Saturday, February 9, 2008

Eratosthenes Sizes Up the Earth

Anaxagoras’s explanation of eclipses was a bold exercise in the use of science to understand a phenomenon well beyond everyday experience. One other such exercise came from Eratosthenes of Cyrene (ca. 276–ca. 194 B.C.E.). A careful observer, Eratosthenes noted that at the town of Syene (present-day Aswan, Egypt), southeast of Alexandria, the rays of the sun are precisely vertical at noon during the summer solstice. That is, a vertical stick in the ground would cast no shadow. He further noted that, at Alexandria, at exactly the same date and time, sunlight falls at an angle of 7.5 degrees from the vertical.

As we’ll see in the next chapter, small differences and apparently inconsequential discrepancies often have profound implications in astronomy. Eratosthenes instinctively understood the importance of details. Assuming—correctly—that the sun is very far from the earth, he reasoned that its rays are essentially parallel when they strike the earth. Eratosthenes believed (as did Aristotle, whom we’ll meet in the next chapter) that the earth was a sphere. He further reasoned that the angle of the shadow cast in Alexandria (7.5 degrees) was equal to the difference in latitude (see Chapter 1, “Naked Sky, Naked Eye: Finding Your Way in the Dark”) between the two cities. How did he figure that? Think of it this way: Imagine poking a stick vertically into the earth at the equator and at the North Pole, and imagine the sun is directly over the stick at the equator. The stick at the equator will have no shadow, and the stick at the North Pole will cast a shadow at an angle of 90 degrees from the stick.

Now, move the stick from the North Pole to a latitude of 45 degrees. The shadow will now fall at an angle of 45 degrees from the stick. As the stick that was at the North Pole gets closer and closer to the equator (where the other stick is), the angle of its shadow will get smaller and smaller until it is beside the other stick at the equator, casting no shadow. Noting that a complete circle has 360 degrees, and 7.5 degrees is approximately 1⁄50 of 360 degrees, Eratosthenes figured that the two cities were separated by 1⁄50 of the earth’s circumference, and that the circumference of the earth must simply be fifty times the distance between Alexandria and Syene.

The distance from Syene to Alexandria, as measured in Eratosthenes’s time, was 5,000 stadia. He apparently paid someone (perhaps a hungry grad student) to pace out the distance between the two cities. So he calculated that the circumference of the earth was 250,000 stadia. Assuming that the stadion is equivalent to 521.4 feet, Eratosthenes calculation of the earth’s circumference comes out to about 23,990 miles and the diameter to about 7,580 miles. These figures are within 4 percent of what we know today as the earth’s circumference—24,887.64 miles—and its diameter, 7,926 miles. And he figured that out with only a few sticks—and one long hike. Eratosthenes made other important contributions to early astronomy. He accurately measured the tilt of the earth’s axis with respect to the plane of the solar system, and compiled an accurate and impressive star catalog and a calendar that included leap years.

We may consider Eratosthenes the first astronomer in the modern sense of the word. He used careful observations and mathematics to venture beyond a simple interpretation of what his senses told him. This combination of observation and interpretation is the essence of what astronomers (and all scientists) do. It is a cruel irony that Eratosthenes lost his eyesight in old age. Deprived of his ability to observe, he committed suicide by starvation.

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