01 / A SHADOW. A WORLD.
One shadow.
An entire world.
No spacecraft. No satellites. Find the size of Earth using the distance between two cities and a small shadow.
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Conceptual diagram · Not to scale
Between the cities800 km
Shadow angle7.2°
02 / YOUR OBSERVATION
Model angle9.60°
↔Observed angle7.20°
Move the slider until the model angle matches 7.2°.
YOUR FIELD RECORD
03 / THE IDEA THAT REACHED AROUND EARTH
How can a shadow tell us the size of Earth?
At the same moment, the Sun is directly overhead in one city while a stick casts a shadow in another. With parallel sunlight and a spherical Earth, the shadow angle equals the central angle between the cities.
800 × (360 ÷ 7.2)
7.2° is 1/50 of a full 360° circle. If the cities are 800 km apart, Earth’s circumference is 800 × 50 = 40,000 km.
An approximate educational model. We assume a spherical Earth, parallel sunlight and two cities on the same meridian. The distance is simplified; Earth’s actual circumference varies with the direction of measurement.
Read about Eratosthenes, his observations and their limits ↗