Science · Middle school

Seasons: tilt and the angle of light

Change the date and the latitude: how does the axial tilt change the angle of sunlight and the length of the day?

In the learning section below the figure, predict, try, complete the tasks and check yourself with short questions.

Fig. 1Seasons: tilt and the angle of light

Slide the date, pick a place or type your own latitude, change the tilt21 June · 73.5°

Date21 June

Place

Your own latitude (north +, south −)

Axial tilt

Your own tilt

Noon Sun height: 73.5°
Daylight: 15 h 0 min
Light per unit area: 93%; relative to light arriving straight down
Distance to the Sun: 152.0; million km

Today is the summer solstice in Ankara.

What if?

Change the axial tilt: at the same place, how do the noon Sun, the length of daylight and polar night change?

Purple: this scenarioDashed: today’s Earth (23.44°)Flat line: the horizon

Noon Sun (over the year): 26.7° – 73.5°
Daylight: 9 h 20 min – 15 h 0 min
Polar night / midnight sun: none
Tropic / polar circle: 23.4° / 66.6°

With today’s tilt the Sun passes overhead somewhere between the two tropics. 40% of the Earth’s surface sees the Sun straight overhead on at least one day a year, and 8% lies inside the polar circles. In Ankara the noon Sun swings between 26.7° – 73.5°, and daylight lasts 9 h 20 min – 15 h 0 min. No polar night: for the Sun to stay down all day here, the tilt would have to pass 50.9°.

In reality: Mars is tilted 25.2°, very close to the Earth: it has seasons too, but a Martian year lasts 687 days, so each season is on average about twice as long.

Assumptions: The orbit, the year and the distance to the Sun stay as they are today; only the axis tilts. Atmosphere, temperature and climate are not modelled, only the geometry of the light. Area shares come from geometry without refraction: the overhead-Sun belt is sin ε, the polar caps 1 − cos ε. The year is scanned at the 365 noons of 2026.

Learn

Progress is kept on this page only; no points are given.

1Predict
2Try
3Explain

If the Earth’s axis were not tilted at all (0°), what would happen to the difference between summer and winter in Ankara?

Gold: sunlight (the patch of light on the ground, daylight on the dial)Purple circle: the chosen latitude; gold dot: the cityEvery number comes from one model: the low-precision formulas astronomers use for the Sun’s position (2026), noon height h = 90° − |φ − δ|, daylight from cos H = (sin(−0.833°) − sin φ sin δ) / (cos φ cos δ), and light per unit area sin h × (1 AU / r)² (atmosphere ignored). Earth is closest to the Sun in January (147 million km) and farthest in July (152 million km); that changes the light by only about 7 percent. In Ankara the light per unit area at summer noon is about twice that at winter noon: what decides it is the tilt, not the distance. The globe’s spin and the passing year are sped up for the display.

What causes the seasons? Axial tilt and the most common misconceptionRead the article