More than 2,200 years ago, an ancient Greek scholar calculated the circumference of the Earth using a stick and the sun |
More than 2,200 years before satellites, GPS and space missions revealed the Earth’s true size, an ancient Greek scholar calculated the Earth’s circumference using only a stick, sunlight and basic geometry. Around 240 BC, Eratosthenes, chief librarian of the Library of Alexandria, conducted one of the most brilliant scientific experiments in history. By comparing the length of the shadows of two Egyptian cities, he produced an estimate of the Earth’s circumference that was surprisingly close to modern measurements, proving that careful observation and mathematics can unlock the secrets of the natural world.
How ancient Greek scholars calculated the circumference of a planet
according to American Physical SocietyEratosthenes heard that on the day of the summer solstice, in Senni (modern-day Aswan), the sun stood directly overhead at noon. At this moment, the sunlight reaches the bottom of the deep well, and the upright objects cast almost no shadows.Curious whether this was true elsewhere, he observed the sun at the same time about 800 kilometers north of Alexandria. Unlike Saini, a vertical stick there casts a distinct shadow. He measured the angle between the stick and the shadow and found it to be approximately 7.2 degrees.This simple difference indicates that the Earth’s surface is curved. If the Earth were flat, both cities would experience the sun at the same angle.
How a simple calculation could measure an entire planet
Eratosthenes knew the approximate distance between Alexandria and Seyne, and professional surveyors who passed this route estimated it to be about 5,000 stadia.He realized that an angle of 7.2 degrees represented one-fiftieth of a complete circle, since 7.2 × 50 equals 360 degrees. If the distance between two cities is one-fiftieth of the Earth’s circumference, multiplying 5,000 by 50 gives a total circumference of approximately 250,000 stadia. He later refined this number to 252,000 sightings, making it easier to divide degrees.Although the length of the stadium used by Eratosthenes is inconsistent, historians have taken this into account and calculated the length to be between 39,000 and 40,000 kilometers. The true circumference of the Earth’s equator is 40,075 kilometers.
Why Eratosthenes’ experiment remains a scientific masterpiece
The success of Eratosthenes’ calculations depended more on careful observation, logical reasoning, and a sound understanding of geometry than on advanced technology. His method assumed that sunlight reaches the Earth in nearly parallel rays and that the Earth is spherical, an idea that turned out to be correct.Although there are some small errors due to the fact that Alexandria and Seyeni are not exactly aligned north and south, and the exact distance between them is only an estimate, the result remains one of the greatest scientific achievements of the ancient world.More than 2,200 years ago, satellites were used to calculate the size of the Earth with astonishing accuracy. Yet even today, Eratosthenes’ contributions are revered as a timeless lesson in how to use curiosity, observation, and mathematics to uncover humanity’s greatest secrets.
