# The Science Guys

#### Science Guys > July 2001

### July 2001

**How did mankind first determine the size of the Earth, and what are the known values today?**

Contrary to popular perception, Columbus and most educated people of his day knew the Earth was a sphere, not flat. But his value for the Earth’s size was adopted from near-contemporary Arab astronomers, whose estimate of the Earth’s circumference was too small by about a third. Thus Columbus tried to journey to East Asia by going west from Spain. And when he landed on Hispaniola on Oct. 2, 1492, he pronounced that he had reached the "Indies." Soon Europeans learned Columbus had reached a New World, not India and East Asia.

They could have saved themselves a lot of trouble. A superb estimate for the circumference of the Earth had already been calculated 200 years before Christ! Even before that, Pythagoras (570-500 BC) and Aristotle (384-322 BC) had proposed that the Earth was a sphere. Aristotle observed that the Earth casts round shadows on the moon during lunar eclipses, but his estimate of the Earth's circumference was too low by about 60 percent.

Eratosthenes (276-194 BC) was working as chief librarian at the renowned library in Alexandria, Egypt. He stumbled across interesting reports detailing observations of the sun made by travelers from Syene (Aswan, Egypt), which is due south from Alexandria. At the summer solstice (the first day of summer), shafts of sunlight illuminate the bottoms of deep wells in Syene. Eratosthenes realized the Sun had to be directly overhead Syene, or at its zenith, on that day. He also knew the Sun was 7 degrees away from the zenith at Alexandria on the solstice (which happens to be about 1/50th of the circumference of a circle). Using simple geometry, Eratosthenes then showed that this implied that the distance from Alexandria to Syene was 1/50th of the Earth’s circumference.

Using the rate that the average camel could travel, and the number of days that it took a camel to travel from Alexandria to Syene, he estimated that the distance from Syene to Alexandria was 5000 stadia. Since he had calculated this distance to also be 1/50th of the Earth’s circumference, then 50 times 5000 stadia yields 250,000 stadia for the Earth’s circumference. Now the stadium (singular of stadia) had different lengths in ancient times. Traditionally, it is assumed that there are 6 stadia in a kilometer (km), meaning that Eratosthenes found the Earth’s circumference to be about 42,000 km (26,000 mi.) Using this definition for stadia, Eratosthenes is only about 4 percent too high in his estimate! Even if he used the larger Olympic stadium for his basic length unit, his estimate is only about 14 percent too large. A calculation this precise based on so few instruments and measurements is an amazing achievement.

Thanks to precise measurements of the Earth’s gravitational field as well as satellite imagery, we now understand that the Earth is not a perfect sphere but actually an oblate spheroid. The Earth bulges a bit along its equator (not unlike us Science Guys!). The distance between the north and south poles is approximately 7900 miles while the equatorial diameter is slightly larger at 7930 miles.

The circumference of the Earth is just its average diameter, 7915 miles, times the number pi, where pi is 3.14159. This gives us about 25,000 miles for the Earth’s circumference. So Eratosthenes only missed the circumference by approximately 4 percent. This was truly remarkable precision for 2200 years ago.