Eratosthenes Experiment

Eratosthenes (276 BC-194 BC) was a Greek mathematician, geographer and astronomer. He was born in Cyrene (now Libya) and died in Ptolemaic Alexandria. He is noted for devising a map system based on latitude and longitude lines and computing the size of the Earth.

Eratosthenes invented the system of latitude and longitude.[
He is the first human known to calculate the circumference of the Earth.
He calculated the circumference of the world with remarkable accuracy relative to the stadium length unit. He is also the first person to calculate the axis tilt.
He calculated the exact distance of the Earth from The Sun .
Using February 29, he eliminated the synchronization problem that appeared on the calendar.
Using his geographical and cartographic knowledge, he drew the first world map with parallel and meridians.
In addition, Eratosthenes was the founder of the scientific chronology and worked to pinpoint literary and political events from the conquest of Troy to Alexander the Great.

Eratosthenes’ other contributions include:

• The Sieve of Eratosthenes as a way of finding prime numbers.

• The measurement of the Sun-Earth distance, now called the astronomical unit (804,000,000 stadia, 1 stadion varies from 157 to 209 meter).

• The measurement of the distance to the Moon (780,000 stadia).

• The measurement of the inclination of the ecliptic with an angle error of 7′.

• He compiled a star catalogue containing 675 stars, which was not preserved.

• A map of the Nile’s route as far as Khartoum.

• A map of the entire known world, from the British Isles to Ceylon, and from the Caspian Sea to Ethiopia.

First, calculate your local noon because it may be quite different from 12:00 noon on the clock. There are several ways to compute its exact occurrence. Basically, local noon is half-way between sunrise and sunset. You can obtain sunrise and sunset times, for June 21, from your local paper or from this link: http://aa.usno.navy.mil… which also calculates local noon (sun transit). You can also obtain it by yourself by using a sundial or find out when the shadow is the shortest around noon time.

On June 21 erect a vertical straight stick or pole of about 1 meter using a carpenter’s level and measure the length of the shadow it casts at your local noon. With simple trigonometry you can obtain the angle of the elevation of the sun. You can also obtain the angle, without trigonometry, by drawing the stick and shadow proportionally and measuring it with a protractor. You can compare your results with a web based applet like this: http://www.jgiesen.de/azimuth but be careful to use it correctly (insert your correct time zone, local noon, coordinates, date and ensure that the dropdown menu points to elevation).

After you get the angle of sun elevation, it’s very easy to calculate the zenith angle by subtracting it from 90°, like Eratosthenes did. Now you’ll have to measure the distance from your location to the Tropic of Cancer latitude line – not by camel caravans of course, the Eratosthenes way. You can use a relatively large scale map, but take in account that maps tend to distort distance and the best option is to use a globe. The distance from your location to the Tropic of Cancer should be measured from north to south. In other words the distance line has to cut the Tropic of Cancer at a right angle. There are also web based calculators for this: https://web.archive.org….

Now it’s easy to calculate the Earth circumference by using the following formula:

Likewise, you can also perform this experiment on the winter solstice that takes place around 21 December, but you’ll have to measure your distance from the Tropic of Capricorn instead from the Tropic of Cancer because on this date the sun reaches its highest degree of elevation on the Tropic of Capricorn (23° 26′ 22″ south of the Equator).

It is also possible to perform this experiment on the two Equinoxes which occur on 20 March and 23 September each year when the sun is crossing the equator at the local noon on those dates and the sun rays are just overhead the equator at a right angle to the ground. But instead to measure your distance from the Tropic of Cancer or the Tropic of Capricorn you’ll have to measure it from the equator.

There is another option and you can perform this experiment on any other date of the year, at local noon time, but you should have some partner located on your longitude willing to measure sun elevation at the same time. Take in account that you’ll have to be a little careful treating correctly the sun angles obtained in this case.