## Flat Earth to Spherical Earth

As we can see from the above, interestingly, ancient and modern civilizations can have widely different interpretations of the way things work, even though they both see the same sky. Generally, the differences occur as a consequence of the precision of observation that can be achieved using the unaided eye thousands of years ago compared to using powerful telescopes today.

The first substantive attack on our primitive model is credited to Eratosthenes, who lived in the ancient Egyptian city of Alexandria around 300 B.C. He used an astonishingly simple method, developed by a sharp intellect, to estimate the size of the spherical Earth, having first disregarded the belief that the Earth was flat. The basics of the method are illustrated in Figure 1.1a. Eratosthenes was somehow aware that at around the time of midsummer, vertical posts did not cast shadows at noon in Syene (point A), which is in a region of southern Egypt traversed by what we now call the Tropic of Cancer. However, at the same time of year and day, he could see that vertical posts in Alexandria (point B) did cast shadows. This supported the idea in his mind that the Earth was not flat, but sphericalâ€”an extraordinary leap of logic. He was also aware, using the geometry shown in Figure 1.1a, that the simple measurements of the angle a, and the distance between Alexandria and Syene, would allow him to measure the circumference of his now spherical world. The distance measurement was simple in principle, but arduous in practice, as he had to employ someone to pace out the 800 km (500 miles) or so between the two centers! His estimate of Earth's circumference was around 40,000 km (25,000 miles), which is amazingly close to our modern estimate of 40,075 km (24,903 miles).

Eratosthenes is remembered today for his ingenuity and vision, but also because he was right. It does make you wonder, though, how many of his fellow Alexandrians believed in his claims of a spherical Earthâ€”something a bit hard to swallow for the average man in the street at that time. In order to draw his conclusion, he needed to assume not only that Earth was spherical, but also that the Sun was a long way away from Earth so that the sunlight illuminated Earth's surface with effectively parallel rays (Fig. 1.1a). An equally good interpretation of his observation of shadow lengths at noon is illustrated in Figure 1.1b, which would probably have gone down better with angles

Parallel Solar Rays angles

Figure 1.1: Alternative interpretations of Eratosthenes's observations of shadows cast by vertical posts at widely separated locations.

his contemporaries. If the Sun is assumed to be closer to Earth, so that the divergence of its rays is apparent, then the flat-Earth model can be saved. Over time, however, Eratosthenes was shown to be right, and the first cornerstone of our primitive model of the universe crumbled.

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