How ancient astronomers measured the size of the Earth?

January 16, 2013

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How ancient astronomers measured the size of the Earth?

by A. Sokolowski

Geometry (Ancient Greek:  geo- “earth“, -metron “measurement“) was originally dealing with measuring of the earth.  Today, geometry has wider meaning: it is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry arose independently in a number of early cultures as a body of practical knowledge concerning lengths, areas, and volumes, with elements of a formal mathematical science.

Modern Units of measuring Length

Modern units of measure are connected with the size of our planet.

Meter

Originally, the meter was designed to be one ten-millionth (1/10,000,000) of a quadrant, the distance between the Equator and the North Pole. In other words, meter was defined as  1/10,000,000 of the distance from the Earth’s equator to the North Pole measured on the circumference through Paris.

Using this unit, the circumference of perfectly round Earth should be exactly 40,000, 000 meters (or 40,000 km).
Today, official value of the Earth’s circumference along the line of longitude is 40,007.86 km.

Nautical Mile

A nautical mile is based on the circumference of the planet Earth. If you divide circumference of the Earth into 360 degrees and then divide each degree into 60 minutes you will get 21,600 minutes of arc.

1 nautical mile is defined as 1 minute of arc (of the circumference of Earth). This unit of measurement is used by all nations for air and sea travel. Using 40,007.86 km as the official circumference of our planet we get value of the nautical mile in kilometers:  1.852 km   (40,007.86/21,600 )

Ancient units of measure reveal that our ancestors were able to measure the size of our planet with very reasonable accuracy…

Measuring circumference of the Earth

Here is simple method of establishing circumference (and diameter) of the earth that (most likely) was used by the ancient astronomers.

This method is based on understanding that Earth, just like the Sun and the Moon, is also round and that stars are very far from our planet (except for the Sun) and they appear to rotate around certain point above the northern horizon (the North Celestial Pole).

stars_circles

Long exposure photography shows apparent movement of stars around the north celestial pole

The measuring process should be done in areas with good visibility of the sky, e.g desert landscape.

On the same night, 2 astronomers at two different locations (A and B) separated by known distance (it is easy to measure ground distance between points located hundreds km away from each other),  would measure the angle above the horizon (with help of the astrolabe with vertical line given by a plumb-bob) of  a certain star at its highest position on the night sky.

A star close to the celestial North Pole (indicating the center of Earth’s rotation axis) would be a good choice for such purpose. In modern days Polaris would be the best choice, however thousands of years ago, due to precession (wobble of the earth axis of rotation), Polaris was not near the North celestial pole (see the image below).

north_celestial_pole_pathAlthough Polaris, the north star, sits within half a degree of the north celestial pole, this was not always so. Earth’s rotational axis undergoes a slow, 26,000-year wobble, known as precession, around the perpendicular to its orbit around the Sun, as a result of which the position of the sky’s rotational pole, around which all the stars seem to go, constantly changes. Around the time of the Greek poet Homer, Kochab was the north pole star. Among the best ever, however, was Thuban, which was almost exactly at the pole in 2700 BC. It remained better than Kochab up to around 1900 BC, and was therefore the pole star during the time of the ancient Egyptians. Other bright stars, including Alderamin, have served as pole star, and will again in the remote future. The star currently closest to the south celestial pole is Sigma Octantis, which is barely visible to the naked eye and lies 1º 3′ from the pole (though it was as close as 45′ just a century ago). [ Credit: The Encyclopedia of Science ]

Careful observation of the night sky would allow to select a bright star (s) most suitable for comparison of altitude of the same star at different location. 

2600BC_Mizar_KochabClick to Enlarge

For example, 2,600 BC (see image above) near Giza, when Mizar and Kochab (rotating each night around the North celestial pole) would align with  vertical line (marked by a plumb-line), Mizar (with easy to measure altitude) would be perfect star for comparison of its altitude at different locations (A and B).

Ancient_Earth_circumfrence

Because the stars are too far from the earth for any parallax effect (a displacement or difference in the apparent position of an object viewed along two different lines of sight), the only reason for the change in the measured angle of the northern star is the curvature of the earth.

Apparent mean angular diameter of the Moon and the Sun is almost the same: 0.5 degree.   

Our astronomer/priest should have no problem observing/measuring position of the northern star with accuracy of 1 degree. Using such angle measuring instrument (astrolabe) calibrated in degrees, he could obtain fairly accurate results(perhaps 0.25 degree accuracy).

simple_astrolab

If one of our astronomers were doing this measurement from location (A) near Giza ( 300 N ),  Mizar would appear about 41 deg above the local horizon.  If the second astronomer were located 120 nautical miles* south from A (* measured in ancient units of length, of course), he would observe that the altitude of the  same star is 39 degrees (2 degrees lower than altitude measured at the location A).

These 2 simple measurements would allow ancient astronomers calculation of the circumference of the Earth with fairly high accuracy:

(360/2)*120 nautical miles = 21,600 nautical miles,
whence the diameter of the earth can be estimated as:
21,600 nautical miles/( 22/7) (ancient Egyptian estimation of the Pi) =
= 6,873 nautical miles = 12,728 km

Note: Modern and accurate data:
Earth’s Circumference Between the North and South Poles:
21,602.6 nautical miles = 24,859.82 miles (40,008 km)
Earth’s Diameter at the Equator:
6,887.7 nautical miles = 7,926.28 miles (12,756.1 km)

 

Copyright 2013 A. Sokolowski
Presented with permission
Any duplication requires proper copyright information
and link to the original article.

{ 9 comments… read them below or add one }

j.a. August 8, 2013 at 4:43 am

Place is first because when evaluation happens do take in account that ancient knowledge and ability is given to design of sorts on earth as it is stated the ancient knew how to make the stars glow with the energy of monuments this keeps universal principles and order as even shown with structures in other lands this is direct intervention with material substance from a cosmic akashic field imagine the power of movement and measure mixed with the sense of the human form as displayed abundance is to all that is a national system much prefer that way of enginered desighn in concepts starvent as for technology the basis has to be straight from the supreme all else is derived from the one that become the many.

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Elijahovah February 2, 2013 at 10:01 am

It also says that Columbus presumed all of Eurasia (11,250miles) covered 225° longitude with 135° of ocean (6750 miles) from Spain to Asia. And Japan another 3700 miles from China so that the total 15,700 miles is leaving an ocean of only 2300 miles from Africa’s Canary Islands to Japan. Neede we say idiot while American schools of 1965 lied and said Columbus knew the world was round when Catholics said it was flat. When in fact Eurasia (8700 miles) covers 130° including Japan (10,000 miles) 150°.

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Elijahovah February 2, 2013 at 9:28 am

Oldest surviving record of measuring the earth accurately. http://en.wikipedia.org/wiki/Eratosthenes
700 egyptian stadia per degree (157.5 meters per stadia) making Earth’s circumference 252,000 egyptian stadia (39,690 km), an error of less than 2%.
Columbus measured the round earth as 18,000 miles instead of 24,000.
http://en.wikipedia.org/wiki/Chistopher_Colombus
Geographical

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Richard January 26, 2013 at 2:45 pm

How you can measure the diameter of the earth [ I believe this should work, if not please let me know]. On the longest day of the year when the sun is at its highest during the day, have a post set at least 10 ft or more perpendicular to the earth (use water at top to level the post, Look at the shadow and determine the angle of the edge of the shadow to the post. Then [360/by angle] X [the distance from your location to the equator] = the circumference of the earth north and south [longitude]. The further away from the equator the more accurate the estimate is and the higher the post or object you use instead of the post. The distance of 67 miles for one degree is needed. I tested this with CAD drawings and it was suprisently accurate, the sun is so far away that it comes in at the same angle as the centre any where so is a costant to thousands of a degree.

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Richard Perry January 22, 2013 at 12:34 am

If I where to measure the earths diameter I would watch the movement of shaddows and see how fast they move over land in a minute and multiply it times 60 x 24 and thats the diameter.

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Alex January 23, 2013 at 8:56 am

Richard, this would not work. Speed of rotation can be established easily as 360deg/(24hx60min/h) = 1/4 deg/min (in 1 minute earth rotates by 0.25 degree). However this does not tell you anything about the size of the radius of the earth. Size of a shadow (of an obelisk) depends only on the height of the obelisk, time of the year, and geographical location…

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shahine ali January 21, 2013 at 10:20 am

Please check my video- “end of the world. a new reality”. If you’re already on youtube, you’ll have to add “-shahine ali” to get it. I have a website, crystalcodex.com where i show our ancestors knew more than we have yet understood( precession, for example). I would really appreciate feedback.

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Brenda Brown January 20, 2013 at 6:36 pm

Hi A Sokolowski, I have no doubt that our ancient ancestors knew about geometry, and could easily have measured the earth with it. However, I very much believe that they knew a whole lot more than that. The few but extremely telling building sites of theirs that remain, reveal a science and knowledge way beyond anything we have ever accomplished, or understand right now. And not only are these sites on earth, but in our Solar System, so I think we’re the ones who need to catch up on many aspects of their every-day culture and know-how.

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Ron O. Cook January 16, 2013 at 2:42 pm

Would that you lived down the street, Alex. I would have enjoyed our conversations immensely. Build an interior chat facility that only certain members would be able to communicate, not unlike a friendly chess game and perhaps many will come — for a price of course.

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