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.