Earth's circumference
Earth's circumference is the distance around Earth. Measured around the equator, it is 40,075.017 km (24,901.461 mi). Measured passing through the poles, the circumference is 40,007.863 km (24,859.734 mi).[1]
Measurement of Earth's circumference has been important to navigation since ancient times. The first known scientific measurement and calculation was done by Eratosthenes, by comparing altitudes of the mid-day sun at two places a known north–south distance apart.[2] He achieved a great degree of precision in his computation.[3] Treating the Earth as a sphere, its circumference would be its single most important measurement.[4] Earth deviates from spherical by about 0.3%, as characterized by flattening.
In modern times, Earth's circumference has been used to define fundamental units of measurement of length: the
History
Geodesy |
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Posidonius
Eratosthenes
The measure of Earth's circumference is the most famous among the results obtained by Eratosthenes,[8] who estimated that the meridian has a length of 252,000 stadia, with an error on the real value between −2.4% and +0.8% (assuming a value for the stadion between 155 and 160 metres;[3] the exact value of the stadion remains a subject of debate to this day; see stadion).
Eratosthenes described his technique in a book entitled On the measure of the Earth, which has not been preserved; what has been preserved is the simplified version described by Cleomedes to popularise the discovery.[9] Cleomedes invites his reader to consider two Egyptian cities, Alexandria and Syene (modern Assuan):
- Cleomedes assumes that the distance between Syene and Alexandria was 5,000 stadia (a figure that was checked yearly by professional bematists, mensores regii).[10]
- He assumes the simplified (but inaccurate) hypothesis that Syene was precisely on the local noon on the summer solsticethe Sun was directly overhead. Syene was actually north of the tropic by something less than a degree.
- He assumes the simplified (but inaccurate) hypothesis that Syene and Alexandria are on the same meridian. Syene was actually about 3 degrees of longitude east of Alexandria.
According to
Eratosthenes' method was actually more complicated, as stated by the same Cleomedes, whose purpose was to present a simplified version of the one described in Eratosthenes' book. Pliny, for example, has quoted a value of 252,000 stadia.[16]
The method was based on several surveying trips conducted by professional bematists, whose job was to precisely measure the extent of the territory of Egypt for agricultural and taxation-related purposes.[3] Furthermore, the fact that Eratosthenes' measure corresponds precisely to 252,000 stadia (according to Pliny) might be intentional, since it is a number that can be divided by all natural numbers from 1 to 10: some historians believe that Eratosthenes changed from the 250,000 value written by Cleomedes to this new value to simplify calculations;[17] other historians of science, on the other side, believe that Eratosthenes introduced a new length unit based on the length of the meridian, as stated by Pliny, who writes about the stadion "according to Eratosthenes' ratio".[3][16]
Aryabhata
Around AD 525, the Indian mathematician and astronomer Aryabhata wrote
Islamic Golden Age
Around AD 830,
A more convenient way to estimate was provided in Al-Biruni's Codex Masudicus (1037). In contrast to his predecessors, who measured the Earth's circumference by sighting the Sun simultaneously from two locations, al-Biruni developed a new method of using trigonometric calculations, based on the angle between a plain and mountain top, which made it possible for it to be measured by a single person from a single location.[21] From the top of the mountain, he sighted the dip angle which, along with the mountain's height (which he determined beforehand), he applied to the law of sines formula. This was the earliest known use of dip angle and the earliest practical use of the law of sines.[22] However, the method could not provide more accurate results than previous methods, due to technical limitations, and so al-Biruni accepted the value calculated the previous century by the al-Ma'mun expedition.[21]
Columbus's error
1,700 years after Eratosthenes's death,
Historical use in the definition of units of measurement
In 1617 the Dutch scientist Willebrord Snellius assessed the circumference of the Earth at 24,630 Roman miles (24,024 statute miles). Around that time British mathematician Edmund Gunter improved navigational tools including a new quadrant to determine latitude at sea. He reasoned that the lines of latitude could be used as the basis for a unit of measurement for distance and proposed the nautical mile as one minute or one-sixtieth (1/60) of one degree of latitude. As one degree is 1/360 of a circle, one minute of arc is 1/21600 of a circle – such that the polar circumference of the Earth would be exactly 21,600 miles. Gunter used Snellius's circumference to define a nautical mile as 6,080 feet, the length of one minute of arc at 48 degrees latitude.[24]
In 1793, France defined the metre so as to make the polar circumference of the Earth 40,000 kilometres. In order to measure this distance accurately, the
See also
References
- ^ Humerfelt, Sigurd (26 October 2010). "How WGS 84 defines Earth". Archived from the original on 24 April 2011. Retrieved 29 April 2011.
- ISBN 978-0-8230-2512-1.
- ^ a b c d Russo, Lucio (2004). The Forgotten Revolution. Berlin: Springer. p. 273–277.[dead link]
- ISBN 978-0-387-30858-6.
- ^ a b Posidonius, fragment 202
- ^ Cleomedes (in Fragment 202) stated that if the distance is measured by some other number the result will be different, and using 3,750 instead of 5,000 produces this estimation: 3,750 x 48 = 180,000; see Fischer I., (1975), Another Look at Eratosthenes' and Posidonius' Determinations of the Earth's Circumference, Ql. J. of the Royal Astron. Soc., Vol. 16, p.152.
- ^ John Freely, Before Galileo: The Birth of Modern Science in Medieval Europe (2012)
- ^ Russo, Lucio. The Forgotten Revolution. p. 68.
- ^ Cleomedes, Caelestia, i.7.49–52.
- ^ Martianus Capella, De nuptiis Philologiae et Mercurii, VI.598.
- ISBN 978-0-226-84882-2.
- ^ "Astronomy 101 Specials: Eratosthenes and the Size of the Earth". www.eg.bucknell.edu. Retrieved 19 December 2017.
- ^ a b "How did Eratosthenes measure the circumference of the earth?". 3 July 2012.
- ^ a b "Eratosthenes and the Mystery of the Stades – How Long Is a Stade? – Mathematical Association of America". www.maa.org.
- doi:10.2307/295030(subscription required).
- ^ a b Pliny, Naturalis Historia, Book 2, Chapter 112.
- S2CID 118004246.
- ].
- ^ "Journal of the Royal Asiatic Society of Great Britain and Ireland". 1907.
- ^ "The_Aryabhatiya_of_Aryabhata_Clark_1930".
- ^ ISBN 9780226316352.
- ^ Gow, Mary. Measuring the Earth: Eratosthenes and His Celestial Geometry, p. 6 (Berkeley Heights, NJ: Enslow, 2010).
- ^ Marine Insight, Why Nautical Mile and Knot Are The Units Used at Sea?
- ISBN 978-0-7432-1676-0.
Bibliography
- Krebs, Robert E.; Krebs, Carolyn A. (2003). "Calculating the Earth's Circumference". Groundbreaking Scientific Experiments, Inventions, and Discoveries of the Ancient World. Greenwood Publishing Group. p. 52. ISBN 978-0-313-31342-4.
- Nicastro, Nicholas (25 November 2008). Circumference: Eratosthenes and the Ancient Quest to Measure the Globe. St. Martin's Press. ISBN 978-1-4299-5819-6.
- Gow, Mary (1 July 2009). Measuring the Earth: Eratosthenes and His Celestial Geometry. Enslow Publishing, LLC. ISBN 978-0-7660-3120-3.
- Lowrie, William (20 September 2007). Fundamentals of Geophysics. Cambridge University Press. ISBN 978-1-139-46595-3.