Eratosthenes Measures Earth (2024)

By around 500 B.C., most ancient Greeks believed that Earth was round, not flat. But they had no idea how big the planet is until about 240 B.C., when Eratosthenes devised a clever method of estimating its circumference.

It was around 500 B.C. that Pythagoras first proposed a spherical Earth, mainly on aesthetic grounds rather than on any physical evidence. Like many Greeks, he believed the sphere was the most perfect shape. Possibly the first to propose a spherical Earth based on actual physical evidence was Aristotle (384-322 B.C.), who listed several arguments for a spherical Earth: ships disappear hull first when they sail over the horizon, Earth casts a round shadow on the moon during a lunar eclipse, and different constellations are visible at different latitudes.

Around this time Greek philosophers had begun to believe the world could be explained by natural processes rather than invoking the gods, and early astronomers began making physical measurements, in part to better predict the seasons. The first person to determine the size of Earth was Eratosthenes of Cyrene, who produced a surprisingly good measurement using a simple scheme that combined geometrical calculations with physical observations.

Eratosthenes was born around 276 B.C., in the region now known as Shahhat, Libya. He studied in Athens at the Lyceum. Around 240 B.C., King Ptolemy III of Alexandria appointed him chief librarian of the library of Alexandria.

Known as one of the foremost scholars of the time, Eratosthenes produced impressive works in astronomy, mathematics, geography, philosophy, and poetry. His contemporaries gave him the nickname “Beta” because he was very good, though not quite first-rate, in all these areas of scholarship. Eratosthenes was especially proud of his solution to the problem of doubling a cube, and is now well known for developing the sieve of Eratosthenes, a method of finding prime numbers.

Eratosthenes’ most famous accomplishment is his measurement of the circumference of Earth. He recorded the details of this measurement in a manuscript that is now lost, but his technique has been described by other Greek historians and writers.

Eratosthenes was fascinated with geography and planned to make a map of the entire world. He realized he needed to know the size of Earth. Obviously, one couldn’t walk all the way around to figure it out.

Eratosthenes had heard from travelers about a well in Syene (now Aswan, Egypt) with an interesting property: at noon on the summer solstice, which occurs about June 21 every year, the sun illuminated the entire bottom of this well, without casting any shadows, indicating that the sun was directly overhead. Eratosthenes then measured the angle of a shadow cast by a stick at noon on the summer solstice in Alexandria, and found it made an angle of about 7.2 degrees, or about 1/50 of a complete circle.

He realized that if he knew the distance from Alexandria to Syene, he could easily calculate the circumference of Earth. But in those days it was extremely difficult to determine distance with any accuracy. Some distances between cities were measured by the time it took a camel caravan to travel from one city to the other. But camels have a tendency to wander and to walk at varying speeds. So Eratosthenes hired bematists, professional surveyors trained to walk with equal length steps. They found that Syene lies about 5000 stadia from Alexandria.

Eratosthenes then used this to calculate the circumference of the Earth to be about 250,000 stadia. Modern scholars disagree about the length of the stadium used by Eratosthenes. Values between 500 and about 600 feet have been suggested, putting Eratosthenes’ calculated circumference between about 24,000 miles and about 29,000 miles. The Earth is now known to measure about 24,900 miles around the equator, slightly less around the poles.

Eratosthenes had made the assumption that the sun was so far away that its rays were essentially parallel, that Alexandria is due north of Syene, and that Syene is exactly on the tropic of cancer. While not exactly correct, these assumptions are good enough to make a quite accurate measurement using Eratosthenes’ method. His basic method is sound, and is even used by schoolchildren around the world today.

Other Greek scholars repeated the feat of measuring the Earth using a procedure similar to Eratosthenes’ method. Several decades after Eratosthenes measurement, Posidonius used the star Canopus as his light source and the cities of Rhodes and Alexandria as his baseline. But because he had an incorrect value for the distance between Rhodes and Alexandria, he came up with a value for Earth’s circumference of about 18,000 miles, nearly 7,000 miles too small.

Ptolemy included this smaller value in his treatise on geography in the second century A.D. Later explorers, including Christopher Columbus, believed Ptolemy’s value and became convinced that Earth was small enough to sail around. If Columbus had instead known Eratosthenes larger, and more accurate, value, perhaps he might never have set sail.

Eratosthenes Measures Earth (2024)

FAQs

Eratosthenes Measures Earth? ›

He made this estimation from the time it took walkers, who were trained to measure distances by taking regular strides, to trek between the cities. By solving the equation, he calculated a circumference of 250,000 stadia, or 25,000 miles (40,000 kilometers).

How did Eratosthenes measure the Earth? ›

Eratosthenes method was very simple; he measured the length of a shadow from a vertical stick of a known height in two cities on the same day. The ratio between the north-south distance between the two cities and the angles measured gave a ratio which allowed Eratosthenes to calculate the size of the Earth.

How did Eratosthenes measure the size of the Earth Quizlet? ›

How did Eratosthenes estimate the size of Earth? They measured the angle of the Sun above the horizon at midday in two places with different latitude and used the angle to estimate the circumference of Earth.

What did Eratosthenes say? ›

The measurement of Earth's circumference is the most famous among the results obtained by Eratosthenes, who estimated that the meridian has a length of 252,000 stadia (39,060 to 40,320 kilometres (24,270 to 25,050 mi)), with an error on the real value between −2.4% and +0.8% (assuming a value for the stadion between ...

How to measure Earth size? ›

The distance between the north and south poles is approximately 7900 miles while the equatorial diameter is slightly larger at 7930 miles. The circumference of the Earth is just its average diameter, 7915 miles, times the number pi, where pi is 3.14159. This gives us about 25,000 miles for the Earth's circumference.

How did Eratosthenes measure the tilt of the Earth's axis? ›

At noon on the summer solstice, Eratosthenes measured the length of the shadow cast by a column of known height at Alexandria. With these two lengths, he could solve for the angle between them (θ).

How was the radius of the Earth first measured? ›

Eratosthenes was able to measure the radius of the earth using the difference in measure- ments of shadow length at two locations directly north-south of each other on the same day. To use this method, you first must accept that the earth is round.

What is the circumference of the earth? ›

What is the tilt of the earth called? ›

Earth's axial tilt (also known as the obliquity of the ecliptic) is about 23.5 degrees. Due to this axial tilt, the sun shines on different latitudes at different angles throughout the year. This causes the seasons. Uranus has the largest axial tilt in the solar system.

What is Eratosthenes best known for? ›

What is Eratosthenes famous for? Eratosthenes measured Earth's circumference mathematically using two surface points to make the calculation. He noted that the Sun's rays fell vertically at noon in Syene (now Aswān), Egypt, at the summer solstice.

Who measured the diameter of the earth first? ›

The first person to determine the size of Earth was Eratosthenes of Cyrene, who produced a surprisingly good measurement using a simple scheme that combined geometrical calculations with physical observations. Eratosthenes was born around 276 B.C., which is now Shahhat, Libya.

How did Eratosthenes tell time? ›

Considering time measurement, he did not need it. He used two cities on approximately the same longitude and measured shadows at noon. Noon is determined when the shadow is shortest, and one does not need any clock for this.

When did Eratosthenes measure the Earth? ›

240 B.C. Eratosthenes Measures the Earth. By around 500 B.C., most ancient Greeks believed that Earth was round, not flat. But they had no idea how big the planet is until about 240 B.C., when Eratosthenes devised a clever method of estimating its circumference.

What is the size of the Earth answer? ›

Size of the Earth
Mass5.9736×1024kg
Mean diameter12,742 km
Surface area510,072,000 km2
Density5.515 g/cm3
Circumference40,041 km
1 more row
Mar 8, 2009

What is Earth's real size? ›

Therefore, the diameter of Earth through its center is 7,926 miles (12,756 km). Again, because of the equatorial bulge, the planet's diameter is slightly smaller when measured from pole to pole, where it is about 7,900 miles (12,712 km). The equatorial circumference of Earth is 24,901 miles (40,075 km).

How did the Egyptians measure the circumference of the Earth? ›

He used the fact that at noon, the Sun was directly overhead at the city of Syene, in Egypt. Then at Alexandria, about 500 miles north, he measured the length of shadow made by a tall straight rod. From the triangle made by the shadow and the rod, he calculated the Earth's circumference to be about 24,800 miles.

How did Eratosthenes measure the shadow? ›

He watched the shadow of the gnomon on the day in question, and measured the length of the shadow at noon. The height of the stick and the length of the shadow allowed him to calculate the angle between the vertical at Alexandria (as indicated by the gnomon) and the direction of the Sun's rays at noon.

What is the actual shape of the Earth? ›

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