Timeline of Earth estimates

This is a timeline of humanity's understanding of the shape and size of the planet Earth from antiquity to modern scientific measurements. The Earth has the general shape of a sphere, but it is oblate due to the revolution of the planet. The Earth is an irregular oblate spheroid because neither the interior nor the surface of the Earth are uniform, so a reference oblate spheroid such as the World Geodetic System is used to horizontally map the Earth. The current reference spheroid is WGS 84. The reference spheroid is then used to create an equigeopotential geoid to vertically map the Earth. A geoid represents the general shape of the Earth if the oceans and atmosphere were at rest. The geoid elevation replaces the previous notion of sea level since the oceans are never at rest.

Shape From the apparent disappearance of mountain summits, islands, and boats below the horizon as their distance from the viewer increased, many ancient peoples understood that the Earth had some sort of positive curvature. Observing the ball-like appearance of the Moon, many ancient peoples thought that the Earth must have a similar shape. Around 500 BCE, Greek mathematician Pythagoras of Samos taught that a sphere is the "perfect form" and that the Earth is in the form of a sphere because "that which the gods create must be perfect." Although there were advocates for a flat Earth, dome Earth, cylindrical Earth, etc., most ancient and medieval philosophers argued that the Earth must have a spherical shape.

The Scientific Revolution of the 17th century provided new insights about Earth. In 1659, Dutch polymath Christiaan Huygens published De vi Centrifuga describing centrifugal force. In October 1666, English polymath Isaac Newton published De analysi per aequationes numero terminorum infinitas explaining his new calculus. In 1671, French priest and astronomer Jean-Félix Picard published Mesure de la Terre detailing his precise measurement of the Meridian of Paris. In November 1687, Newton first published Philosophiæ Naturalis Principia Mathematica explaining his three laws of motion and his law of universal gravitation. Newton realized that the rotation of the Earth must have forced it into the shape of an oblate spheroid. Newton made the assumption that the Earth was an oblate spheroid (correct) of essentially uniform density (incorrect) and used Picard's Mesure de la Terre and calculus to calculate the oblateness of the Earth from the ratio of the force of gravity to the centrifugal force of the rotation of the Earth at its equator as +0.434%, remarkably accurate given his assumptions.

In 1720, Jacques Cassini, director of the Paris Observatory, published Traité de la grandeur et de la figure de la terre. Cassini rejected Newton's theory of universal gravitation, after his (erroneous) measurements indicated that the Earth was a prolate spheroid. This dispute raged until the French Geodesic Mission to the Equator of 1735-1751 and the French Geodesic Mission to Lapland of 1736–1737 decided the issue in favor of Newton and an oblate spheroid. In 1738, Pierre Louis Maupertuis of the Lapland expedition published La Figure de la Terre, déterminée par les Observations, the first direct measurement of Earth's oblateness as +0.524%. Modern measurements of Earth oblateness are +0.335281% ± 0.000001%.

Size The pronouncement by Pythagoras (c.570-495 BCE) that the Earth was a sphere prompted his followers to speculate about the size of the Earth sphere. Aristotle (384–322 BCE) writes in De caelo, writes that "those mathematicians who try to calculate the size of the earth's circumference arrive at the figure 400,000 stadia." Archimedes (c.287-212 BCE) felt that the Earth must be smaller at about 300,000 stadia in circumference. These were merely informed guesses. Since the length of a stadion varied from place to place and time to time, it is difficult to say how much these guesses overstated the size of the Earth.

Eratosthenes (c.276-194 BCE) was the first to use empirical observation to calculate the circumference of the Earth. Although Eratosthenes made errors, his errors tended to cancel out to produce a remarkably prescient result. If Eratosthenes used a stadion of between , his 252,000-stadion circumference was within 5% of the modern accepted Earth volumetric circumference.

Subsequent estimates employed various methods to calculate the Earth's circumference with varying degrees of success. Some historians believe that the ever optimistic Christopher Columbus (1451–1506) may have used the obsolete 180,000-stadion circumference of Ptolemy (c.100-170) to justify his proposed voyage to India. Columbus was very fortunate that the Antilles were in his way to India.

It was not until the development of the theodolite in 1576 and the refracting telescope in 1608 that surveying and astronomical instruments attained sufficient accuracy to make precise measurements of the Earth's size. The acceptance of Newton's oblate spheroid in the 18th century opened the new era of Geodesy. Geodesy has been revolutionized by the development of the first practical atomic clock in 1955, by the launch of the first artificial satellite in 1957, and by the development of the first laser in 1960.

Timeline +Some historical estimates of the size of the EarthEstimates of the Earth as a sphere YearEstimateDeviation from WGS 84CircumferenceCircumferenceSurface areaVolumePlato~387 BCE400,000 stadia~64,000 km+60%+156%+309%Aristotle~350 BCEEratosthenes of Cyrene~250 BCE252,000 stadia~40,320 km+0.7%+1.5%+2.2%Archimedes of Syracuse~237 BCE300,000 stadia~54,000 km+35%+82%+145%Posidonius of Apameia~85 BCE240,000 stadia~38,400 km-4.1%-8.0%-11.7%Marinus of Tyre~114180,000 stadia~28,800 km-28%-48%-63%Claudius Ptolemy~150Aryabhata~4763,300 yojana~26,400 km-34%-57%-71%Brahmagupta~6284,800 yojana~38,400 km-4.1%-8.0%-11.7%Yi Xing~726128,300 lǐ~56,869 km+42%+102%+187%Caliph al-Ma'mun~83020,400 Arabic miles~40,253 km+0.6%+1.1%+1.7%al-Biruni~103780,445,739 cubits~36,201 km-10%-18%-26%Bhāskara II11504,800 yojana~38,400 km-4.1%-8.0%-11.7%Nilakantha Somayaji15013,300 yojana~26,400 km-34%-57%-71%Jean Fernel152524,514.56 Italian miles~39,812 km-0.546%-1.089%-1.629%Jean Picard167120,541,600 toises40,036 km24,876 miles+0.013%+0.027%+0.040%Measurements of the Earth as a spheroidYearMeasurementDeviation from WGS 84CircumferenceCircumferenceSurface areaVolumeEquatorialMeridionalEquatorialMeridionalIsaac Newton1687, 1713, 172620,586,135 toises40,122 km24,931 miles20,541,600 toises40,036 km24,876 miles+0.118%+0.069%+0.203%+0.305%Jacques Cassini172020,541,960 toises40,036 km24,877 miles20,554,920 toises40,062 km24,893 miles-0.097%+0.134%+0.073%+0.109%Pierre Louis Maupertuis173840,195 km24,976 miles40,008 km24,860 miles+0.300%+0.206%+0.475%+0.713%Plessis181740,065 km24,895 miles40,000 km24,854 miles-0.025%-0.020%-0.043%-0.065%George Everest183040,070 km24,898 miles40,003 km24,857 miles-0.013%-0.012%-0.024%-0.027%George Biddell Airy183040,071 km24,899 miles40,004 km24,858 miles-0.009%-0.008%-0.017%-0.026%Friedrich Wilhelm Bessel184140,070 km24,899 miles40,003 km24,857 miles-0.012%-0.011%-0.023%-0.034%Alexander Ross Clarke188040,075.721 km24,901.899 miles40,007.470 km24,859.489 miles+0.001758%-0.000982%-0.000139%-0.000219%Friedrich Robert Helmert190640,075.413 km24,901.707 miles40,008.268 km24,859.985 miles+0.000988%+0.001012%+0.002008%+0.003012%John Fillmore Hayford191040,076.594 km24,902.441 miles40,009.153 km24,860.535 miles+0.003935%+0.003225%+0.006923%+0.010382%IUGG 241924NAD 27192740,075.453 km24,901.732 miles40,007.552 km24,859.540 miles+0.001088%-0.000777%-0.000312%-0.000475%Feodosy Krasovsky194040,076.695 km24,901.883 miles40,008.550 km24,860.160 miles+0.001693%+0.001717%+0.003419%+0.005128%Irene Fischer196040,075.130 km24,901.531 miles40,007.985 km24,859.810 miles+0.000282%+0.000306%+0.000597%+0.000895%WGS 66196640,075.067 km24,901.492 miles40,007.911 km24,859.764 miles+0.000125%+0.000121%+0.000245%+0.000368%IUGG 67196740,075.161 km24,901.551 miles40,008.005 km24,859.822 miles+0.000361%+0.000355%+0.000714%+0.001070%WGS 72197240,075.004 km24,901.453 miles40,007.851 km24,859.726 miles+0.000031%+0.000030%+0.000061%+0.000091%GRS 80198040,075.016685578 km24,901.460896849 miles40,007.862916921 km24,859.733479555 miles0.000000%-0.000000126%-0.000000168%-0.000000252%WGS 84198440,075.016685578 km24,901.460896849 miles40,007.862917250 km24,859.733479760 milesWGS 84 reference

WGS 84 World Geodetic System 1984 (WGS 84) oblate spheroid model: equatorial circumference = 40,075.016685578 km = 24,901.460896849 miles meridional circumference = 40,007.862917250 km = 24,859.733479760 miles volumetric circumference = 40,030.178555815 km = 24,873.599774700 miles oblateness = +0.335281066% surface area = 510,065,622 km2 = 196,937,438 square miles volume = 1,083,207,319,801 km3 = 259,875,256,206 cubic miles

Timeline of Earth estimates

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