See also the main article on geodesy. Geodesy (dʒiːˈɒdɪsi also called geodetics, a branch of Earth sciences, is the scientific discipline that deals

Humanity has always been interested in the Earth. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 During very early times this interest was limited, naturally, to the immediate vicinity of home and residency, and the fact that we live on a near spherical globe may or may not have been apparent. As humanity developed, so did its interest in understanding and mapping the size, shape, and composition of the Earth.

Contents 1 Hellenic world 2 Ancient India 3 Medieval Persia 4 The Middle Ages 5 Scientific revolution 6 19th century 7 See also 8 Notes 9 References

Hellenic world

Early ideas about the figure of the Earth held the Earth to be flat, and the heavens a physical dome spanning over it. Two early arguments for a spherical earth were that lunar eclipses were seen as circular shadows which could only be caused by a spherical Earth, and that Polaris is seen lower in the sky as one travels South. Polaris (α UMi / α Ursae Minoris / Alpha Ursae Minoris commonly North(ern Star or Pole Star, and sometimes Lodestar

The early Greeks, in their speculation and theorizing, ranged from the flat disc advocated by Homer to the spherical body postulated by Pythagoras — an idea supported one hundred years later by Aristotle. The term ancient Greece refers to the period of Greek history lasting from the Greek Dark Ages ca Homer ( Ancient Greek:, Homēros) is a legendary ancient Greek epic Poet, traditionally said to be the author of the epic poems the "Pythagoras of Samos" redirects here For the Samian statuary of the same name see Pythagoras (sculptor. Aristotle (Greek Aristotélēs) (384 BC – 322 BC was a Greek philosopher a student of Plato and teacher of Alexander the Great. Pythagoras was a mathematician and to him the most perfect figure was a sphere. "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe He reasoned that the gods would create a perfect figure and therefore the earth was created to be spherical in shape. Anaximenes, an early Greek scientist, believed strongly that the earth was rectangular in shape.

Since the spherical shape was the most widely supported during the Greek Era, efforts to determine its size followed. Plato determined the circumference of the earth to be 400,000 stadia while Archimedes estimated 300,000 stadia, using the Hellenic stadion which scholars generally take to be 185 meters or 1/10 of a geographical mile. Biography Early life Birth and family Plato was born in Athens Greece Archimedes of Syracuse ( Greek:) ( c. 287 BC – c 212 BC was a Greek mathematician, Physicist, Engineer Stadia can refer to The plural of Stadium. Stadia rod, a surveyors instrument The geographical mile is a unit of length determined by 1 minute of arc along the Earth 's Equator, approximately equal to 1855 Plato's figure was a guess and Archimedes' a more conservative approximation. Meanwhile, in Egypt, a Greek scholar and philosopher, Eratosthenes, is said to have made more explicit measurements. Eratosthenes of Cyrene ( Greek; 276 BC - 194 BC was a Greek Mathematician, Poet, athlete, Geographer and

He had heard that on the longest day of the summer solstice, the midday sun shone to the bottom of a well in the town of Syene (Aswan). Solstices occur twice a year when the tilt of the Earth's axis is most oriented toward or away from the Sun, causing the Sun to reach its northernmost and southernmost extremes Aswan (formerly spelled Assuan (in standard أسوان Aswān) Egyptian: Swenet ( trade) Coptic: Swān; Greek Figure 1. At the same time, he observed the sun was not directly overhead at Alexandria; instead, it cast a shadow with the vertical equal to 1/50th of a circle (7° 12'). Alexandria ( Egyptian Arabic: اسكندريه Eskendereyya; Standard Arabic: ar الإسكندرية Al-Iskandariyya; Ἀλεξάνδρεια To these observations, Eratosthenes applied certain "known" facts (1) that on the day of the summer solstice, the midday sun was directly over the Tropic of Cancer; (2) Syene was on this tropic; (3) Alexandria and Syene lay on a direct north-south line. For the novel by Henry Miller, see Tropic of Cancer (novel. The Tropic of Cancer, or Northern tropic, is one of five Legend has it that he had someone walk from Alexandria to Syene to measure the distance: that came out to be equal to 5000 stadia or (at the usual Hellenic 185 meters per stadion) about 925 kilometres.

From these observations, measurements, and/or "known" facts, Eratosthenes concluded that, since the angular deviation of the sun from the vertical direction at Alexandria was also the angle of the subtended arc (see illustration), the linear distance between Alexandria and Syene was 1/50 of the circumference of the Earth which thus must be 50×5000 = 250,000 stadia or probably 25,000 geographical miles. In Astronomy, Geography, Geometry and related sciences and contexts a direction passing by a given point is said to be vertical if The circumference of the Earth is 24,902 miles (40,075. 16 km). Over the poles it is more precisely 40,008 km or 24,860 statute miles. The actual unit of measure used by Eratosthenes was the stadion. No one knows for sure what his stadion equals in today's units, but most current specialists in antiquities accept that it was the regular Hellenic 185 meter stadion, and few if any would incline to an obscure definition that happened to make Eratosthenes's result correct.

Had the experiment been carried out as described, it would not be remarkable if it agreed with actuality. What is remarkable is that the result was probably about one sixth too high. Eratosthenes of Cyrene ( Greek; 276 BC - 194 BC was a Greek Mathematician, Poet, athlete, Geographer and His measurements were subject to several inaccuracies: (1) though at the summer solstice the noon sun is overhead at the Tropic of Cancer, Syene was not exactly on the tropic (which was at 23° 43' latitude in that day) but about 22 geographical miles to the north; (2) Syene lies 3° east of the meridian of Alexandria; (3) the difference of latitude between Alexandria (31. 2 degrees north latitude) and Syene (24. 1 degrees) is really 7. 1 degrees rather than the perhaps rounded (1/50 of a circle) value of 7° 12' that Eratosthenes used; (4) the actual solstice zenith distance of the noon sun at Alexandria was 31° 12' − 23° 43' = 7° 29' or about 1/48 of a circle not 1/50 = 7° 12', an error closely consistent with use of a vertical gnomon which fixes not the sun's center but the solar upper limb 16' higher; (5) the most importantly flawed element, whether he measured or adopted it, was the latitudinal distance from Alexandria to Syene (or the true Tropic somewhat further south) which he appears to have overestimated by a factor that relates to most of the error in his resulting circumference of the earth. In Astronomy, a celestial coordinate system is a Coordinate system for mapping positions in the sky Eratosthenes of Cyrene ( Greek; 276 BC - 194 BC was a Greek Mathematician, Poet, athlete, Geographer and The gnomon is the part of a Sundial that casts the Shadow. Gnomon (γνώμων is an Ancient Greek word meaning "indicator" "one who

There is some cause to question the reality of the legendary "experiment". First, pacing the distance would be physically intimidating, across plenty of desert since the Nile isn't linear. Second, a traveller from Alexandria near the west extreme of the Nile delta would have had to veer on average over 20° east of due south to hit Syene, a nonsubtle conflict with Eratosthenes's reported experiment which put Syene directly south of Alexandria ^[1]. Third, if the Hellenic stadion is assumed for Hellenic Eratosthenes, the resulting 250,000 stadia (later given as 252,000 for divisibility) is pretty close to the overlarge size of the earth one would find by simple mathematics and enormously less travel, through measuring a sea horizon's angular dip as seen from a known height, since the computational result will be about 6/5 of the correct result (1/5 too high) due to atmospheric refraction which for horizontal light is 1/6 of the curvature of the earth. Atmospheric Refraction is the deviation of Light or other Electromagnetic wave from a straight line as it passes through the atmosphere due to the

A parallel later legendary ancient measurement of the size of the earth was made by another influential Greek scholar, Posidonius. Posidonius ( Greek: Ποσειδώνιος / Poseidonios "of Apameia " (ὁ Απαμεύς or "of Rhodes " (ὁ Ρόδιος (ca He is said to have noted that the star Canopus was hidden from view in most parts of Greece but that it just grazed the horizon at Rhodes. Posidonius is supposed to have measured the elevation of Canopus at Alexandria and determined that the angle was 1/48th of circle. He assumed the distance from Alexandria to Rhodes to be 5000 stadia, and so he computed the earth's circumference in stadia as 48 times 5000 = 240,000 ^[2]. Rhodes (Ρόδος Ródos, ˈɾo̞ðo̞s Rodi ردوس Rodos; Ladino: Rodi or Rodes) is a Greek island Some scholars see these results as luckily semi-accurate due to cancellation of errors. But since the Canopus observations are both mistaken by over a degree, the "experiment" may be not much more than a recycling of Eratosthenes's numbers, while altering 1/50 to the correct 1/48 of a circle. Later either he or a follower appears to have altered the base distance to agree with Eratosthenes's Alexandria-to-Rhodes figure of 3750 stadia since Posidonius's final circumference was 180,000 stadia, which equals 48×3750 stadia ^[3]. The 180,000 stadia circumference of Posidonius is suspiciously close to that which results from another unlaborious method of measuring the earth, by timing ocean sun-sets from different heights, a method which produces a size of the earth too low by a factor of 5/6, again due to horizontal refraction.

The abovementioned larger and smaller sizes of the earth were those used by Claudius Ptolemy at different times, 252,000 stadia in the Almagest and 180,000 stadia in the later Geographical Directory. Claudius Ptolemaeus ( Greek: Klaúdios Ptolemaîos; after 83 &ndash ca Almagest is the Latin form of the Arabic name ( الكتاب المجسطي, al-kitabu-l-mijisti, i The Geographia or Geography is Ptolemy 's main work besides the Almagest. His midcareer conversion resulted in the latter work's systematic exaggeration of degree longitudes in the Mediterranean by a factor close to the ratio of the two seriously differing sizes discussed here, which indicates ^[4] that the conventional size of the earth was what changed, not the stadion.

Ancient India

The great Indian mathematician Aryabhata (476 - 550 AD) was a pioneer of mathematical astronomy. Āryabhaṭa ( Devanāgarī: आर्यभट (AD 476 &ndash 550 is the first in the line of great mathematician-astronomers from the classical age of Indian mathematics He describes the earth as being spherical and that it rotates on its axis, among other things in his work Aryabhatia. Aryabhatiya is divided into four sections. Gitika,Ganitha (mathematics), Kalakriya (reckoning of time) and Gola (celestial sphere). The discovery that the earth rotates on its own axis from west to east is described in Aryabhatiya ( Gitika 3,6; Kalakriya 5; Gola 9,10;) [1]. For example he explained the apparent motion of heavenly bodies is only an illusion (Gola 9), with the following simile;

Just as a passenger in a boat moving downstream sees the stationary (trees on the river banks) as traversing upstream, so does an observer on earth see the fixed stars as movin g towards the west at exactly the same speed (at which the earth moves from west to east.

Aryabhatiya also estimates the circumference of Earth, accurate to 1% which is remarkable. Āryabhatīya, an astronomical treatise is the Magnum opus and only extant work of the 5th century Indian mathematician Aryabhata. Aryabhata gives the radius of planets in terms of the Earth-Sun distance as essentially their periods of rotation around the Sun. Āryabhaṭa ( Devanāgarī: आर्यभट (AD 476 &ndash 550 is the first in the line of great mathematician-astronomers from the classical age of Indian mathematics He also gave the correct explanation of lunar and solar eclipses and that the Moon shines by reflecting sunlight [2].

Medieval Persia

The medieval Persian geodesist Abu al-Rayhan al-Biruni (973-1048) is sometimes regarded as the "father of geodesy" for his significant contributions to the field. See Also Persian Empire History of Iran and Greater Iran (also referred to as the " Iranian Cultural Continent ^[5][6]

John J. O'Connor and Edmund F. Robertson write in the MacTutor History of Mathematics archive:

"Important contributions to geodesy and geography were also made by al-Biruni. The MacTutor History of Mathematics archive is an award-winning website maintained by John J Geography (from Greek γεωγραφία - geografia) is the study of the Earth and its lands features inhabitants and phenomena He introduced techniques to measure the earth and distances on it using triangulation. In Trigonometry and Geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either He found the radius of the earth to be 6339. Remote Authentication Dial In User Service ( RADIUS) is a networking protocol that provides centralized access authorization and accounting management for people or computers 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. "^[7]

The Middle Ages

Revising the figures attributed to Posidonius, another Greek philosopher determined 18,000 miles as the earth's circumference. This last figure was promulgated by Ptolemy through his world maps. Claudius Ptolemaeus ( Greek: Klaúdios Ptolemaîos; after 83 &ndash ca The maps of Ptolemy strongly influenced the cartographers of the Middle Ages. It is probable that Christopher Columbus, using such maps, was led to believe that Asia was only 3 or 4 thousand miles west of Europe. Christopher Columbus (1451 &ndash May 20 1506 was an Italian Navigator, colonizer It was not until the 15th century that his concept of the earth's size was revised. During that period the Flemish cartographer, Mercator, made successive reductions in the size of the Mediterranean Sea and all of Europe which had the effect of increasing the size of the earth. A separate article is about the mathematician Nicholas Mercator.

Scientific revolution

The invention of the telescope and the theodolite and the development of logarithm tables allowed exact triangulation and grade measurement. The period which many historians of science call the Scientific Revolution can be roughly dated as having begun in 1543 the year in which Nicolaus Copernicus published A telescope is an instrument designed for the observation of remote objects and the collection of Electromagnetic radiation. A theodolite ( is an instrument for measuring both horizontal and vertical Angles as used in Triangulation networks The common logarithm is the Logarithm with base 10 It is also known as the decadic logarithm, named after its base In Trigonometry and Geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either Grade measurement is the geodetic determination of the local radius of curvature of the Figure of the Earth by determining the difference in astronomical Latitude

Jean Picard performed the first modern arc measurement. Jean-Felix Picard ( July 21, 1620 &ndash July 12, 1682) was a French Astronomer and priest born in La Flèche He measured a base line by the aid of wooden rods, used a telescope in his angle measurements, and computed with logarithms. Jacques Cassini later continued Picard's arc northward to Dunkirk and southward to the Spanish boundary. Jacques Cassini ( February 8, 1677 – April 18, 1756) was a French - Italian Astronomer, son of the famous Italian Dunkirk ( French: Dunkerque, dœ̃kɛʀk or; Dutch:; is a harbour city and a commune in the northernmost part of France, in the Cassini divided the measured arc into two parts, one northward from Paris, another southward. Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city When he computed the length of a degree from both chains, he found that the length of one degree in the northern part of the chain was shorter than that in the southern part. Figure 2.

This result, if correct, meant that the earth was not a sphere, but an oblong (egg-shaped) ellipsoid -- which contradicted the computations by Isaac Newton and Christiaan Huygens. An ellipsoid is a type of quadric surface that is a higher dimensional analogue of an Ellipse. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements Christiaan Huygens (ˈhaɪgənz in English ˈhœyɣəns in Dutch) ( April 14, 1629 &ndash July 8, 1695) was a Dutch Newton's theory of gravitation predicted the Earth to be an oblate ellipsoid flattened at the poles to a ratio of 1:230. Newton 's law of universal Gravitation is a physical law describing the gravitational attraction between bodies with mass An oblate Spheroid is a rotationally symmetric Ellipsoid having a polar axis shorter than the diameter of the equatorial circle whose plane

The issue could be settled by measuring, for a number of points on earth, the relationship between their distance (in north-south direction) and the angles between their astronomical verticals (the projection of the vertical direction on the sky). In Astronomy, Geography, Geometry and related sciences and contexts a direction passing by a given point is said to be vertical if On an oblate Earth the distance corresponding to one degree would grow toward the poles.

The French Academy of Sciences dispatched two expeditions. The French Academy of Sciences ( French: Académie des sciences) is a Learned society, founded in 1666 by Louis XIV at the One expedition under Pierre Louis Maupertuis (1736-37) was sent to Lapland (as far North as possible). Pierre-Louis Moreau de Maupertuis ( July 17, 1698 &ndash July 27, 1759) was a French Mathematician, Philosopher Year 1736 ( MDCCXXXVI) was a Leap year starting on Sunday (link will display the full calendar of the Gregorian calendar (or a Leap year Etymology Sápmi (and corresponding terms in other Sámi languages refers to both the Sámi land and the Sámi people The second mission under Pierre Bouguer was sent to what is modern-day Ecuador, near the equator (1735-44). The French Geodesic Mission (also called the Geodesic Mission to Peru, First Geodesic Mission and the Spanish-French Geodesic Mission) was an 18th-century Pierre Bouguer ( February 16, 1698 &ndash August 15, 1758) was a French Mathematician and astronomer For a topic outline on this subject see List of basic Ecuador topics. Year 1735 ( MDCCXXXV) was a Common year starting on Saturday (link will display the full calendar of the Gregorian calendar (or a

The measurements conclusively showed that the earth was oblate, with a ratio of 1:210. Thus the next approximation to the true figure of the Earth after the sphere became the oblong ellipsoid of revolution. Equation A spheroid centered at the origin and rotated about the z axis is defined by the implicit equation \left(\frac{x}{a}\right^2+\left(\frac{y}{a}\right^2+\left(\frac{z}{b}\right^2

In South America Bouguer noticed, as did George Everest in the 19th century Great Trigonometric Survey of India, that the astronomical vertical tended to be "pulled" in the direction of large mountain ranges, obviously due to the gravitational attraction of these huge piles of rock. South America is a Continent of the Americas, situated entirely in the Western Hemisphere and mostly in the Southern Hemisphere, with a Colonel Sir George Everest ( 4 July, 1790 &ndash 1 December, 1866) was a Welsh surveyor, Geographer and The Great Trigonometric Survey was a project of the Survey of India throughout most of the 19th century Gravitation is a natural Phenomenon by which objects with Mass attract one another As this vertical is everywhere perpendicular to the idealized surface of mean sea level, or the geoid, this means that the figure of the Earth is even more irregular than an ellipsoid of revolution. The geoid is that Equipotential surface which would coincide exactly with the mean ocean surface of the Earth if the oceans were in equilibrium at rest and extended through Thus the study of the "undulations of the geoid" became the next great undertaking in the science of studying the figure of the Earth.

19th century

In the late 19th century the Zentralbüro für die Internationale Erdmessung (that is, Central Bureau for International Geodesy) was established by Austria-Hungary and Germany. Lithography is a method for Printing using a plate or stone with a completely smooth surface Bavaria ( German:, with an area of 70553 Km² (27241 square miles and almost 12 Munich (München; Minga is the capital city of Bavaria, Germany. Munich (München; Minga is the capital city of Bavaria, Germany. The 19th century of the Common Era began on January 1, 1801 and ended on December 31, 1900, according to the Gregorian calendar Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. One of its most important goals was the derivation of an international ellipsoid and a gravity formula which should be optimal not only for Europe but also for the whole world. An ellipsoid is a type of quadric surface that is a higher dimensional analogue of an Ellipse. Gravitation is a natural Phenomenon by which objects with Mass attract one another The Zentralbüro was an early predecessor of the International Association for Geodesy (IAG) and the International Union of Geodesy and Geophysics (IUGG) which was founded in 1919. The International Union of Geodesy and Geophysics, or IUGG, is a Non-governmental organisation dedicated to the scientific study of the Earth using Year 1919 ( MCMXIX) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Common

Most of the relevant theories were derived by the German geodesist F.R. Helmert in his famous books Die mathematischen und physikalischen Theorien der höheren Geodäsie (1880). Friedrich Robert Helmert ( July 31 1843 &ndash June 15 1917) was a German Geodesist and an important writer on the theory Year 1880 ( MDCCCLXXX) was a Leap year starting on Thursday (link will display the full calendar of the Gregorian calendar (or a Leap year Helmert also derived the first global ellipsoid in 1906 with an accuracy of 100 meters (0. Year 1906 ( MCMVI) was a Common year starting on Monday (link will display full calendar of the Gregorian calendar (or a Common year starting 002 percent of the Earth's radii). The US geodesist Hayford derived a global ellipsoid in ~1910, based on intercontinental isostasy and an accuracy of 200 m. The United States of America —commonly referred to as the Isostasy (Greek isos = "equal" stásis = "standstill" is a term used in Geology to refer to the state of gravitational equilibrium between the It was adopted by the IUGG as "international ellipsoid 1924".

See also

• Figure of the Earth

Notes

References

• An early version of this article was taken from the public domain source at http://www.ngs.noaa.gov/PUBS_LIB/Geodesy4Layman/TR80003A.HTM#ZZ4.
• J. L. Greenberg: The problem of the Earth's shape from Newton to Clairaut: the rise of mathematical science in eighteenth-century Paris and the fall of "normal" science. Cambridge : Cambridge University Press, 1995 ISBN 0-521-38541-5

• M. R. Hoare: Quest for the true figure of the Earth: ideas and expeditions in four centuries of geodesy. Burlington, VT: Ashgate, 2004 ISBN 0-7546-5020-0

• D. Rawlins: "Ancient Geodesy: Achievement and Corruption" 1984 (Greenwich Meridian Centenary, published in Vistas in Astronomy, v. 28, 255-268, 1985)

• D. Rawlins: "Methods for Measuring the Earth's Size by Determining the Curvature of the Sea" and "Racking the Stade for Eratosthenes", appendices to "The Eratosthenes-Strabo Nile Map. Is It the Earliest Surviving Instance of Spherical Cartography? Did It Supply the 5000 Stades Arc for Eratosthenes' Experiment?", Archive for History of Exact Sciences, v. 26, 211-219, 1982

• C. Taisbak: "Posidonius vindicated at all costs? Modern scholarship versus the stoic earth measurer". Centaurus v. 18, 253-269, 1974

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