Two sticks measure a planet.
Around 240 BC, Eratosthenes compared shadow angles cast by the sun at two Egyptian cities a known distance apart — and worked out the size of the whole Earth without leaving the ground.
Distance apart d
d ∝ C, D
100 kmhow far apart the sticks are2000 km
Stick 1 angle θ₁
from vertical
0°first measured angle20°
Stick 2 angle θ₂
Δθ = |θ₂ − θ₁|
0°second measured angle20°
Earth's diameter, estimated
km
Try
| Measurement | Date and time | Latitude | Longitude | Angle from vertical | |
|---|
Eratosthenes knew that at noon on the summer solstice, the sun sat directly overhead at Syene (near modern Aswan) — a vertical stick cast no shadow at all. On the same day, a stick in Alexandria, about 800 km north, cast a shadow 7.2° off vertical. Since the sun's rays arrive essentially parallel (it's 150 million km away), that angle difference can only come from the ground curving between the two cities. A 7.2° wedge is 1/50th of a full circle, so the circumference is 50×800 km = 40,000 km. The corresponding diameter is C/π, about 12,732 km. The diagram exaggerates Earth’s curvature and is not to scale; the small globe shows the actual wedge. This also assumes both sticks sit on the same meridian and are measured at the same solar noon. Read more on Wikipedia.
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