Seasons: Why Tilt Matters
Season (N/S)
/
Day length
Noon altitude
deg
Declination
deg
Distance
AU
Distance varies a little (not the cause)
Test how tilt changes sunlight angle and day length across the year.
Common myth: seasons are caused by Earth being closer to the Sun.
In fact, Earth is closest in January (Northern Hemisphere winter)!
- Observable: Day length and sun angle change systematically with the calendar.
- Model: Axial tilt ($\varepsilon$) causes the Sun's declination ($\delta$) to cycle annually.
- Inference: Tilt, not distance, drives seasons. Opposite hemispheres have opposite seasons at the same time.
- Declination uses a simplified geometry (toy model): $$\delta = \sin^{-1}(\sin\varepsilon\,\sin L)$$ where $\varepsilon$ is axial tilt and $L$ is treated as uniform in time (about $1^\circ$ accuracy vs ephemeris).
- Earth–Sun distance uses a first-order eccentric model (not a Kepler solver): $$r \approx 1 - e\cos\theta$$ Perihelion is anchored near day 3 (Jan 3) with an uncertainty of about ±2 days.
- Key idea: opposite hemispheres have opposite seasons; distance variations are small and not the main cause.