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Home/Astronomy & The Sky/Seasons & Axial Tilt

Seasons & Axial Tilt

Understanding the seasons requires connecting Earth's orbital motion to its tilted axis. This simulator visualizes the relationship between axial tilt (obliquity), the subsolar point's declination throughout the year, and the resulting noon sun angle at any given latitude. The core astronomical principle is that Earth's rotational axis is tilted approximately 23.4° relative to the plane of its orbit (the ecliptic). As Earth revolves around the Sun, this fixed tilt causes the latitude where the Sun is directly overhead at noon—the subsolar point—to shift between the Tropics of Cancer and Capricorn. The model calculates solar declination (δ) using a simplified sinusoidal approximation: δ ≈ 23.4° * sin(360° * (day_of_year - 80) / 365.25). From this, the solar altitude (h) at local solar noon for a specific latitude (φ) is found using the equation: h = 90° - |φ - δ|. This directly shows how the sun's maximum daily height changes with season and location, explaining the intensity of solar radiation. Key simplifications include treating Earth's orbit as circular (ignoring eccentricity's minor effect), using a mean solar day, and not accounting for atmospheric refraction or the finite size of the solar disk. By adjusting the latitude slider and watching the declination and altitude plots update, students learn that seasons are primarily caused by the variation in solar altitude (and thus beam spreading and day length), not by Earth's changing distance from the Sun.

Who it's for: High school and introductory undergraduate astronomy or Earth science students learning the geometric cause of seasons. It is also valuable for educators demonstrating the relationship between axial tilt, latitude, and solar insolation.

Key terms

  • Axial Tilt (Obliquity)
  • Solar Declination
  • Solar Altitude
  • Subsolar Point
  • Seasons
  • Tropic of Cancer
  • Tropic of Capricorn
  • Analemma

Earth & date

172
48°

δ(t) is a smooth model of declination; noon altitude uses the meridian formula cos z = sin φ sin δ + cos φ cos δ (hour angle 0).

Measured values

Declination δ23.44°
Noon altitude65.44°

How it works

Axial tilt keeps the ecliptic obliquity ~23.4°: the subsolar latitude moves between ±δ over the year, changing flux and day length — not Earth–Sun distance.

Frequently asked questions

If the Earth is closest to the Sun in January (perihelion), why isn't it summer in the Northern Hemisphere then?
The variation in Earth-Sun distance due to orbital eccentricity is minor compared to the effect of axial tilt. Seasons are driven primarily by the solar altitude, which controls the concentration of solar energy on a surface. In January, the Northern Hemisphere is tilted away from the Sun, resulting in low solar altitude and short days, despite being slightly closer. The axial tilt effect overwhelms the small variation in distance.
Does the simulator show why days are longer in summer?
Indirectly, yes. The solar altitude plot shows the sun's position at noon, its highest point. The simulator's declination model is key: when the Sun's declination matches your hemisphere's latitude (e.g., +23.4° in June for the Northern Hemisphere), the Sun is higher and its daily arc across the sky is longer, leading to more daylight hours. The exact sunrise/sunset times require a more complex calculation involving the observer's latitude and the Sun's declination.
Why is the solar declination curve not a perfect sine wave?
The model here uses a perfect sine wave for simplicity, which is a very good approximation. In reality, the curve has slight asymmetries due to Earth's elliptical orbit (Kepler's Second Law), meaning Earth moves faster at perihelion. This causes the seasons to have slightly unequal lengths. The more accurate representation of the Sun's position throughout the year, incorporating this and other factors, is a figure-8 pattern called the analemma.
Can I use this model to find the Sun's noon altitude for my exact location on a specific date?
Yes, with two important notes. First, ensure you use your latitude correctly (positive for north, negative for south). Second, the model uses a standard calendar and declination formula; for a precise calculation on a specific date, you would need the exact astronomical declination. However, for educational purposes and understanding seasonal trends, this simulator provides an excellent and accurate estimation.