Sun–Earth — axial tilt, day & night, saṃpāta (equinoxes), ayana (solstices) and the seasons

Mean obliquity (the same expression the engine uses) ε = 23.43929111° − 0.0130042°·T − 1.64e-7°·T² + 5.04e-7°·T³, T = Julian centuries from J2000. The Sun's declination δ is taken from the engine's apparent equatorial position (not from a formula) and is cross-checked against sin δ = sin ε · sin λ☉. Day length from the real δ at latitude φ: H₀ = arccos(−tan φ · tan δ), hours = 2H₀/15 (polar cases → 24 h or 0 h); it is printed beside the engine's own sun_day.day_length_h (true altitude + refraction + real geometry) so the two can be compared. Solar noon = midpoint of the engine's rise/set; the equation of time = solar noon − 12:00 in minutes — the real apparent-vs-clock offset for this place and date. The four cardinal points come from the precomputed catalogue (data/limb/ayana.bin, DE441 span): index 0/2 = Meṣādi / Tulādi saṃpāta (March / September equinox, δ = 0), index 1/3 = Uttarāyaṇa / Dakṣiṇāyana (June / December solstice, δ = ±ε). The sidereal spokes come from sankranti.bin (the Sun's nirayana rāśi ingresses), so they sit about one ayanāṃśa (~24.2°) away from the tropical cardinal spokes — that visible gap is the ayanāṃśa, live. The cardinal instants are the engine's own ayana transitions as stored in the catalogue; because they are produced inside the engine's sidereal/ayanāṃśa reckoning, the tropical λ☉ shown at that instant may differ by a few tenths of a degree (a few hours) from an exact λ☉ = 0°/90°/180°/270° crossing — the catalogue value is authoritative here. The orbit view is a top-down map: the path is the engine's own r(t) and λ☉(t) from the year series, so the Sun really sits at a focus (Kepler's 1st law) — perihelion ≈ 147.1 M km (early January), aphelion ≈ 152.1 M km (early July), e ≈ 0.0167. The Orbit shape box multiplies only the drawn radial deviation (1 = true shape); all numbers stay real. The globe uses real Earth-fixed geography: Natural Earth 110m land outlines (public domain), simplified to 0.3° and embedded in this page — no network needed. Its rotation is the real sidereal angle (GAST) for the instant, the viewer looks along the vernal-equinox direction, and the axis is drawn at the true obliquity. The sub-solar point is the real geographic point below the Sun (λ = GAST − RA☉, φ = δ), and the “you” marker is your true latitude/longitude, coloured by the same test that produces the night shading (u·ṡ > 0 = day side), so the dot can never contradict the shaded hemisphere.