Explaining Day Length and Shadows in a Botswana School Yard
Learners at a school in Gaborone (about 24°S) place a vertical 1 m stick in the ground on a sunny day and mark the tip of its shadow every hour from 08:00 to 16:00. They find that the shadow is longest at 08:00 and 16:00, shortest around midday, and that at midday the shadow points almost due south. They repeat the activity in June and December and find the midday shadow is much longer in June than in December. A learner claims the Sun moves around the Earth, which is why the shadow changes. Another asks why the midday shadow points south rather than north.
1. Explain why the shadow length changes during the day and why it is shortest at midday.
Read the worked answer
The shadow changes because the Earth rotates on its axis once about every 24 hours, so the Sun appears to move across the sky from east to west. The shadow is cast in the opposite direction to the Sun.
- Early morning and late afternoon: the Sun is low in the sky, so its rays strike the ground at a small angle. A low Sun casts a long shadow.
- Midday: the Sun is highest in the sky, so its rays are closer to vertical. A high Sun casts a short shadow.
The stick's height is fixed (1 m), so the shadow length depends only on the Sun's altitude (angle above the horizon). The shortest shadow occurs when the Sun is highest, around local midday. The learner's claim that the Sun moves around the Earth is not correct: the apparent motion is caused by Earth's rotation, which is why the pattern repeats daily.
2. Explain why the midday shadow points almost due south in Gaborone, and why it is longer in June than in December.
Read the worked answer
Gaborone is at about 24°S, south of the equator. At midday the Sun is roughly north of the observer (between the equator and the Tropic of Capricorn for much of the year), so the shadow falls to the south. The exact direction depends on the season: when the Sun is directly overhead or slightly north, the shadow points south.
Seasonal difference: Earth's axis is tilted (about 23.5°). In June, the Southern Hemisphere is tilted away from the Sun, so the Sun is lower in the sky at midday in Gaborone - a lower Sun casts a longer shadow. In December, the Southern Hemisphere is tilted towards the Sun, so the midday Sun is higher - a shorter shadow. This also explains why June is winter in Botswana and December is summer. The change is due to Earth's tilt and its orbit around the Sun, not to the Sun moving closer.
3. A learner says: 'The shadow is shortest at exactly 12:00 on the school clock.' Evaluate this statement.
Read the worked answer
The statement is not reliable. The shortest shadow occurs when the Sun is highest in the sky at the observer's location - local solar noon - which is not necessarily 12:00 on the school clock.
Reasons:
- Clock time is set for a standard meridian, not for Gaborone's longitude, so local solar noon can differ from 12:00 by many minutes.
- The Equation of Time (caused by Earth's elliptical orbit and axial tilt) shifts solar noon by up to about ±15 minutes through the year.
- Measurement error: marks made hourly may miss the true minimum, which could occur between readings.
A better test is to mark the shadow every 10–15 minutes around midday and find the shortest shadow directly, or to note when the shadow changes direction (from pointing one way to the other). The claim should be checked with data, not assumed from the clock.