Science 7–10 · Year 7
Eratosthenes: measuring Earth's circumference with a partner school
Earth and space sciences (no ACARA Year 7 to 10 content description covers measuring Earth's size; coded here to Year 7 science inquiry, including the outcome on analysing a method for its assumptions and sources of error; NSW Stage 4 focus area: Observing the Universe)
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
Two noon shadows at different latitudes on the same day give the angle between the two sites, and the north-south distance between them scaled by 360 degrees over that angle gives Earth's circumference.
What you need
- 1 vertical stick exactly 1.000 m tall on a levelled base (the Eratosthenes Experiment standard)
- 1 metre ruler and 1 plumb line
- 1 partner school on a similar longitude but a different latitude, or the virtual school on the equator the Eratosthenes Experiment provides
- the two schools' latitudes, and the north-south distance between them from a map with a kilometre scale bar or an online map's distance tool (never calculated from the latitudes)
- 1 recording table for the shadow length at local solar noon (from the NOAA Solar Calculator for the date and place)
How to do it
- On the agreed day (the Eratosthenes Experiment runs on the equinox, 23 September 2026 for the spring event) find local solar noon for the school from the NOAA Solar Calculator.
- Level the base, hang the plumb line to check the stick is vertical and measure the shadow length at solar noon three times within two minutes; use the mean.
- Compute the Sun's zenith angle z = arctan(shadow length / 1.000 m).
- Exchange z with the partner school and take the difference in zenith angles (add them if the schools are on opposite sides of the sub-solar latitude).
- Measure the north-south distance between the schools independently: on a map with a kilometre scale bar, or with an online map's distance tool along the meridian between the two latitudes. Do not convert the latitude difference with 111.2 km per degree: that figure comes from Earth's radius, so it would return 40,030 km whatever the shadows show.
- Circumference = distance x 360 / angle difference. Compare with the 40,008 km pole-to-pole circumference from the NASA Earth Fact Sheet radii.
What you should see
On the equinox the zenith angle at each site equals its latitude, so a Sydney school (33.85 degrees S) measures a 0.671 m shadow (tan 33.85 x 1.000 m) and the equator partner measures 0 m, an angle difference of 33.85 degrees. The surveyed north-south distance from Sydney's latitude to the equator is 3,747 km (the meridian arc on the ellipsoid with the NASA Earth Fact Sheet equatorial radius 6,378.137 km and polar radius 6,356.752 km), so 3,747 x 360 / 33.85 = 39,850 km, 0.4 percent short of the 40,008 km pole-to-pole circumference from the same radii. Only an independent distance makes this a measurement: a distance worked out from the latitude difference at 111.2 km per degree builds Earth's radius in and returns 40,030 km (2 pi x 6,371.0 km) whatever the shadows show. How close a real pair lands depends on vertical sticks, correct noon timing and the map distance: a 1 cm shadow error at Sydney shifts the angle by 0.39 degrees, about 1.2 percent of the result.
What changes
- What you change
- latitude of the observing site
- What you measure
- noon zenith angle of the Sun
- What you keep the same
- date
- stick height
- solar noon timing
- vertical alignment
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Sun rays spread out from a nearby point, so different shadow angles do not need a curved Earth; the Sun is far enough that its rays arrive parallel.
- The two schools must be on the same longitude; each school measures at its own local solar noon and only the north-south distance between them enters the calculation, so a partner at another longitude works when both measure on the same date.
Safety card
Hazards
- sun exposure
- never look directly at the Sun
Controls
- hat and sunscreen
- short time outdoors at noon
Note
No hazardous chemical and no flame or heating apparatus: a generic classroom risk assessment (CSIS 1.7 or RiskAssess) covers trips, spills, warm lamps and sharp edges.
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 7-10 Syllabus (2023), NSW Education Standards Authority (implemented from 2026; codes read at curriculum.nsw.edu.au on 22 and 23 September 2026)SC4-OTU-01SC4-WS-01SC4-WS-04SC4-WS-06
- Australian Curriculum v9AC9S7I06AC9S7I04AC9S7I05
Sources
The pages the author read to write this activity.