TKS Ephemeris · Laboratory · sidereal frame
Ayanāṃśa comparison — one engine, several definitions
An ayanāṃśa is the offset between the tropical (sāyana) and sidereal (nirayana) zodiac. Every school fixes it
differently, and the choice moves every sidereal longitude, nakṣatra and rāśi. This page quantifies the differences
with our own engine only — the same ICRS → true-ecliptic-of-date chain (IAU-2006-style precession + nutation) and the
Hipparcos position of Spicā (α Vir, Chitrā) with its real proper motion. Nothing here is imported from an almanac:
tropical longitudes come from our chain, and each ayanāṃśa definition is applied to them.
The four things compared
- TKS true Chitrāpakṣa — the ayanāṃśa that keeps Spicā’s own (proper-motion-propagated) ecliptic longitude of date
at exactly 180°. This is the observational definition of Chitrāpakṣa, so the star cannot drift out of Chitrā.
- Lahiri — our analytic model of the official Chitrapaksha, anchored to the Calendar Reform Committee value
23°15′ on 21 March 1956 (reproduces 23.250018°).
- Spicā frozen — Spicā at its catalogue position with no proper motion. The TKS − frozen difference is exactly
the proper-motion contribution to the ayanāṃśa (the star is moving ~40 mas/yr in longitude).
- Named schools by their anchors — KP (Krishnamurti) 291.5 CE, Raman 398 CE, Fagan–Bradley 221 CE,
Yukteshwar 499 CE, Lahiri (convention) 285 CE: each row is A(t) = our precession integral from that
anchor + offset. Type any published constant into the offset (arc-seconds) to reproduce that school’s printed table exactly.
1 · Zero-point years and modern values
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2 · The decisive test — Spicā’s nirayana longitude under each system
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Under true Chitrāpakṣa this is 180° by construction (that is what the definition says). Any fixed-offset system makes
Spicā creep away from 180° with time — the numbers below are exactly that creep, in arc-seconds. A system that keeps a
fixed ayanāṃśa-rate can never hold a star fixed for millennia.
3 · Curves and differences (arc-seconds)
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Method, accuracy and limits
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