Mon Prof Augmenté
Measuring Earth with Shadows
Age 16 · Science
Eratosthenes compared the noon shadows in Syene and Alexandria on the summer solstice to estimate the size of Earth. The difference in the shadow angles gave a fraction of a full circle, and a simple proportion turned that into a circumference.
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In the picture
- The rod at Syene: a rod rising straight out from the surface with no shadow beside it.
- The rod at Alexandria: a second rod rising straight out from the surface farther north.
- The shadow at Alexandria: the short slanted dark line cast by the second rod.
- The parallel sunbeams: evenly spaced light rays arriving from the left.
- The central wedge: the narrow angle formed where lines from the two rods meet at the centre.
Examples
- A lamppost casts a longer shadow when the Sun is low than when it is high.
- A flashlight shining straight down on a ball lights a small spot, while a tilted beam lights a longer oval.
Key takeaways
- A rod’s shadow angle depends on how high the Sun is in the sky.
- If two places are a known distance apart and their noon shadow angles differ, that difference is a fraction of Earth’s circumference.
Quiz: Measuring Earth with Shadows (Age 16)
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What does the angle of a rod’s noon shadow depend on?
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If two places are a known distance apart and their noon shadow angles differ, what does that difference help calculate?
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What did Eratosthenes compare to estimate Earth’s circumference?
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