MMathematicsPhysicsS3 to S6Astronomy

Astronomy lab: measure the Earth from Rwanda

More than 2 000 years ago, Eratosthenes measured the Earth with shadows. Near the equator, Rwanda is a perfect place to repeat his experiment with partner schools.

▶ Start the lab 🧠 Questions 📄 My report

LevelS3 to S6 (and IGCSE, A Level)

TimeAbout 35 min

You useTrigonometry, angles, proportion

PriceFree: no account

🎯 Aim

To measure noon shadows at two places on the same day and use Eratosthenes’ method to calculate the circumference of the Earth.

You will learn to

Use tan to find the angle of the sun’s rays from a shadow.
Explain why the angle changes with latitude.
Calculate the circumference with C = 360° ÷ θ × d.
Discuss errors and why distant schools give better results.

🧭 What to do

Choose Kigali and 20 March (equinox). Read the shadow and the angle.
Tap Measure and record the shadow.
Choose Alexandria on the same date and record again: read the circumference.
Try Kigali and Huye, and other dates.
Answer the questions with the class data.
Write your conclusion and download your lab report.

🔬 Lab bench

📋 The data

Noon shadows of a 1.000 m stick on 20 March in Kigali and Alexandria, and the north–south distance between them.

🧠 Investigate: answer from the data

Type your answer and tap Check. Use 💡 Hint first; open the method only when you are stuck.

📄 My lab report

Your report collects the aim, your data table, the graphs, your answers and your conclusion. It is made on your phone or computer: nothing is sent to anyone.

My conclusion

Check your conclusion

On the equinox the noon sun is overhead at the equator, so the shadow in Kigali is very short (1.95° from the vertical) and in Alexandria much longer (31.2°). The angle between the two places is 33.15°, so the circumference is 360 ÷ 33.15 × 3 687 km ≈ 40 000 km and the radius about 6 400 km. Schools far apart give a reliable result; schools close together give a very uncertain one.

➕ Get more from this experiment

📝 Free

Print the worksheet (button above), download the data, and save your report. Teachers can project this page in class.

📦 Premium Lab Pack

1 000 RWF

Practical worksheet: measure noon shadows at your school
Partner-school data sheet and trigonometry practice
Teacher guide and answer key
Exam-style questions with marking scheme

See the pack

👩‍🏫 For teachers

Use it as a practical when apparatus is missing, as homework, or as a project. Free lesson plans help you plan, teach and assess.

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DONAT STEM Interactive Labs · original work by BIZIYAREMYE Donat · data are realistic models for learning · free forever