TKS · deep-time discoveries
Computational extremes, distributions and secular trends found by scanning the JPL DE441 reference states and the precomputed TKS catalogues. Every card states its method and its independent reference — none of these is a bare number.
Secular trend of the osculating semimajor axis, recovered from DE441 reference states.
LLR observed ≈ +3.8 cm/yr
Full analysis & A/B/C →Closest Earth–Moon approach in the whole DE441 span.
modern record ≈ 356,400 km
Farthest Earth–Moon separation in the whole DE441 span.
modern record ≈ 406,700 km
Minimum new-moon → new-moon interval in 373,385 lunations.
data/limb/moonphase.binmean 29.530584 d · USNO ≈ 29.530589 d
Maximum new-moon → new-moon interval — the spread is the finding, not the mean.
range 29.2576 – 29.8500 d
Interval between successive solar transits (hour angle = 0), from the DE441 apparent Sun. An interior extreme, not a coverage-boundary artifact.
longest 24h00m33s · 9608 BCE-06-17
TKS finds a 7m43.6s total solar eclipse in 10868 BCE — 14.3 seconds longer than NASA's 7m29.28s greatest-duration point for the famous 2186 eclipse.
solar_eclipse_local_place · geocentric C2→C3 for the same event is 4.0 min (a different quantity) · grid scan confirms 7.727 minNASA stated theoretical maximum: 7m32.1s (present-epoch assumption) · domain DE441 −13,201…+17,191 · NASA-5MC cross-checked
Explore Eclipse Extremes →Longest total lunar eclipse, and the largest magnitudes in the interval.
largest solar mag 1.0422 (9939 BCE-12-08) · largest lunar umbral mag 1.8913 (6128 BCE-03-19)
Minimum sunrise→sunset (dinamāna) with the −0.833° limit — near the obliquity maximum (~8700 BCE).
longest 13h37m13s · 8272 BCE-06-19
Every equal-tropical-longitude conjunction of the 7 classical bodies.
data/limb/conjunctions.binrarest Jupiter–Saturn 1,942 · most frequent Moon–Saturn 402,549
Explore via API →The catalogue is not past-only — it answers forward queries too. Last met 2020-12-21.
period ≈ 19.86 yr
Every tithi × nakṣatra pair occurs many times and the spread is small — so none of the 810 is genuinely “rare”. This is a frequency distribution, not a rarity claim.
least frequent Krishna Amavasya + Mula 12,905 d · most Shukla Shashthi + Chitra 87,370 d · mean 13,704 d
Of tithi × vāra × nakṣatra × yoga, this combination occurred exactly once in the whole span: Shukla Dvitiya + Thursday + Punarvasu + Harshana.
85.9% of the 153,090 quadruples never occur at all
The longest and shortest single tithi among 11,201,578 transitions — the lunar–solar rate at its most extreme. A normal tithi is ≈ 24 h.
data/limb/tithi.bin · integer-minute transitionsshortest 20h 01m (0.8340 d) · 12995 BCE-11-08 · range 20h 01m → 26h 51m
A pure-gravity integration shows no secular expansion — the control that makes the +3.997 a real tidal signal, not an integration artifact.
vs tidal +3.80 cm/yr
Method & A/B/C →Source of state. All planetary/lunar positions come from the JPL DE440 / DE441 reference states, read by the independent TKS SPK/DAF evaluator. TKS does not re-fit these states.
Event catalogues. Transitions were precomputed once over the full DE441 span (tithi, nakṣatra, yoga, karaṇa, moon phases, conjunctions) and served by O(log n) lookups.
Framing. Each finding is a computational result with a stated method and an independent reference where one exists. Extremes inside DE441 coverage are reference-based; nothing here is extrapolated beyond the kernel.
Reproduce. cargo run --release -p tks-ephemeris --example great_extremes · --example recession_detail · --example tidal_evolution · --example engine_b_moon_gravity
Honest limits. The lunar recession trend is inherited from DE441; the tidal module is a constant-Q secular model; short-window distance trends are oscillation-dominated and not used. Numerical precision ≠ physical accuracy ≠ observational uncertainty.
See also: Lunar Recession · Stellar Encounters · Lunar Observatory · Ayanāṃśa · Dhruva (pole star) · Research.