TKS Ephemeris · heliacal phenomena

Udaya-asta — heliacal rise & setting of planets

Beta · under development

First and last visibility of the planets. Primary: the shāstrīya Sūrya-siddhānta Ch.9 lagnāntara-asu method (K = lagnantara-asu ÷ 60, visible ⟺ K > C) on TKS apparent (DE441) longitudes. Also shown: Ptolemaic arcus visionis and a Schaefer photometric model. Engine A (reference DE path).

0 · At a glance

status
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Aṣṭāṃśa limits (Sūrya-siddhānta ch. 9)

Moon12°
Mercury12° / 14°
Venus8° / 10°
Mars17°
Jupiter11°
Saturn15°
Sun–planet apparent ecliptic-of-date elongation < limit → asta (invisible); otherwise udaya (visible). For Mercury and Venus the limit switches between the retrograde and direct values (12/14°, 8/10°).

Models

Shāstrīya — lagnāntara-asu

Sūrya-siddhānta Ch.9
K = lagnantara-asu ÷ 60 ; visible ⇔ K > C
Classical rising-time (asu) method on apparent longitudes with dṛkkarma. C = kalāṃśa (Venus 8°/10°, Mercury 12°/14°, Jupiter 11°, Saturn 15°, Mars 17°, Moon 12°).

Arcus visionis (Ptolemaic)

geometric
visible ⇔ |elongation| > arcus(body)
Mercury 10° · Venus 5° · Mars 11.5° · Jupiter 10° · Saturn 13°.

Schaefer photometric

physical
visible ⇔ m_planet(extincted) < m_limit(μ_sky)
Planet magnitude from distance + phase; Kasten–Young airmass extinction; twilight surface brightness μ from solar depression and Sun–planet angle; limiting magnitude from Crumey (2014).

Compute

Validation

methods

Shāstrīya (primary). Sūrya-siddhānta Ch.9 — K = lagnantara-asu ÷ 60, visible ⟺ K > C. TKS apparent (DE441) longitudes + classical rising-time (asu) method; independent of the elongation-orb approximation.

Arcus visionis (Ptolemaic). visible ⟺ elongation > arcus(body): Mercury 10°, Venus 5°, Mars 11.5°, Jupiter 10°, Saturn 13°.

Schaefer photometric. planet magnitude (Astronomical Almanac) + Kasten & Young (1989) air-mass + twilight [Schaefer (1990) decay · Krisciunas & Schaefer (1991) scattering] + Crumey (2014) limiting magnitude; visible when mobserved < mlimit.

संस्करणः bin-1790611335