Measuring the Earth with a Shadow

How can a stick and its shadow tell you the size of the whole Earth? About 2,200 years ago, Eratosthenes found that the Sun's rays at Alexandria tilted about 7.2 degrees, one fiftieth of a circle, while in Syene they came straight down. So the 5,000 stadia between the two cities had to be one fiftieth of the way around, and the Earth about 250,000 stadia. That works out to about 24,000 to 28,000 miles (38,000 to 46,000 km), close to the true 24,901 miles (40,075 km) around the equator. This video also covers the myth that people thought the Earth was flat until Columbus, why parallel sunlight makes the shadow angle equal the angle at the Earth's center, why nobody knows exactly how long a stadion was (about 500 to 600 feet, or 152 to 183 meters), how close his answer came (between about 5% too small and 14% too big), and the simplifications he made. It ends with the method as three steps you could try yourself: subtract the two shadow angles, divide 360 degrees by the result, then multiply the distance between the places by that number. Try it yourself: ▶ https://www.metric-conversions.org/length/kilometers-to-miles.htm ▶ https://www.metric-conversions.org/length/feet-to-meters.htm Chapters: 0:00 The question 0:25 Two cities, two shadows 1:16 Scaling up 1:51 The catch: how long is a stadion? 2:46 Simplifications 3:04 Try it yourself Sources: • APS News: This Month in Physics History, June 2006: https://www.aps.org/publications/apsnews/200606/history.cfm • Myth of the flat Earth (Wikipedia, citing Russell, Gould, Lindberg and Numbers): https://en.wikipedia.org/wiki/Myth_of_the_flat_Earth • NASA Earth Fact Sheet: https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html Is there anything else you'd like us to cover? Let us know in the comments below.