Research programme — the Indian sidereal reference frame
Beta · under development
Reconstruction of the Indian sidereal astronomical reference frame — Nakṣatra stellar coordinates, Chitrāpakṣa and historical Pañcāṅga — computed with the TKS engine. Phase I (Ayanāṃśa) is computed live below.
TKS RESEARCHPHASE I · AYANĀṂŚA · LIVESERVER-SIDE · ONE REQUESTMODEL-DERIVED · ROOT-FOUNDPHASES II–V · PLANNED
Programme title
“Reconstruction of the Indian Sidereal Reference Frame: From Nakṣatra Stellar Coordinates and Chitrāpakṣa to Historical Pañcāṅga.” Ayanāṃśa is one chapter of this programme, not the whole of it.
Scientific framing
Epoch-dependent stellar reference not a constant-rate model
A_TKS(t) = λ_app,Spicā(t) − 180°, where Spicā's position is propagated with the epoch.
Therefore A_TKS ≠ A₀ + constant_rate × Δt; rather
A_TKS = f(stellar astrometry · proper motion · precession · nutation · ecliptic transformation · epoch/time-scale) Consequently dA/dt is epoch-dependent and d²A/dt² ≠ 0.
Key numerical evidence
TKS − Lahiri divergence non-monotonic
2026 CE
+57.26″
both near, but not identical models
3001 BCE
−0.54″
near-coincidence (a re-crossing)
5001 BCE
+308.29″ = 5′08.29″
divergence re-opens
10001 BCE
+3708.22″ = 1°01′48″
large model divergence
Δ is not monotonic — a constant differential rate cannot reproduce it. Alongside, the Spicā proper-motion contribution grows to +537.34″ (20001 BCE) (table below).
Roadmap · phase-wise
Phase I · Astronomical foundation live
TKS Ayanāṃśa (true Chitrāpakṣa)
Divergence vs Lahiri (root-found thresholds)
Zero-point & 30° timeline
Rate of change dA/dt, d²A/dt²
Spicā proper-motion contribution
Reference-star sensitivity planned
Precession · obliquity · fixed stars
Phase II · Pañcāṅga mathematics planned
Tithi dynamics (duration min/max, kṣaya/adhika)
Nakṣatra stellar framework
Yoga · Karaṇa
Saṅkrānti instants
Sunrise/Sunset · lunar months
Tithi–Nakṣatra–Saṅkrānti correlation
Phase III · Phenomena planned
Eclipse catalogue (−13000 … +17000)
Heliacal rising/setting · combustion
Graha-yuddha (astronomical definition)
Retrograde reconstruction
Planetary conjunction · 13–14-day eclipse pairs
Phase IV · Historical astronomy planned
Vedāṅga Jyotiṣa epoch reconstruction
Ancient Nakṣatra positions
Uttarāyaṇa / Makara-saṅkrānti timeline
Historical Pañcāṅga reconstruction
Ancient eclipse verification
Phase V · Validation & reproducibility planned
DE440 / DE441 comparison
Skyfield / Swiss comparison
Historical observations
Error budget per quantity
Long-term stability
Method — optimized & double-checked this engine
One server request, all quantities computed concurrently
Full epoch-dependent model (no constant-rate shortcut)
TKS zero-point epoch = the root of A_TKS(t)=0 (here ≈285 CE), and each 30° crossing thereafter. These are model roots, not a proven historical Chitrā epoch. The intervals are unequal (e.g. 2156 yr then … 2581 yr) — direct demonstration that this is not a constant-rate extrapolation.
2 · Divergence thresholds (TKS vs Lahiri) full model
Δ
Forward
Backward
Model B: full epoch-dependent TKS computation + full Lahiri model, root-found (not a constant differential rate).
Instantaneous dA/dt (which includes nutation and the other terms of the Spicā/apparent-ecliptic model — hence “effective ayanāṃśa rate”, not idealized precession alone) and its variation. A constant 50.8″/yr approximation is inadequate over multi-millennial timescales.
5 · Spicā proper-motion contribution PM vs fixed
Epoch
ΔA_PM
ΔA_PM(t) = A(epoch-propagated Spicā incl. proper motion) − A(Spicā frozen at catalogue position). TKS Chitrā ayanāṃśa uses the epoch-propagated astrometric position of Spicā, rather than treating the catalogue position as an eternally fixed direction.
Approximate error / sensitivity budget indicative
Catalogue position (Hipparcos ICRS)
~0.001″
Precession model (IAU 2006)
~0.1″
Nutation model (IAU 2000B)
sub-″
Ecliptic transformation
sub-″
Time-scale (TT/UT)
~0.1″
Numerical precision
negligible
Proper motion (grows with |t|)
dominant long-term
Indicative order-of-magnitude components — these are not independent, statistically-combined uncertainties and no covariance propagation has been done. The Spicā proper-motion term (table left) dominates over long spans.
Divergence curve · TKS vs Lahiri
ΔA(t) = TKS − Lahiri arcsec · −12000…+12000
Model-derived Δ(t) (arcsec). The curve is not a straight line — its slope changes with epoch, so a constant differential rate cannot reproduce it.
Phase I-b · Reference-star sensitivity
Implied ayanāṃśa if a different star anchors the sidereal zero Δ vs Spicā
Reference
2026
1 CE
3001 BCE
8001 BCE
Δ = A_star − A_Spicā (arcsec), each star anchored at the start of its nakṣatra (equal division). Large offsets (esp. Regulus/Aldebaran ≈ 6°) show the Chitrāpakṣa does not place other yogatārās at their equal-division starts — the sidereal zero-point is genuinely reference-dependent. Anchors are illustrative; Hipparcos ICRS + PM.
Phase II · Nakṣatra stellar framework first result
Principal star vs equal 13°20′ division J2000 ICRS · no PM · TKS ayanāṃśa
Nakṣatra
yogatārā
HIP
start°
star nir.°
SS dhruva°
vikṣepa°
offset
mag
“Nakṣatra = 27 equal 13°20′ divisions” vs “Nakṣatra = stellar reference”: the principal (brightest) star of each nakṣatra is generally not at the division start. Offsets are in arcmin. Stellar positions are J2000 ICRS without proper motion (indication only).
Phase II · Pañcāṅga dynamics
Tithi long-term dynamics 1 year · root-found
Tithi = (λ☾−λ☉)/12°; every duration root-found over one year. Mean ≈ synodic-month/30. “short” / “long” counts indicate kṣaya / vṛddhi potential (exact kṣaya/vṛddhi needs sunrise anchoring — planned).
Boundary sensitivity % of time within ε of a boundary
Empirical fraction of sampled time (1 yr, Moon/Sun) within ε arcsec of a division boundary — how often a tiny longitude shift flips rāśi / nakṣatra / pada / tithi / yoga.
Phase IV · Uttarāyaṇa vs Makara-saṅkrānti
Tropical winter solstice vs TKS sidereal Makara-saṅkrānti timeline
Two distinct questions, kept in separate columns: Sun nakṣatra = from the Sun's nirayana longitude (e.g. 2026 solstice → Mūla-2); Moon nakṣatra = the Pañcāṅga nakṣatra (from the Moon). Winter solstice = tropical λ☉=270°; Makara-saṅkrānti = TKS nirayana λ☉=270° (tropical 270°+A_TKS). The two coincide (Δ→0) around the Common Era; ancient Makara-saṅkrānti fell before the solstice (negative Δ). Dates use the proleptic calendar (Julian before 1582). Snapshot is geocentric (no sunrise/vāra).
Historical Pañcāṅga · any epoch · any place
Place-based TKS reconstruction sunrise · vāra · five limbs · māsa · ṛtu · ayana
Reconstructed at local sunrise (fallback 06:00 if polar). Saṅkrānti = next crossing of the Sun's nirayana λ through a 30° boundary. BCE = negative astronomical year (3139 BCE → −3138). Numerical precision ≠ physical accuracy; far epochs carry model/ΔT uncertainty. β still experimental (Engine A / DE441 within coverage).
Full eclipse catalogue · Kurukshetra · 13000 BCE → now
Precomputed catalogue & solar↔lunar pairs 15,026 yr · JPL DE441 · Engine A
Built from a dedicated scan at Kurukshetra (29.97°N, 76.88°E — Mahābhārata region), stored as data/eclipse_catalogue_kurukshetra.json. Note: the solar↔lunar pairs below are among locally-visible eclipses (consecutive opposite-type eclipses near a node within ~15 days). ≤13-calendar-day pairs are the rare ones (11 in 15,026 years at Kurukshetra); pairs with an exact gap ≤ 14.0 days number 200. Every event row also carries a visibility flag (Sun/Moon above the horizon at greatest eclipse) and its local altitude — 30,127 of 48,949 events are visible, and the pairs are built from those only. Sort by date / gap / calendar-day difference.
All Phase-I numbers are computed by this engine on one request (server-side, single source of truth) and are reproducible. Far-epoch values (|year| ≳ 2,200) are extrapolations of the Lahiri polynomial — flagged in each response. This page is a research index; Phase II–V items are planned.