Friday, 7 March 2014

Geodesy - The Circumference Of The Earth

I came across a new term the other day "Geodesy" .... which is the history of the measurement and representation of the Earth throughout history. Now given that the scientifically measured circumference of the world is 24,901 miles (40,075 km), I find it amazing how close our ancestors actually got to getting this right .... this obviously excludes those who believed the Earth was flat, or rectangular (yes, at least one ancient Greek philosopher, Anaximenes, believed strongly that the Earth was rectangular in shape!).

So just to give you an idea of what I mean by 'close', here's a brief history of the history of studying the circumference of the Earth:

  • Plato guessed the circumference of the Earth to be 400,000 stadia (between 39,250 miles and 46,250 miles) 
  • Archimedes estimated 300,000 stadia ( 34,687 miles ), using the Hellenic stadion (which scholars generally take to be 185 meters or 1/10 of a geographical mile). 

After that they actually tried to calculate it 'scientifically:

  • Greek scholar and philosopher, Eratosthenes (276 BC– 195 BC), used maths to determine a figure of 250,000 stadia (25,000 geographical miles). The missing 99 geographical miles can be attributed to the fact that his belief that the town of Syene was actually on the 'Tropic of Cancer' was wrong, (it was actually 22 geographical miles to the north), and that accounts to most of the error in his resulting circumference of the Earth.

Eratosthenes Calculations of The Earth's Circumference.

Unfortunately for history, the other Greeks didn't stick to this calculation, but kept trying other methods, such as by timing ocean sunsets from different heights, which produces a size of the earth too low by a factor of 5/6, due to horizontal atmospheric refraction. So that they actually got less accurate results than Eratosthenes.

  • The Indian mathematician Aryabhata (AD 476 - 550), got the figure to within an accuracy of 1%, at 24,835 miles ....
  • Around AD 830, the Arabs calculated that the Earth's circumference was 24,000 miles.
  • Later, the medieval Persian Abu Rayhan Biruni (973-1048) estimated the Earth radius at 6,339.9 km, which was only 16.8km less than the modern value of 6,356.7km. With this radius figure you could get a circumference of 23,915.5303 miles

Meanwhile back in Europe, there were two schools of thought on the subject which competed for centuries .... by the way, the idea that the Church and leadership of Europe thought the Earth was flat is a complete fallacy, largely propagated by the author Washington Irving, in his popular 1828 biography of Christopher Columbus. In fact all educated people in Europe knew the Earth was round, a fact reflected by many writers, including 'The Venerable Bede' in his book 'Reckoning of Time', written around 723 AD. The modern historian Jeffrey Burton Russell states that the flat-earth error flourished most between 1870 and 1920, and that "with few exceptions no educated person in the history of Western Civilization from the third century B.C. onward believed that the earth was flat."
The myth that there was ever a strong belief in a flat earth, in fact has more to do with the ideological setting created by the struggles over Darwinism, and the theory of evolution in the late 19th and early 20th centuries.

The real issue in educated Europe in the Middle Ages was over the exact circumference, not on sphericity: For example, in 1492 Columbus held to the Ptolemy calculations, which were either 252,000 stadia in the Almagest, and 180,000 stadia in the later Geographical Directory - so that's why he thought he had landed in China when he reached the Americas. However some cartographers recognised the maths of Eratosthenes, so for example chapter 20 of Mandeville's Travels (c. 1357) gives the Earth's circumferences and distances based on those calculations.

  • In 1699–70 the first modern meridian arc measurement was carried out by Jean-Félix Picard a French astronomer and priest and found that the Earth was oblate (egg shaped) and this changed the debate for scientists (who turned the debate into one of the study of the "undulation of the geoid") ..... and thus ended the normal debate. 

So now, for practical purposes, we use a circumference figure of 24,901 miles (40,075 km) as though the Earth is a perfect spherical object, but in fact the answer now depends upon where you take the measurement .....


  1. Excellent piece. It's indeed incredible how accurate some of the early estimations were.

    Jean Picard however had the advantage of the Enterprise and his X-men.

    1. Glad you enjoyed it. It just illustrates that we are no cleverer, we just sit on the shoulders of giants .... or mutant powers.

    2. Referring to the image in your post showing a very bumpy earth; our planet is actually smoother than a billiard ball, proportionally speaking.

    3. Illustrative picture only .....

  2. Really enjoyed the post. Informative and well written.


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