Twenty-two centuries ago, Eratosthenes of Cyrene (276–194 B.C) measured the Earth using only sunlight and shadows. At noon on the summer solstice in Alexandria, Egypt, sunlight reach the bottom of a deep well, meaning that the sun stood directly overhead. At the same moment, to the north some 5000 stadia (the common unit of distance was the length of a Greek stadium) in Syene (now Aswan, Egypt), a vertical stick cast a shadow of the Sun 7° from the zenith. This is all he needed to know.

If the Earth is spherical (which Greeks knew from our shadow during lunar eclipses) and the Sun’s is far enough away that its rays are parallel, the rest is easy. Since the angular difference of 7° is 1/50 of a circle of 360°, the circumference of the Earth is about 50 times the inter-city distance, roughly 250,000 stadia. 

This is an excellent measurement. But what if the ancient Greeks had used the Global Positioning System, better known as GPS? Although satellites and silicon microchips are decidedly 20th-century inventions, the geometric principles of intersecting circles (actually spheres) of time signals to determine the location of a point would be instantly understood. Moreover, a much shorter measurement baseline would work because of GPS’s incredible accuracy: about 3 m (10’) or so.

Earlier this year, Eratosthenes’ experiment was re-enacted in its original form. Sponsored by the World Year of Physics, school groups from all over the country measured noon shadow angles and reported their results. The kids did remarkably well, especially given that measuring shadows requires considerable care. The accuracy is ultimately limited by the fact that the Sun is a disk a half degree across—hence the Sun’s shadow has a soft edge. All together, the classes’ average estimate was just 3% higher than the modern value.

To make my (admittedly smaller) point, I “repeated” the Eratosthenes experiment using a handheld GPS unit, a 100-m measuring tape oriented north-south as my baseline, and stretched it over a level area. I took GPS readings at each end, recording all the decimal places, averaging several values since I knew each 3rd decimal place represent about 2 m. The north end was latitude 38° 47.1913’, and the south 38° 47.1390’, a difference of just 0.000872°. Using the same proportionality as Eratosthenes, "my" Earth’s circumference is 41,274 km, 3.3% too big. 

So, how well did Eratosthenes do? Quite well indeed, but just how accurately is still debated. The answer depends critically on the assumed length of his measuring unit, stadium or stadia. Several values have been documented, and because there were many venues for Olympic games, this value probably differed from region to region. The best-case guess of 185 m, gives Eratosthenes’ estimate of 39,690 km, accurate to less than a percent, while the other extreme gives a value about 17% too high. In all, not too bad for two thousand years old technology.

While the elevation of the noon Sun is no longer used for position reckoning, latitude and longitude are "must-have" info for modern go-to telescopes, and many high-end models come with GPS built-in. Navigating great circles, estimating distances, and even viewing the surface from above is easy with GPS coordinates. And with a hand-held GPS, you too can measure the Earth from the ball field at Tuckahoe!

The modern value for the polar circumference of the Earth is 39,941 km or 24,818 miles. Moondark is written by Doug Miller, published online, and printed in the Delmarva Star Gazers' Star Gazer News. Last revised on 26 June 2005. Text and images are copyright © 2005 by Douglas C. Miller, All Rights Reserved. This material may not be reproduced in any form without prior permission.