Planetary rise/transit/set in three separate definitions — geometric, apparent, and heliacal/visibility — with elongation, magnitude and Engine A/B. Mathematical rise/set ≠ actual visibility.
Rise/Set (apparent, geometric+refraction+dip) and Visibility are different quantities — never merged. Visibility uses elongation + magnitude (Schaefer model = advanced view, planned).
2 · Inner planets & Agastya laboratory
Inner planets: morning star = west of Sun (rises before Sun) · evening star = east of Sun (sets after Sun). Jupiter = outer (opposition). Agastya = Canopus (fixed star); its udaya/asta has special traditional significance.
3 · Three definitions
Geometric rise / transit / set
Geometric: purely the horizon crossing (altitude = 0°). Apparent: with refraction (34′·P/T) + observer dip (1.76′·√h). Heliacal: first/last actual visibility from the elongation-orb / Schaefer model.
4 · Observer & atmosphere
Refraction uses P/T; horizon dip uses elevation. Cloud/topography not modelled (see disclaimer).
5 · Disclaimer & provenance
Mathematical rise/set ≠ actual visibility — detailsMathematical rise/set ≠ actual visibility. Real visibility depends on atmospheric extinction, cloud, horizon obstructions, light pollution and observer conditions; local topography cannot be fully predicted.
Heliacal (first/last appearance) additionally depends on magnitude, elongation, extinction and eye/optics — Engine A (DE path) here; Engine B + deep-time = later phase.
6 · Heliacal events calendar (year)
First & last appearances heliacal
Udaya (first appearance) / Astamaya (last appearance) from the elongation-orb (aṣṭāṃśa). Astronomical visibility ≠ combustion.
Verdict from elongation + magnitude (naked-eye limit ≈ 6). Twilight loss near the Sun; full Schaefer model (extinction, sky contrast, optics) = advanced view.