Measure the Earth

Using a stick, a measuring tape, and basic geometry, students can replicate Eratosthenes’ ancient experiment to measure the size of the Earth. By measuring the length of a stick’s shadow during the equinox, they calculate Earth’s circumference with surprising accuracy.

1. On a sunny day (ideally the equinox), place a straight stick vertically into flat ground.
2. Measure the height of the stick.
3. At local noon (when the Sun is highest), measure the length of the stick’s shadow.
4. Use trigonometry to calculate the angle of the Sun above the horizon.
5. Compare the angle measured at your location with data from another location at the same time (historically done between Alexandria and Syene by Eratosthenes).
6. Use the difference in angles and the distance between the two locations to estimate the circumference of the Earth.

Measure the Earth: An Easy, At-Home Science Experiment - Plateau Astro:

📄 The Eratosthenes experiment: calculating the Earth’s circumference - Science in School: https://scienceinschool.org/article/2023/calculating-earths-circumference/

• Collaborate with another school in a different city or country to share shadow data.
• Try the experiment on different days to compare results with equinox measurements.
• Use different stick lengths to check for accuracy and consistency.

• Do not look directly at the Sun during the experiment.
• Ensure the stick is firmly placed so it does not fall.
• Perform measurements in a safe, open area away from traffic.

• Why is the equinox the best time to perform this experiment? (The Sun is positioned such that shadow angles are easier to compare between different locations.)
• What assumptions did Eratosthenes make about the Earth when performing his experiment? (That Earth is spherical and the Sun’s rays are parallel.)
• How accurate do you expect this method to be compared with modern measurements? (Eratosthenes’ original estimate was within a few percent of today’s accepted value.)
• What are some potential sources of error in this experiment? (Uneven ground, incorrect measurement of shadow length, imprecise timing of local noon.)