Measuring the Earth like Eratosthenes – Shadows and Parallel Sunlight
GeographyEarth in SpaceAges 11–12
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Sign in to playSunlight reaches Earth as almost parallel rays. At noon, vertical sticks at two places on the same meridian make different angles with the rays, and the difference equals the angle at Earth's centre between the two places. Drag the red measuring arm onto the sunlight to measure the angles at Syene and Alexandria, then use the distance of 5,000 stadia (≈ 800 km) to work out Earth's circumference and radius. Free mode lets you pick two latitudes and the subsolar latitude, and add a distance error or a tilted stick to discuss sources of error.
Lesson: Earth's shape and size; Eratosthenes' measurement of Earth's circumference
What it shows
Around 240 BC Eratosthenes knew that at noon on the summer solstice the Sun shone straight down a well at Syene, so a vertical stick cast no shadow, while at Alexandria, almost due north, a stick did cast one. Because sunlight arrives in parallel rays, the shadow angle at Alexandria equals the angle at Earth's centre between the two cities, about 7.2°, or 1/50 of a circle. Fifty times the distance between the cities gives Earth's circumference, close to today's value of about 40,000 km.
How to use
In each small panel, drag the red measuring arm until it lies along the yellow sunlight, or use the − and + buttons for 0.1° steps, and read the angle. The result box then computes the circumference from your two angles and the distance. Switch the mode to Choose two places to set your own latitudes and subsolar latitude, try Distance error and Stick B tilt, and press Show true angles to check the measurements.
Parameters you can change
- Mode Eratosthenes' measurement (Syene – Alexandria), Choose two places
- Latitude of place A (free mode, negative = South) -60–60 °
- Latitude of place B (free mode, negative = South) -60–60 °
- Latitude where the Sun is overhead (free mode) -23.44–23.44 °
- Error in the measured distance A–B -20–20 %
- Tilt of stick B from vertical (positive = towards the north) -3–3 °
- Show the true angles
Questions to explore
- Why does this method work only if we assume the Sun's rays reaching Earth are parallel?
- Would the result be more or less accurate if the two places were farther apart, and why?
- If Earth were flat, how would the shadows of the two sticks compare at noon?
