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.
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).
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).
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).
Although 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.
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).
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).
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
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