Astronomy / Earth
Seasons and obliquity
Why summer is warm: not because the Earth is closer to the Sun (it is closer in January) but because the axis leans, and a leaning hemisphere gets a higher Sun for longer. The Earth on its orbit with its axis fixed in space, lit from where the Sun is; an observer at any latitude with the day's Sun arc over the horizon; day length, noon altitude and daily insolation from the geometry, and the two hemispheres through the year.
What happens
The Earth is nearest the Sun in January. That is not when the north is warm, so distance is not the reason - the axis is. It leans 23.4° and points the same way in space all year, so in June the northern hemisphere is tipped toward the Sun: the Sun climbs higher at noon, stays up longer, and puts more energy on each square metre of ground. Six months later the same lean tips it away. The tilt changes Munich's daily sunlight five-fold between June and December; the changing distance changes it by seven percent, and the wrong way round for the north. Slide the obliquity to zero and the seasons vanish; slide it to 90° and the poles take turns facing the Sun. Tick the observer's sky to see the day's Sun arc from the ground.
Equations used in the module
Equations δ = asin(sin ε · sin λ) H = acos(−tan φ · tan δ) Q = (S₀/π)(a/r)² (H sin φ sin δ + cos φ cos δ sin H) r/a = (1 − e²)/(1 + e cos ν) day length = 24 H/π, noon altitude = 90° − |φ − δ|
