Mathematics 11–12 · Year 11
Solar noon from a shadow: longitude, 15 degrees per hour and standard time
Time and location: Positions on the Earth’s surface (Mathematics Standard, Year 11); Time and location: Time and time differences (Mathematics Standard, Year 11)
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The idea
The sun is highest when it crosses the local meridian, so the clock time of solar noon, found halfway between two equal shadow lengths either side of it, shows how far the observer sits from the standard-time meridian, at 15 degrees of longitude per hour.
What you need
- A vertical metre stick, chalk, a watch set to Australian Eastern Standard Time
- The observer's latitude and longitude from a map app (Sydney city is near 151.21 degrees east)
- The Geoscience Australia Sun and Moon Azimuth and Elevation calculator
How to do it
- Mark the shadow tip and its time every 10 minutes from 9:30 am to 2:30 pm standard time.
- With a string held at the foot of the stick, draw arcs through three morning tips taken about 1.5 to 2 hours before noon; where each arc crosses the afternoon path of tips, find the afternoon time by interpolating between the two neighbouring 10-minute marks.
- Take the midpoint of each morning and afternoon time pair as solar noon and average the three; note also the time of the shortest shadow and compare how sharply each method fixes noon.
- Compute how far your longitude is from 150 degrees east, the meridian of UTC+10, and convert it to minutes at 4 minutes per degree.
- Predict the clock time of solar noon from that offset, then enter the site and date in the calculator at 10-minute steps from 11 am to 1 pm and find the time of greatest elevation, which also includes the equation of time for the date.
- Compute the solar time difference between Sydney (151.21 degrees east) and Perth (115.86 degrees east) at 15 degrees per hour and compare it with the 2-hour difference between UTC+10 and UTC+8.
What you should see
Sydney lies 1.21 degrees east of 150 degrees east, so solar noon comes 4.8 minutes before 12:00 standard time, about 11:55 am, before the equation of time moves it earlier or later by up to about a quarter of an hour depending on the date. Sydney and Perth are 35.35 degrees of longitude apart, 2 h 21 min of solar time, against a 2-hour difference in standard time. Near noon the shadow barely changes: in Sydney a 1 m stick's shadow is only 2 to 4 mm longer 10 minutes either side of solar noon and 8 to 16 mm longer 20 minutes either side, depending on the season, less than the 1 cm fuzziness of the tip, so the shortest shadow places solar noon only to within about 20 minutes. Between 1.5 and 2 hours from noon the shadow lengthens by about 4 to 10 mm a minute, so matching equal lengths to 1 cm fixes each time to within about 1 to 3 minutes and the midpoint gives solar noon to within a few minutes. The learner knows it worked when the equal-shadow midpoint falls within a few minutes of the calculator's time of greatest elevation for the day.
What changes
- What you change
- clock time
- What you measure
- shadow length
- What you keep the same
- vertical stick
- level ground
- watch checked against a time signal
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Noon on the clock is when the sun is highest; that happens only on the zone meridian and only on the days the equation of time is zero.
- Time zones follow longitude exactly; Perth's clocks are 2 hours behind Sydney's although the solar difference is 2 h 21 min.
Safety card
Hazards
- sun exposure
Controls
- hats and sunscreen; read the shadow, never look at the sun
Note
No chemicals and no heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; outdoor work follows the school's grounds or excursion risk assessment (RiskAssess where the school uses it).
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics Standard 11–12 Syllabus (2024), Year 11 focus area Time and location; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-11-06
- Australian Curriculum v9No Australian Curriculum v9 code is listed.
Sources
The pages the author read to write this activity.