Timeline of Earth estimates

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. 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 a 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 we know the oceans are never at rest.

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 insight into our home planet. 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^[1] explaining his new calculus. In 1671, French priest and astronomer Jean-Félix Picard published Mesure de la Terre^[2] detailing his precise measurement of the Meridian of Paris. In November 1687, Newton first published Philosophiæ Naturalis Principia Mathematica^[3] 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.^[4]

In 1720, Jacques Cassini, director of the Paris Observatory, published Traité de la grandeur et de la figure de la terre.^[5] 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,^[6] the first direct measurement of Earth's oblateness as +0.524%. Modern measurements of Earth oblateness are +0.335281% ± 0.000001%.

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,^[7] 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 150.9 and 166.8 meters (495 and 547 feet), 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.

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

equitorial circumference^[m] = 40,075.016685578 km = 24,901.460896849 miles

meridional circumference^[n] = 40,007.862917250 km = 24,859.733479760 miles

volumetric circumference^[o] = 40,030.178555815 km = 24,873.599774700 miles

oblateness^[p] = +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

• Earth
  • Figure of the Earth
    • Earth ellipsoid
    • Empirical evidence for the spherical shape of Earth
    • Flat Earth
    • Spherical Earth
  • Geodesy
    • Earth's circumference
    • Earth's radius
    • Geodetic datum
    • History of geodesy
    • World Geodetic System

• How Newton Derived the Shape of Earth
• World Geodetic System 1984 (WGS 84)