Architecture

Module layout

src/
  math/         Numerical utilities
  time/         Time scale conversions
  spk/          JPL kernel reader
  frames/       Earth orientation transforms
  observer/     Observer model and refraction
  bodies/       Moon/Sun state computation
  events/       Rise/set and event finding
  visibility/   Crescent visibility criteria
  api/          User-facing API and kernel management
  cli/          Command-line interface

Each module has zero application-level side effects and no circular dependencies. The layering is strict: lower layers never import from higher ones.

math  <──  time  <──  spk  <──  frames  <──  observer  <──  bodies  <──  events  <──  visibility  <──  api
                                                                                                          └──  cli

Data flow for a sighting report

User calls: getMoonSightingReport(date, observer)
   │
   ├── computeTimeScales(date)
   │     UTC → JD(UTC) → ΔAT → JD(TAI) → JD(TT) → JD(TDB) → JD(UT1)
   │
   ├── getSunMoonEvents(date, observer, kernel)
   │     For 48 time samples across the civil day:
   │       computeAzAlt(Moon, observer, ts)
   │       computeAzAlt(Sun, observer, ts)
   │     Brent root-finding on altitude crossings
   │     → sunsetUTC, moonsetUTC, lag, twilight times
   │
   ├── bestTimeHeuristic(sunsetUTC, moonsetUTC)
   │     T_b = T_sunset + (4/9) × Lag
   │
   ├── At best time T_b:
   │     computeTimeScales(T_b)
   │     getMoonGeocentricState(kernel, ET)    ← DE442S SPK evaluation
   │     getSunGeocentricState(kernel, ET)     ← DE442S SPK evaluation
   │     gcrsToItrs(moonGCRS, ts)              ← IERS Q·R·W chain
   │     geodeticToECEF(observer)              ← WGS84
   │     topocentricPosition(moon, observer)   ← parallax correction
   │     enuToAzAlt(moonENU)                   ← local horizon coords
   │
   ├── computeCrescentGeometry(moonAzAlt, sunAzAlt, moonVec, sunVec)
   │     → { ARCL, ARCV, DAZ, W, lag }
   │
   ├── computeYallop(geometry, W')             ← q parameter, category A–F
   ├── computeOdeh(geometry)                   ← V parameter, zone A–D
   │
   └── buildGuidanceText(...)
         → "Best time to look: ..."

Ephemeris evaluation

The DE442S kernel is the most important external dependency. It is a JPL SPK file containing Chebyshev polynomial fits to the positions of the Sun, Moon, and planets from 1849 to 2150. Reading it requires:

DAF parser: reads the binary Double Precision Array File header, iterates summary records, and builds a segment index keyed by (target, center) NAIF ID pairs.
Segment chaining: DE442S does not store Moon-relative-to-Earth directly. Instead it stores Moon-relative-to-EMB and Earth-relative-to-EMB; the code adds these vectors to get Moon-relative-to-Earth. Similarly for Sun-relative-to-Earth via SSB segments.
Type 2 Chebyshev evaluation: each time interval has a fixed set of Chebyshev coefficients. Given an ET, the code locates the correct record, computes the normalized time argument x ∈ [−1, 1], and evaluates the degree-n polynomial via the Clenshaw recurrence for each of X, Y, Z.

See Ephemeris for the full technical description.

Frame transformation

JPL ephemerides are expressed in the ICRF (International Celestial Reference Frame), essentially the J2000 inertial frame. Topocentric alt/az requires Earth-fixed (ITRS) coordinates. The transformation chain (IERS Conventions 2010) is:

[ITRS] = W(t) · R(t) · Q(t) · [GCRS]

Q(t): IAU 2006 precession + IAU 2000A nutation (celestial motion), parameterized by CIP coordinates X, Y and CIO locator s.
R(t): Earth rotation angle (ERA) from UT1, a simple rotation about the pole.
W(t): polar motion (xp, yp), typically < 0.5 arcsec; defaults to zero.

This is the largest code in the project (large nutation series tables), but far smaller than the ephemeris data.

See Reference Frames for implementation details.

Observer model

Observer position is computed in three stages:

Geodetic → ECEF: WGS84 ellipsoid, exact formula using N(φ) (prime vertical radius of curvature). Output in meters.
ECEF → GCRS: Apply the inverse of the Q·R·W transform (since ECEF = ITRS, and GCRS is the inertial frame at that epoch).
Topocentric parallax: Subtract observer GCRS vector from body GCRS vector to get the topocentric direction.
ENU → az/alt: Project topocentric vector onto local East-North-Up basis, then compute azimuth and altitude.

Atmospheric refraction (Bennett 1982) is applied as a post-processing step on the computed altitude. For the Yallop/Odeh criteria, airless (refraction-free) altitudes are used. For rise/set times and practical "where to look" output, refracted altitudes are used.

See Observer Model for details.

Two operating modes

Full mode (kernel loaded): all features available, DE442S accuracy.

Lite mode (no kernel): getMoonPhase() only. Uses Meeus Ch. 25 (Sun) and Ch. 47 (Moon) low-accuracy positions. Error is < 1° in ecliptic longitude. Not suitable for crescent sighting reports.

The API is designed so getMoonPhase() never throws for missing kernel; it always works.

Performance design

Segment index is built once at kernel load time: O(1) lookup by (target, center, ET).
Chebyshev records are cached per segment (last-used-record cache). Repeated evaluations in the same time interval cost only the polynomial evaluation, not a binary search.
Float64Array for coefficient storage enables V8/SpiderMonkey typed array optimization paths.
Clenshaw recurrence avoids the instability of naive power series and is numerically identical to the SPICE SPKE02 implementation.
The rise/set solver samples at 30-minute intervals before applying Brent, meaning each event finder costs ~48 ephemeris evaluations for bracketing plus ~10 iterations of Brent per root. Total per event: ~60–100 evaluations, each taking tens of microseconds.

Target: a full sighting report (sunset + moonset + best-time geometry + Yallop + Odeh) in 5–15 ms on Node.js.

Error budget

A crescent sighting report's accuracy is limited by the worst source in the chain:

Source	Contribution
DE442S position error	< 1 km (~0.001 arcsec at Moon distance)
IERS Q·R·W transform (with user-supplied EOP)	< 1 mas
IERS Q·R·W transform (polynomial ΔT approximation)	< 5 arcsec
WGS84 observer position	< 1 m (negligible in angle)
Bennett refraction (standard atmosphere)	< 1 arcmin for alt > 5°
Bennett refraction (non-standard conditions)	up to 15 arcmin near horizon

In practice, refraction uncertainty dominates all other error sources for crescent sighting near the horizon.

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