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Timeline of Earth measurement
[edit]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.
Shape
[edit]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.[1]
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%.
Size
[edit]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,[2] 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 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.
WGS 84
[edit]World Geodetic System 1984 (WGS 84) oblate spheroid model:
- equitorial circumference[a] = 40,075.016 69 km = 24,901.460 90 miles
- meridional circumference[b] = 40,007.862 92 km = 24,859.733 48 miles
- volumetric circumference[c] = 40,030.178 56 km = 24,873.599 77 miles
- oblateness[d] = +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
Timeline
[edit]| Estimates of the Earth as a sphere[e] | Year | Estimate | Deviation from WGS 84[f] | ||||
|---|---|---|---|---|---|---|---|
| Circumference | Circumference | Surface area | Volume | ||||
| Plato[3][g] | ~387 BCE | 400,000 stadia ~64,000 km[h] |
+60% | +156% | +309% | ||
| Aristotle[2] | ~350 BCE | ||||||
| Eratosthenes of Cyrene[4] | ~250 BCE | 252,000 stadia ~40,320 km[h] |
+0.7% | +1.5% | +2.2% | ||
| Archimedes of Syracuse[5] | ~237 BCE | 300,000 stadia ~54,000 km[h] |
+35% | +82% | +145% | ||
| Posidonius of Apameia[6] | ~85 BCE | 240,000 stadia ~38,400 km[h] |
-4% | -8% | -12% | ||
| Marinus of Tyre | ~114 | 180,000 stadia ~28,800 km[h] |
-28% | -48% | -63% | ||
| Claudius Ptolemy | ~150 | ||||||
| Aryabhata | ~510 | 3,299 yojana ~39,588 km[i] |
-1.1% | -2.2% | -3.3% | ||
| Varahamihira | ~555 | 3,200 yojana ~38,400 km[i] |
-4% | -8% | -12% | ||
| Brahmagupta | 628 | 5,000 yojana ~60,000 km[i] |
+50% | +125% | +237% | ||
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|
~726 | 128,300 lǐ ~56,869 km[j] |
+42% | +102% | +187% | ||
| Caliph al-Ma'mun[7] | ~830 | 20,400 Arabic miles ~39,270 km[k] |
-1.9% | -3.8% | -5.6% | ||
| al-Biruni | ~1037 | 80,445,739 cubits ~38,614 km[l] |
-4% | -7% | -10% | ||
| Bhāskara II | 1150 | 4,967 yojana ~59,604 km[i] |
+49% | +122% | +230% | ||
| Nilakantha Somayaji | 1501 | 3,300 yojana ~39,600 km[i] |
-1.1% | -2.1% | -3.1% | ||
| Jean Fernel[8] | 1525 | 24,514.56 Italian miles ~39,812 km[m] |
-0.546% | -1.089% | -1.629% | ||
| Jean Picard[9] | 1670 | 20,541,600 toises ~40,036 km[n] |
+0.013% | +0.027% | +0.040% | ||
| Measurements of the Earth as an oblate spheroid | Year | Measurement | Deviation from WGS 84 | ||||
| Circumference | Circumference | Surface area | Volume | ||||
| Equitorial | Meridional | Equitorial | Meridional | ||||
| Pierre Louis Maupertuis | 1738 | 40,195 km 24,976 miles |
40,008 km 24,860 miles |
+0.300% | +0.206% | +0.475% | +0.713% |
| Plessis[10] | 1817 | 40,065 km 24,895 miles |
40,000 km 24,854 miles |
-0.025% | -0.020% | -0.043% | -0.065% |
| George Everest[11] | 1830 | 40,070 km 24,898 miles |
40,003 km 24,857 miles |
-0.013% | -0.012% | -0.024% | -0.027% |
| George Biddell Airy[11] | 1830 | 40,071 km 24,899 miles |
40,004 km 24,858 miles |
-0.009% | -0.008% | -0.017% | -0.026% |
| Friedrich Wilhelm Bessel[11] | 1841 | 40,070 km 24,899 miles |
40,003 km 24,857 miles |
-0.012% | -0.011% | -0.023% | -0.034% |
| Alexander Ross Clarke[11] | 1880 | 40,075.721 km 24,901.899 miles |
40,007.470 km 24,859.489 miles |
+0.001 758% | -0.000 982% | -0.000 139% | -0.000 219% |
| Friedrich Robert Helmert | 1906 | 40,075.413 km 24,901.707 miles |
40,008.268 km 24,859.985 miles |
+0.000 988% | +0.001 012% | +0.002 008% | +0.003 012% |
| John Fillmore Hayford[11] | 1910 | 40,076.594 km 24,902.441 miles |
40,009.153 km 24,860.535 miles |
+0.003 935% | +0.003 225% | +0.006 923% | +0.010 382% |
| IUGG 24[11] | 1924 | ||||||
| NAD 27 | 1927 | 40,075.453 km 24,901.732 miles |
40,007.552 km 24,859.540 miles |
+0.001 088% | -0.000 777% | -0.000 312% | -0.000 475% |
| Feodosy Krasovsky[11] | 1940 | 40,076.695 km 24,901.883 miles |
40,008.550 km 24,860.160 miles |
+0.001 693% | +0.001 717% | +0.003 419% | +0.005 128% |
| Irene Fischer[12] | 1960 | 40,075.130 km 24,901.531 miles |
40,007.985 km 24,859.810 miles |
+0.000 282% | +0.000 306% | +0.000 597% | +0.000 895% |
| WGS 66[11] | 1966 | 40,075.067 km 24,901.492 miles |
40,007.911 km 24,859.764 miles |
+0.000 125% | +0.000 121% | +0.000 245% | +0.000 368% |
| IUGG 67[11] | 1967 | 40,075.161 km 24,901.551 miles |
40,008.005 km 24,859.822 miles |
+0.000 361% | +0.000 355% | +0.000 714% | +0.001 070% |
| WGS 72[11] | 1972 | 40,075.004 km 24,901.453 miles |
40,007.851 km 24,859.726 miles |
+0.000 031% | +0.000 030% | +0.000 061% | +0.000 091% |
| GRS 80[11] | 1980 | 40,075.016.69 m 131,479,713.5 feet |
40,007.862.87 m 131,259,392.6 feet |
0.000 000% | -0.000 000 126% | -0.000 000 168% | -0.000 000 252% |
| NAD 83 | 1983 | 40,075.016.69 m 131,479,713.5 feet |
40,007.862.92 m 131,259,392.8 feet |
0.000 000% | -0.000 000 001% | -0.000 000 001% | -0.000 000 002% |
| WGS 84[13] | 1984 | 40,075.016.69 m 131,479,713.5 feet |
40,007.862.92 m 131,259,392.8 feet |
WGS 84 reference | |||
| ETRS 89 | 1989 | 40,075.016.69 m 131,479,713.5 feet |
40,007.862.92 m 131,259,392.8 feet |
0.000 000% | -0.000 000 001% | -0.000 000 001% | -0.000 000 002% |
Notes
[edit]- ^ The equitorial circumference of a spheroid is measured around its equator.
- ^ The meridional or polar circumference of a spheroid is measured through its poles.
- ^ The volumetric circumference of an ellipsoid is the circumference of a sphere of equal volume as the ellipsoid.
- ^ The oblateness of a spheroid is the difference of its equitorial radius minus its polar radius divided by its equitorial radius.
- ^ Ancient units of length such as the cubit, stadion, yojana, Roman mile, Arabic mile, Italian mile, or toise varied considerably by author, location, era, and use. The conversion to modern units used here are only approximations. Other assumptions will yield substantially different results. (Some modern authors will use a conversion that will best illustrate their point.)
- ^ Spherical deviations are calculated for a sphere of the same volume as the World Geodetic System 1984 (WGS 84) oblate spheriod model (1,083,207,320,000 km3).
- ^ In De caelo,[2] Aristotle writes that "those mathematicians who try to calculate the size of the earth’s circumference arrive at the figure 400,000 stadia." Prominent among those mathematicians was his tutor Plato.
- ^ a b c d e The stadion was a unit of length used in ancient Greece that could range from about 150 to 210 meters (492 to 689 feet). This calculation assumes a stadion of 160 meters (524.9 feet).
- ^ a b c d e The yojana was a unit of length used in ancient India and Southeast Asia that could range from about 3,500 to 15,000 meters (11,483 to 49,213 feet). This calculation assumes a yojana of 12,000 meters (39,370 feet).
- ^ The lǐ is a Chinese unit of distance that varied from about 300 to 576 meters (984 to 1,890 feet). This calculation assumes a Tang dynasty distance of 443.25 meters (1,454.23 feet).
- ^ The Arabic mile was a historical Arabic unit of length that could range from about 1,800 to 2,000 meters (5,906 to 6,562 feet). This calculation assumes a Arabic mile of 1,925 meters (6,316 feet).
- ^ The cubit used by al-Biruni may have ranged from about 40 to 52 centimeters (15.7 to 20.5 inches). This calculation assumes a cubit of 48 centimeters (18.898 inches).
- ^ The Italian mile is an old Italian unit of distance equal to about 1,624 meters (5,328 feet).
- ^ The toise is an old French unit of length equal to about 1.949 meters (6.394 feet).
References
[edit]- ^ Ohnesorge, Miguel (October 13, 2022). "How Newton Derived the Shape of Earth". American Physical Society. Retrieved December 13, 2024.
- ^ a b c Aristotle (1922). Stocks, John Leofric (ed.). "De caelo". Oxford, Clarendon Press. pp. 297b. Retrieved December 15, 2024.
- ^ Findlay, J.N. (1974). "Plato: The Written and Unwritten Doctrines". London: Routledge & Keegan Paul. Retrieved December 15, 2024.
- ^ Gainsford, Peter (June 10, 2023). "How Eratosthenes measured the earth. Part 2". blogspot.com. Retrieved December 15, 2024.
- ^ Smith, James Raymond (1997). "Introduction to geodesy: the history and concepts of modern geodesy". Wiley. p. 7. Retrieved December 15, 2024.
- ^ Smith, James Raymond (1997). "Introduction to geodesy: the history and concepts of modern geodesy". Wiley. pp. 10–11. Retrieved December 15, 2024.
- ^ Smith, James Raymond (1997). "Introduction to geodesy: the history and concepts of modern geodesy". Wiley. pp. 12–13. Retrieved December 15, 2024.
- ^ Smith, James Raymond (1997). "Introduction to geodesy: the history and concepts of modern geodesy". Wiley. p. 17. Retrieved December 15, 2024.
- ^ Smith, James Raymond (1997). "Introduction to geodesy: the history and concepts of modern geodesy". Wiley. p. 17. Retrieved December 15, 2024.
- ^ Alder., K (2002). The Measure of All Things: The Seven-year Odyssey and Hidden Error that Transformed the World. Free Press. ISBN 978-0-7432-1675-3.
- ^ a b c d e f g h i j k "Geodesy for the Layman". Defense Mapping Agency. March 16, 1984. Retrieved December 15, 2024.
- ^ Fischer, Irene Kaminka (September 1974). A continental datum for mapping and engineering in South America. Washington, DC: International Federation of Surveyors.
- ^ "World Geodetic System 1984". EPSG.io. 1984. Retrieved December 15, 2024.