Three kinds of animals. Diurnal animals are active in the day, nocturnal animals at night, and crepuscular animals around dawn and dusk (twilight). The coloured bars show typical behaviour; real animals change with season, weather, food, safety and people.
Why different hours? Eyes (big eyes gather dim light; cones give colour in daylight), hearing and smell (useful in the dark), body temperature (cold-blooded animals such as butterflies need warmth to move; frogs and hedgehogs need damp, cool air), and food (insects, mice or plants are available at different times). Safety also matters: many animals avoid the hours when they would be easy to spot.
Where is the Sun? For a place at latitude φ on day N the Sun's declination is δ = 23.44° · sin(2π(284+N)/365). With hour angle H = 15° × (hour − 12), the height of the Sun above the horizon is sin(el) = sin φ sin δ + cos φ cos δ cos H.
Sunrise and sunset. Setting el = 0 gives cos H₀ = −tan φ · tan δ, so sunrise is at 12 − H₀/15 and sunset at 12 + H₀/15 hours. Day length is 2·H₀/15 hours. At the equator it is always about 12 h; in the UK it swings from about 7½ h (winter) to about 16½ h (summer).
Simplifications (honest list). Times are solar time (noon = Sun highest), not the clock on the wall (no time zone, no summer time, no equation of time, up to ±16 min). The sunrise/sunset in the scene use the centre of the Sun at the horizon, with no air bending the light, and twilight glow is only approximate. The Moon is drawn as a permanent full Moon opposite the Sun. Animal hours are typical patterns, not exact. Winter sleep (hibernation) is shown for the hedgehog, bat, frog and butterfly in the Winter season outside the tropics. The animals are drawn bigger than life so you can see them.
Independent check (recomputed when this page loads):
The last two rows compare the model with published London sunrise tables (using the usual horizon of −0.833° for refraction and the Sun's radius). The other rows compare the closed-form formula with a numerical bisection of the height curve, and with simple geometry.