth}}
 *[http://www.straightdope.com/classics/a2_087.html You say the earth is round? Prove it] (from [[The Straight Dope]])
+*[http://www.nasa.gov/centers/goddard/earthandsun/earthshape.html NASA – Most Changes in Earth's Shape Are Due to Changes in Climate]
-*[http://regentsprep.org/Regents/earthsci/units/introduction/oblate.cfm Oblate Spheroid]
+*[http://www.phy6.org/stargaze/Scolumb.htm The Round Earth and Christopher Columbus], educational web site
-*[http://www.nasa.gov/centers/goddard/earthandsun/earthshape.html NASA-Most Changes in Earth's Shape Are Due to Changes in Climate]
+*[http://www.smarterthanthat.com/astronomy/top-10-ways-to-know-the-earth-is-not-flat Top 10 Ways to Know the Earth is Not Flat], science education site
 {{Greek astronomy}}
+[[Category:Ancient astronomy]]
 [[Category:Ancient Greek astronomy]]
 [[Category:Cartography]]
 [[Category:Earth]]
-[[Category:History of astronomy]]
 [[Category:Early scientific cosmologies]]
-[[Category:Ancient astronomy]]
+[[Category:Geodesy]]
+[[Category:Spheres]]
-[[de:Sphäre]]
-[[id:Bumi yang bulat]]
-[[nl:Bolvormige Aarde]]
-[[zh:地圆说]]

v t e Ancient Greek astronomy
Astronomers	Aglaonice Agrippa Anaximander Andronicus Apollonius Aratus Aristarchus Aristyllus Attalus Autolycus Bion Callippus Cleomedes Cleostratus Conon Eratosthenes Euctemon Eudoxus Geminus Heraclides Hicetas Hipparchus Hippocrates of Chios Hypsicles Menelaus Meton Oenopides Philip of Opus Philolaus Posidonius Ptolemy Pytheas Seleucus Sosigenes of Alexandria Sosigenes the Peripatetic Strabo Thales Theodosius Theon of Alexandria Theon of Smyrna Timocharis
Works	Almagest (Ptolemy) Catasterismi (Eratosthenes) On Sizes and Distances (Hipparchus) On the Sizes and Distances (Aristarchus) On the Heavens (Aristotle)
Instruments	Antikythera mechanism Armillary sphere Astrolabe Dioptra Equatorial ring Gnomon Mural instrument Triquetrum
Concepts	Callippic cycle Celestial spheres Circle of latitude Counter-Earth Deferent and epicycle Equant Geocentrism Heliocentrism Hipparchic cycle Inferior and superior planets Metonic cycle Octaeteris Solstice Spherical Earth Sublunary sphere Zodiac
Influences	Babylonian astronomy Egyptian astronomy
Influenced	Medieval European science Indian astronomy Medieval Islamic astronomy