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Science project idea

Eratosthenes’ method: estimating Earth’s size from two cities’ shadows

Two sticks in two cities, measured at noon on the same day, give different shadow angles. The difference, together with the distance between the cities, gives the circumference of Earth.

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What it shows

Two sticks in two cities, measured at noon on the same day, give different shadow angles. The difference, together with the distance between the cities, gives the circumference of Earth.

The science

Earth is a sphere and the Sun’s rays are practically parallel. A stick in two places on the same north-south line points in different directions in space, so the Sun’s angle to it differs. The angle difference is the same as the angle between the two places at Earth’s centre, and a fraction of 360 degrees tells how much of the full circumference lies between them.

Materials

Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.

  • A vertical stick, 1 m long, at each city (a partner school or friend can help)
  • A plumb line and a tape
  • A map or an app for the distance between the two places in km
  • A calculator and protractor
  • A phone to share the shadow lengths

Safety

For this project: Do not look at the Sun. Stay in shade between readings, and have an adult supervise.

Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.

All the safety rules

Step by step

8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.

  1. Choose two places on roughly the same north-south line, such as Delhi and Jaipur’s neighbouring schools, at least 200 km apart.

  2. Agree a day, ideally an equinox, and local solar noon at each place.

  3. At each place set the stick vertical using the plumb line.

  4. Mark the shadow tip every five minutes around noon and keep the shortest shadow.

  5. Find the Sun angle at each place as the inverse tangent of shadow length divided by stick height.

  6. Subtract the two angles to find the difference in degrees.

  7. Divide 360 by this difference and multiply the answer by the north-south distance between the places.

  8. Compare the result with the true circumference of about 40,000 km and write the sources of error.

What you should see

An estimate of Earth’s circumference within 10 to 20 per cent of 40,000 km. A big gap usually comes from the distance chosen or from poor noon timing.

Viva questions

A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.

1Who first did this?

Eratosthenes, a Greek scholar in Egypt, about 2,200 years ago.

2Why must the cities be on the same line?

So the distance between them lies along one meridian.

3Why are the Sun’s rays treated as parallel?

The Sun is so far away that the rays arrive nearly parallel.

4What would happen if Earth were flat?

Both shadows would be the same length at the same time.

Free ebook: Viva Questions for Science Projects

Take it further

Use shadow data from a school in another continent through an online project to improve the result.

Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.

Free ebooks for this project

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