The astronomer who arrived at a surprisingly accurate calculation of the Earth's circumference was Eratosthenes.
Eratosthenes: Pioneer of Earth Measurement
Eratosthenes, a brilliant Greek mathematician, geographer, and chief librarian at the Library of Alexandria, conducted the first remarkably accurate measurement of the Earth's circumference. His groundbreaking work, performed around 200 BC—more than 2200 years ago—demonstrated an ingenious understanding of geometry and celestial observations. Born around 276 BC, Eratosthenes applied scientific principles to derive a measurement that was astonishingly close to modern values.
The Ingenious Method
Eratosthenes' method for calculating the Earth's circumference was elegantly simple yet profoundly effective. He utilized the principles of geometry and the observed angles of the sun's rays at two different locations on the summer solstice.
Here's how he did it:
- Observation in Syene (modern Aswan): He knew that at noon on the summer solstice, the sun's rays shone directly into a deep well in Syene, indicating the sun was directly overhead (zero angle).
- Observation in Alexandria: At the same time, he measured the angle of the sun's rays in Alexandria, located directly north of Syene, by observing the shadow cast by an obelisk. He found this angle to be about 7.2 degrees.
- Calculating Distance: Eratosthenes estimated the distance between Syene and Alexandria to be approximately 5,000 stadia (an ancient unit of length).
- Applying Geometry: He reasoned that the 7.2-degree angle observed in Alexandria was equivalent to the angle subtended at the Earth's center by the arc connecting Syene and Alexandria. Since a full circle is 360 degrees, and 7.2 degrees is 1/50th of 360 degrees, the distance between the two cities represented 1/50th of the Earth's total circumference.
Accuracy and Significance
By multiplying the distance between Syene and Alexandria (5,000 stadia) by 50, Eratosthenes calculated the Earth's circumference to be 250,000 stadia. While the exact length of a stadium varied, if he used the Egyptian stadium (approximately 157.5 meters), his calculation would be about 39,375 kilometers (24,466 miles). This figure is remarkably close to the modern accepted circumference of approximately 40,075 kilometers (24,901 miles) at the equator.
Key Facts about Eratosthenes' Calculation
| Feature | Description |
|---|---|
| Pioneer | First person to accurately calculate Earth's circumference. |
| Era | Around 200 BC (more than 2200 years ago). |
| Methodology | Used sun angles and known distance between Syene and Alexandria. |
| Key Locations | Syene (Aswan, Egypt) and Alexandria, Egypt. |
| Result (Approx.) | 250,000 stadia (roughly 39,375 km or 24,466 miles). |
| Accuracy | Within 2-15% of the true value, depending on the stadium unit used, a remarkable feat for his time. |
| Significance | Demonstrated the Earth's spherical shape and provided a practical method for measuring its size. |
Eratosthenes' work was not just a mathematical triumph; it was a testament to the power of observation, reason, and scientific inquiry. His measurement provided crucial empirical evidence for the Earth's spherical shape and laid foundational groundwork for the fields of geography and geodesy. For more details on his groundbreaking work, you can explore resources like Britannica on Eratosthenes.
