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This is a timeline of our 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, and it is further a lumpy oblate spheroid because neither the interior nor the surface of the Earth are uniform.

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.

In October 1666, English polymath Isaac Newton published De analysi per aequationes numero terminorum infinitas explaining his calculus. In November 1687, Newton 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 the newly published work of Jean Richer 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.{{cite web|url=https://www.aps.org/apsnews/2022/10/newton-earth-shape|title=How Newton Derived the Shape of Earth|first=Miguel|last=Ohnesorge|publisher=American Physical Society|date=October 13, 2022|access-date=December 13, 2024}}

In 1713, Giovanni Domenico Cassini, director of the Paris Observatory and astronomer and astrologer to King Louis XIV, 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 the first measurement of Earth oblateness as +0.524%. Modern measurements of Earth oblateness are +0.335 281% ± 0.000 001%.

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,{{cite web|url=https://archive.org/details/decaeloleofric00arisuoft/decaeloleofric00arisuoft/page/n101/mode/2up|pp=297b|title=De caelo|last=Aristotle|editor-first1=John Leofric|editor-last1=Stocks|publisher=Oxford, Clarendon Press|year=1922|access-date=December 15, 2024}} 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 {{convert|150.9|and|166.8|m|ft|0|abbr=off|sp=us}}, 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 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.

World Geodetic System 1984 (WGS 84) oblate spheroid model:

:equitorial circumference{{efn|name=equitorial circumference|The equitorial circumference of a spheroid is measured around its equator.}} = 40,075.016 69 km = 24,901.460 90 miles

:meridional circumference{{efn|name=meridional circumference|The meridional or polar circumference of a spheroid is measured through its poles.}} = 40,007.862 92 km = 24,859.733 48 miles

:volumetric circumference{{efn|name=volumetric circumference|The volumetric circumference of an ellipsoid is the circumference of a sphere of equal volume as the ellipsoid.}} = 40,030.178 56 km = 24,873.599 77 miles

:oblateness{{efn|name=oblateness|The oblateness of a spheroid is the difference of its equitorial radius minus its polar radius divided by its equitorial radius.}} = +0.335 281 066%

:surface area = 510,065,622 km² = 196,937,438 square miles

:volume = 1,083,207,320,000 km³ = 259,875,256,000 cubic miles

Earth ellipsoid

[https://www.aps.org/apsnews/2022/10/newton-earth-shape Newton]

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