Academic journal article The Science Teacher

Focus on Physics

Academic journal article The Science Teacher

Focus on Physics

Article excerpt

When Our Round Earth Was First Measured

Our Earth is round, although it was not always thought to be that way. It looks flat. But if the Earth is viewed from a tall building, especially near the ocean when the horizon is clear, its curvature can be seen with the naked eye. This is helped with the aid of a straightedge held at arm's length aligned with the horizon (Figure 1), a popular activity of residents of tall high-rises near the seashore.

Eratosthenes' observations

The first person credited with measuring the roundness of Earth was the Greek scholar and geographer Eratosthenes of Cyrene in 235 BC. This man of learning was the chief librarian at the Library of Alexandria in Egypt. Just as the Sun and Moon are round, Eratosthenes assumed Earth was also round. He proceeded to measure "how round" and more.



From library information, Eratosthenes learned that the Sun is directly overhead at the summer solstice in the southern city of Syene (now called Aswan). At this special time in June, sunlight shining straight down a deep well in Syene was reflected up again--the only time the Sun's reflection could be seen in the well. A nearby vertical stick in the ground at this time would cast no shadow, but farther north, in Alexandria, a vertical stick would cast a shadow.

This was evident to Eratosthenes, who noted the shadow cast by a tall, vertical pillar near his library during the summer solstice (Figure 2). He measured the shadow, the shortest shadow of the year, to be 1/8 the height of the vertical pillar.

Eratosthenes' calculations

Eratosthenes correctly assumed that rays from the faraway Sun are parallel. He then learned that while these parallel rays were vertical in Syene, they were nonvertical in Alexandria. Furthermore, he reasoned that if a line along the vertical well in Syene were extended into Earth, it would pass through Earth's center. Likewise for a vertical line in Alexandria (or any point on the spherical Earth).

His knowledge of geometry told him that if the verticals at both locations were extended to the center of Earth, they would form the same angle that the Sun's rays make with the pillar at Alexandria. Knowing the 8:1 ratio of the pillar's height to the shadow length, Eratosthenes could calculate these angles to be 7. …

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