echoesof.science · Ages 15–16
Seasons: Sun angle, day length and energy per square metre
Name: Date:
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the game and the quiz
echoesof.science/school/day-night-seasons/ages-15-16/
Read
Earth rotates once every 23.9 hours and orbits the Sun once every 365.25 days. Its rotation axis is tilted by about 23.4° to the perpendicular of its orbit. In June the Northern Hemisphere is tilted towards the Sun and in December the Southern Hemisphere is.
Distance is not the cause. Earth's distance from the Sun varies by only about 3%: about 147 million km in January (perihelion) and 152 million km in July (aphelion). The Northern Hemisphere is in winter when Earth is closest, and the two hemispheres have opposite seasons at the same distance.
The Sun's height at noon depends on latitude φ and the Sun's declination δ, which changes through the year from about +23.4° (June solstice) through 0° (equinoxes) to about −23.4° (December solstice). In the Northern Hemisphere the noon elevation is α = 90° − φ + δ. Example: on the equator (φ = 0°) on 21 June the noon Sun is about 67° high.
Experiment: Measure the Sun's height with a shadow stick
- On flat, level ground, stand the stick exactly vertical (check with the level or plumb line). Measure its height h above the ground.
- From about 20 minutes before local solar noon until 20 minutes after, mark the tip of the shadow with chalk every 5 minutes.
- Find the shortest shadow: this is local solar noon. Measure its length L.
- Calculate the Sun's elevation: tan α = h / L, so α = arctan(h / L).
- Look up your latitude φ and today's solar declination δ (for example from an almanac or a solar-position tool) and calculate α = 90° − φ + δ.
- Compare the measured and calculated angles. Then calculate sin α: what fraction of the full overhead sunlight is reaching each square metre of ground?
| Time | Shadow length L (cm) | α = arctan(h/L) (°) | sin α |
|---|---|---|---|
| −20 min | |||
| −10 min | |||
| Noon (shortest) | |||
| +10 min | |||
| +20 min |
Questions
Calculate the noon Sun elevation at latitude 51° N on the June solstice, the December solstice and an equinox.
Using S_horizontal = S_incident · sin α, how many times more solar power falls on each square metre at noon at 51° N in June than in December?
Explain, with numbers, why the changing distance between Earth and the Sun cannot explain the seasons.
Your shadow stick: h = ____ cm, L = ____ cm, measured α = ____°, calculated α = ____°. Give two sources of uncertainty.
Sources for every fact on this sheet: echoesof.science/school/day-night-seasons/sources/