Tantrakulam · TKS Ephemeris

TKS Ephemeris — Independent Astronomical Computation & Pañcāṅga Engine

JPL DE kernels as reference state data · independent time-scale · SPK evaluation · apparent-place reduction · ecliptic · sidereal · dynamics

What this page shows

TKS converts a planetary state into an apparent astronomical position and then into traditional sidereal / Pañcāṅga quantities: state → apparent place → ecliptic longitude → ayanāṃśa → nirayana longitude → rāśi / nakṣatra / tithi.
Numerical precision ≠ physical accuracy ≠ observational uncertainty — all three are distinct.

Status · Provenance

Layer status

State source: JPL DE440 / DE441 reference
State evaluation: Independent Rust DAF/SPK + Chebyshev type-2
Astronomical reduction: IAU 2006 precession · IAU 2000B nutation
Sidereal models: Lahiri (ICRC 1956) · Chitra (true Spica)
Dynamical engine: TKS-B N-body · EIH 1PN · J2–J6 · C22/S22
Validation: jplephem · Skyfield · xalen-time

Provenance

JPL: reference planetary states
TKS: independent numerical evaluation and astronomical reduction
IAU: reference astronomical conventions (precession/nutation/frames)
TKS-B: independent numerical dynamics (N-body)

Architecture — pipeline

JPL DE440 / DE441reference state source

↓

TKS SPK / DAF evaluatorChebyshev type-2 · independent Rust

↓

Geometric → Apparentlight-time · aberration · deflection · precession · nutation

↓

Ecliptic of datetropical λ, β

↓

SiderealLahiri / Chitra → nirayana

↓

PAÑCĀṄGAtithi · nakṣatra · yoga · karaṇa · rāśi · saṅkrānti

DE440 / DE441reference

│

Engine Areference path

│ initial state ↓

TKS Engine BN-body + 1PN + J2/J3/J4

↓

Common Ephemeris APItrait Ephemeris

Engine A and Engine B expose the same State API; the layers above are unchanged.

Live result

Date Time Place Lat Lon Body

Engine B · TKS Dynamics

Configuration

Mode: independent numerical propagation
Integrator: DOPRI5 (adaptive)
Bodies: 11 (Sun · 8 planets · Moon · Pluto)
Gravity: Newtonian N-body
Relativity: EIH 1PN toggle
Gravity field: Earth J2–J6 · C22/S22 · Sun J2 toggle
Initial conditions: DE440-derived
Asteroids: offline / optional (16 perturbers)
Validation reference: DE440

1000-year benchmark Δpos vs DE440 (planets + Moon)

Sun	322 km	Venus	316 km
Mercury	324 km	Mars	469 km
Earth	414 km	Jupiter	382 km
Moon	2205 km	Saturn	336 km
Uranus	1223 km	Neptune	5805 km
Pluto	7299 km

Δpos = trajectory divergence from DE440 — not absolute observational error. Run live (choose Δt):

Δt (years) 1PN gravity field

Udaya-asta · heliacal & eclipses

Aṣṭāṃśa limits · Sūrya-siddhānta ch. 9 layer 4

Moon	12°	Venus	8° / 10°
Mercury	12° / 14°	Jupiter	11°
Mars	17°	Saturn	15°

Sun–planet apparent ecliptic-of-date elongation < limit → asta (set/invisible); otherwise udaya (rise/visible). Retrograde/direct branch gives Venus 8/10°, Mercury 12/14°.

Body Days From

Comparison with SS siddhāntic positions. The SS engine (graha::visibility) uses the same orb method but from Sūrya-siddhānta sphuṭa longitudes. Venus differs by up to ~3.7° → transition dates by up to ~2 weeks; Jupiter/Saturn by ~5 days. SS = classical tradition; TKS = modern apparent reality. Traditional elongation-orb — not physical heliacal (arcus visionis).

Next solar / lunar eclipse layer 3 · 4

Place-dependent solar eclipse (topocentric) and geocentric lunar eclipse. Method: syzygy search in the TKS apparent pipeline → vector geometry; lunar shadow angle = π_Moon ± s_Sun (atmosphere +2%).

Search window (days)Code (admin)

Validation · 2026. Lunar: 3 March Total (umag 1.15, P1 08:44 → P4 14:26 UTC) · 28 August Partial (umag 0.93). Solar: 12 August Total (Reykjavik) · 17 February Annular (Antarctica ~70°S, 140°E) — both match known (NASA/Espenak) values. Full-series catalogue now precomputed over the whole DE441 range (−13000…+17189; 71,440 solar + 72,728 lunar) — see the Eclipse page.

Observational phenomena & validation

Conjunction · opposition · station · retrograde · greatest elongation layer 3

Daily scan of TKS apparent longitudes + bisection/extremum search. Station = zero of daily motion; opposition = elongation 180° (outer planets); greatest elongation = inner planets.

Body Days

Visibility · arcus visionis + Schaefer. arcus visionis (Ptolemaic solar-elongation limit): Mercury 10° · Venus 5° · Mars 11.5° · Jupiter 10° · Saturn 13°. Schaefer photometric: planet magnitude (distance + phase + extinction) vs limiting magnitude from sky surface brightness (Crumey 2014); topocentric altitude + solar depression. Schaefer twilight approximation (constants from literature); full validation needs observational data.

Independent validation own checks

Check	Result
TKS SPK vs jplephem (DE421 · DE440 · DE441)	position ≤ 1.1 m · velocity ≈ 10⁻¹⁰ km/s
Apparent astronomy vs Skyfield	ICRF RA/Dec ≈ 0.046″ · ecliptic λ/β ≈ 0.047″
Time scale vs xalen	tests 8/8 · Δ = 0 s

SPK figures are numerical reproduction relative to a reference evaluator — not “JPL accuracy”. Numerical precision ≠ physical accuracy ≠ observational uncertainty.

Error budget & deep-time

Sources

SPK evaluation	validated
Time conversion	validated
Light-time	iterative
Aberration	included (relativistic)
Solar deflection	included
Precession	IAU 2006
Nutation	IAU 2000B
ΔT	model-dependent
UT1	observational
Ayanāṃśa	model-dependent
Lunar dynamics (Engine B)	engine-dependent

Numerical precision ≠ physical accuracy ≠ observational uncertainty. Our SPK evaluator matches the reference evaluator numerically (≤1 m), but that does not prove the positions are physically identical everywhere — over long spans model/observational uncertainty dominates.

Deep-time ephemeris proven

Reference range DE441 ≈ ±15,000 years. Long-term propagation of Engine B (full 11-body, tight tolerance) — diagnostics: Δλ · Δβ · Δr · Δv · energy/angular-momentum drift (with Moon). Large Δt is slow (faster in release); 1 kyr–1 Myr = offline batch (experimental).
Disclaimer: deep-time results are dynamical reconstructions, not equivalent to modern observational ephemeris accuracy.

Δt (years)

Śāstra / textual reconstruction planned — input: epoch · planet · textual longitude · reference system · ayanāṃśa · calendar interpretation; output: source vs TKS Δλ (kala/vikala). This will distinguish TKS from the general Pañcāṅga site.

Long-term uncertainty · σλ(t)

Engine-B initial-condition Monte-Carlo — σλ(t), arcsec 10 members · σp = 1 km · σv = 1e-6 km/s · offline

Δt (yr)	Earth/EMB	Mercury	Venus	Mars	Jupiter	Saturn	Uranus	Neptune	Pluto
10	1.4	9.7	1.7	0.78	0.30	0.10	0.03	0.01	0.01
100	13.7	49.8	17.7	9.4	2.1	1.1	0.57	0.54	0.28
1000	137	420	176	88	23	14	7.5	3.9	5.4
10000	1321	7027	1778	840	274	125	70	39	20

Sensitivity to the initial state only (model error excluded); σλ grows ≈ linearly in time and scales linearly with the assumed σ. Reproduce: cargo run --release -p tks-ephemeris --example uncertainty (env TKS_MEMBERS, TKS_SKIP_MC).

Engine-B vs DE441 model divergence — |Δλ|, arcsec offline · planets + EMB

Δt (yr)	Earth/EMB	Mercury	Venus	Mars	Jupiter	Saturn	Uranus	Neptune	Pluto
100	16	101	0.5	0.02	0.01	0.00	0.01	0.04	0.02
1000	166	8557	53	0.4	0.09	0.04	0.15	0.58	0.51
10000	1777	5105	5446	6.4	0.09	0.60	1.3	1.8	0.63

True model error of the simplified N-body (point masses + 1PN EIH + J2–J6 + C22/S22; no asteroids) against JPL DE441. Threshold 5′ = 300″: the outer planets (Mars through Pluto) stay within at 10 kyr; Mercury, Venus, Earth exceed 5′ by ≈1–2 kyr (values wrap past ~1°). DE440 and DE441 agree to <0.01″ within their overlap, so their difference is not a usable uncertainty proxy.

Provenance & reproducibility

TKS Ephemeris · v0.1 · Engine A (reference) + Engine B (dynamics)
Kernel: dynamic (active kernel below) · Frame: ICRF · Origin: barycentric/geocentric · Reduction: IAU 2006 / IAU 2000B · Ayanāṃśa: Lahiri (ICRC 1956) · Sidereal: true-Spica (Chitra).