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Solar Radiation &
Earth's Seasons

Explore how axial tilt and the angle of incidence of sunlight drive seasonal changes in energy, temperature, and daylight across the planet.

AP Environmental Science

What Is Solar Radiation?

Solar radiation is the electromagnetic energy emitted by the Sun. It reaches Earth as a spectrum of wavelengths: ultraviolet, visible light, and infrared. The total power arriving at the top of the atmosphere is described by the solar constant:

Not all of this energy reaches the surface: about 30% is reflected back to space (Earth's albedo), and the rest is absorbed by the atmosphere and surface, driving weather, climate, and seasons.

Earth's Axial Tilt: \(23.5^\circ\)

Sun Earth Orbital plane normal N S
\(23.5^\circ\)
NH SH

Why Tilt Matters

Angle of Incidence
When the Sun is high in the sky, rays strike more directly, concentrating energy over a smaller area: more heating.
Day Length
A tilted hemisphere toward the Sun receives more hours of daylight, increasing total daily energy input.
Seasonal Cycle
As Earth orbits, each hemisphere alternately tilts toward and away from the Sun, producing summer and winter.

The Angle of Incidence Rule

Ground Surface Summer Small area
\(90^\circ\)
Winter Large area
\(30^\circ\)

Key Positions in Earth's Orbit

June Solstice December Solstice March Equinox Sept Equinox
Solstices
Maximum tilt toward/away from Sun. Longest & shortest days of the year.
Equinoxes
Neither hemisphere tilted toward Sun. Day and night are approximately equal everywhere.

Solstices vs Equinoxes

Solstice Equinox
Dates (approx.) June 21 & Dec 21 March 20 & Sept 22
Tilt Orientation Max toward or away Neither toward/away
Daylight Distribution Most unequal Approximately equal
Sun's Zenith Position Tropic of Cancer/Capricorn Equator
NH Season Starts Summer (June) / Winter (Dec) Spring (March) / Fall (Sept)

Insolation and Latitude

Insolation (incoming solar radiation) varies with latitude because of the angle at which sunlight strikes Earth's curved surface. Higher latitudes receive less concentrated energy year-round.

Insolation (W/m²) Latitude 90°S 60°S 0° 60°N 90°N 0 200 400 600 Annual Average June Solstice

The Intensity Formula

The solar energy intensity on a tilted surface depends on the sine of the solar elevation angle. This gives us a quantitative way to compare seasonal heating:

1
Overhead Sun (\(\theta = 90°\)): \(I = 1361 \cdot \sin(90°) = 1361 \; \text{W/m}^2\) : full intensity.
2
Mid-latitude winter (\(\theta = 30°\)): \(I = 1361 \cdot \sin(30°) = 680.5 \; \text{W/m}^2\) : half intensity.
3
Near horizon (\(\theta = 10°\)): \(I = 1361 \cdot \sin(10°) \approx 236 \; \text{W/m}^2\) : very weak.

How to Determine the Season

1
Identify the hemisphere of the location (Northern or Southern).
2
Check the date relative to the four key positions: solstices (June 21, Dec 21) and equinoxes (March 20, Sept 22).
3
Determine tilt direction: is the hemisphere tilted toward or away from the Sun?
4
Infer the season: tilted toward = summer, tilted away = winter. Equinox dates mark spring and fall transitions.
5
Remember the opposite: the other hemisphere always has the opposite season.

Example 1: Solar Intensity

Problem: On a summer day, the Sun reaches an elevation angle of \(72°\) at a city in the Northern Hemisphere. What is the solar intensity on the surface?

1
Write the formula: \(I = S \cdot \sin(\theta)\)
2
Substitute values: \(I = 1361 \cdot \sin(72°)\)
3
Calculate: \(\sin(72°) \approx 0.951\), so \(I \approx 1361 \times 0.951 = 1294 \; \text{W/m}^2\)

Example 2: Comparing Seasons

Problem: At latitude \(45°\)N, the maximum solar elevation is about \(68.5°\) in summer and \(21.5°\) in winter. Compare the peak surface intensity for each season.

Summer
\(I = 1361 \cdot \sin(68.5°)\)
\(= 1361 \times 0.930\)
\(\approx 1266 \; \text{W/m}^2\)
Winter
\(I = 1361 \cdot \sin(21.5°)\)
\(= 1361 \times 0.366\)
\(\approx 499 \; \text{W/m}^2\)

Example 3: Seasonal Identification

Problem: It is July 15. Sydney, Australia (\(34°\)S) has short daylight hours and a low solar elevation. Buenos Aires, Argentina (\(34°\)S) also has short days. Meanwhile, London (\(51°\)N) has long, warm days. Explain.

1
July 15 is after the June solstice: the Northern Hemisphere is tilted toward the Sun.
2
Northern Hemisphere = summer: London experiences long days, high solar elevation, and warm temperatures.
3
Southern Hemisphere = winter: Sydney and Buenos Aires are tilted away from the Sun, resulting in short days and low solar angles.

Day Length and Energy Budget

Hours of Daylight Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 6 9 12 15 18 12h 45°N 0°

Common Mistakes

✕ Distance Causes Seasons
Earth's orbit is nearly circular. The ~3% distance variation has minimal effect. Axial tilt, not distance, drives seasons.
✕ Same Season Everywhere
Hemispheres always have opposite seasons. July is summer in the NH but winter in the SH.
✕ Equator Has No Seasons
Equatorial regions do have seasonal variation (wet/dry), but temperature variation is minimal due to consistent solar angle.

Summary of Key Concepts

Concept Definition Key Detail
Solar Constant Energy flux at top of atmosphere \(\approx 1361 \; \text{W/m}^2\)
Axial Tilt Earth's axis angle from orbital normal \(23.5°\)
Insolation Formula Surface intensity \(I = S \cdot \sin(\theta)\)
Solstice Max/min tilt toward Sun June 21 & Dec 21
Equinox Equal day/night globally March 20 & Sept 22
Albedo Fraction of light reflected Earth average: ~0.30

Question 1 of 5

What is the primary cause of Earth's seasons?

Question 2 of 5

Using the formula \(I = S \cdot \sin(\theta)\), what is the approximate surface intensity when the Sun is at an elevation angle of \(45°\)?

Question 3 of 5

It is December 21. Which of the following correctly describes conditions in both hemispheres?

Question 4 of 5

Earth reaches perihelion (closest distance to the Sun) in early January. Why does this not cause summer in the Northern Hemisphere?

Question 5 of 5

A location at the equator receives approximately 12 hours of daylight year-round. Which factor best explains why the equator experiences relatively constant temperatures throughout the year?