Nowadays, the circumference of the Earth can be measured using measuring equipment and satellites. He calculated the size of the Earth without leaving the walls of the library where he worked.
How did Eratosthenes measure the circumference of the earth?
Eratosthenes is a Greek scholar who lived in the Egyptian city of Alexandria from 276 to 196 BC. He worked in the Alexandrian Museon. Partly it was a museum, partly a scientific center of that time.
The museum had a botanical garden, a vivarium, an astronomical observatory and laboratories. Some scholars conducted scientific disputes in the audience of the museum, while others dined and talked in the triclinium (that is, in the dining room).
Interesting fact: Greek scientist Eratosthenes calculated the circumference of the Earth more than 2000 years ago.
Eratosthenes was in charge of the Museyon library, which kept about 100 thousand books written on papyrus scrolls (a type of paper made from the fibers of the papyrus plant). Eratosthenes was interested in everything. He studied philosophy, history and science, was a theater critic. Many colleagues in the museon considered him an amateur, that is, a person who is interested in everyone but knows nothing deeply in truth.
From traveling travelers, Eratosthenes heard of the unusual phenomenon that they observed in Siena, a city located south of Alexandria. Travelers said that at noon on the first day of summer - the longest day of the year - shadows disappeared in Siena.The sun at that time stood directly above his head, its rays falling to the ground sheer down. Carefully peering into the water of the reservoir, it was possible to consider the reflection of the Sun at the bottom.
Interesting fact: Earth's circumference is approximately 40,000 kilometers.
Eratosthenes traveled to Siena and was convinced of this himself. Returning to Alexandria, he found that on the longest day of the year at noon, the walls of the museon continued to cast a shadow on the ground. Based on this simple observation, he was able to calculate the circumference of the Earth. This is how he did it.
Circle calculations
Eratosthenes knew that because of the enormous distance from the Earth to the Sun, the rays of the latter reach both Siena and Alexandria in parallel rays. That is, the rays of the Sun falling on the earth in Alexandria are parallel to the rays falling on the earth in Siena at the same time. If the Earth were flat, then the shadows would disappear on it everywhere on June 21. But since, he reasoned, the Earth is curved, then in Alexandria, 500 miles from Siena (1 mile equals 1.609 kilometers) to the north, the local walls and columns are tilted with respect to the Siena walls and columns to us at some angle.
So, at noon on the first day of summer, Eratosthenes measured the shadow cast by the obelisk, which was not far from the museion. Knowing the height of the obelisk, he was able to easily calculate the length of the line connecting the top of the obelisk and the end of the shadow. The result was an imaginary triangle. After the triangle was "outlined", it remained, using the geometry rules known at that time, to calculate its angles. And Eratosthenes calculated them.He found that the angle of deviation of the obelisk from the sun's beam is a little more than 7 degrees.
Since vertical objects in Siena did not cast shadows, the angle between them and the sunbeam was zero degrees. In short, there was no angle. This meant that Alexandria was 7 degrees apart from Siena on the earth's circumference. This angle between the cities is1/ 50 part of the circle. Each circle contains 360 degrees, the earth's circle in this sense is no exception. Eratosthenes multiplied the distance between Siena and Alexandria - 500 miles - by 50 and got the value of the circumference of the Earth. It turned out to be equal to 25 thousand miles. Modern scientists who measured the circumference of the Earth using high-quality technology have found it equal to 24,894 thousand miles. All the same, Eratosthenes turned out to be a first-class scientist, not an amateur.
Determination of distances on the earth's surface
Currently, there is a whole science - geodesy, which deals with determining distances on the earth's surface. Surveyors use special instruments to determine angular distances. They study the fluctuations of gravity on our planet to reveal the true shape of the Earth. Satellites are used to calculate angles. Such a satellite moves to the top of an imaginary triangle, its other two angles are placed at predetermined points on the earth's surface.
