Science and Technology K–6 · Year 6

Measuring the Earth with two shadows: an Eratosthenes experiment between two schools

Science as a human endeavour: Nature and development of science

Practical, model not builtLow risk

This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.

The idea

Because Earth is a sphere, the noon Sun stands at different heights at places north and south of each other, and the difference in angle together with the distance between them gives Earth's circumference, a measurement that needs two groups working together.

What you need

a partner class at a school at least 500 km due north or south (for example Sydney (151.21 degrees east) and Brisbane (153.03 degrees east), less than 2 degrees of longitude apart)
at each school, a straight stick exactly 1.000 m long set vertical with a spirit level on level ground
a tape measure reading to 1 mm, chalk and a clock (the noon shadow, not a compass, gives the north-south line)
a shared online table for both schools' results
a map tool to measure the north-south distance between the two schools

How to do it

Agree a date within a week of an equinox and a spare date in case of cloud.
At each school, starting 15 minutes before the expected solar noon, mark the tip of the shadow every 2 minutes for 30 minutes. The shortest shadow is the noon shadow; measure it to the nearest millimetre, three times.
Find the Sun's noon elevation from the shadow: enter the measured shadow length in the live model, which converts it to an angle (the conversion uses trigonometry, which learners meet in Year 9). A scale drawing measured with a protractor is only a rough check here, because the two schools' angles differ by just a few degrees.
Exchange results. The difference between the two elevations is the angle between the two schools at Earth's centre.
Measure the north-south distance between the schools on the map.
Circumference = 360 / angle difference x north-south distance. Compare with the measured value, 40,008 km round the poles.
List the sources of error and work out how much a 5 mm error in one shadow would change the answer.

What you should see

Near an equinox a 1.000 m stick casts a 0.671 m noon shadow in Sydney (33.87 degrees south, elevation 56.13 degrees) and 0.520 m in Brisbane (27.47 degrees south, 62.53 degrees): a difference of 6.40 degrees. The two cities are 709.5 km apart north to south, so the circumference is 360 / 6.40 x 709.5 = 39,910 km, within 0.3 percent of 40,008 km. A 5 mm error in the Sydney shadow shifts the angle by about 0.2 degrees and the answer to between about 38,700 and 41,200 km; errors of 5 mm at both schools in opposite directions (0.42 degrees together) widen that to about 37,400 to 42,700 km, so a class result in that range is a good measurement.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

The noon Sun is at the same height everywhere at the same time.
People did not know the Earth was round until modern times (Eratosthenes measured it more than 2,200 years ago).
One measurement is enough to find the size of the Earth.

Safety card

Low riskLearners carry it out

Hazards

looking at the Sun
sun exposure

Controls

never look at the Sun; measure the shadow only
hats, sunscreen and shade breaks

Note

Risk assessment before the lesson using Primary RiskAssess or the school's own template.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Science and Technology K-6 Syllabus (2017), current, taught until 2026; the only 2017 outcome this activity maps to: the Stage 3 content under ST3-10ES-S is the planets of our solar system and sudden geological and extreme weather change, and no content in the syllabus covers Earth's shape or size, so the mapping is to Working Scientifically and, for 2024, to the data outcome; code read from the syllabus document on 22 September 2026ST3-1WS-S
Science and Technology K-6 Syllabus (2024), implemented from 2027; NESA's timeline is 2026 plan and prepare and 2027 start teaching, and schools may choose to implement it during 2026; code read from the outcomes page on 22 September 2026ST3-DAT-01
Australian Curriculum v9AC9S6H01AC9S6I03AC9S6I05

Sources

The pages the author read to write this activity.

All Concept Studio activities