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c02f197ece
Complete rewrite from plain JavaScript to TypeScript with dual CJS/ESM output via tsup. Removes all legacy .js source files and the old CommonJS-only index. Key changes: - Full TypeScript source in src/ with strict mode and declaration maps - tsup build: dist/index.cjs + dist/index.mjs + dual .d.ts / .d.mts types - 14 traditional fixed-angle methods (UOIF through MUIS) + MSC seasonal method - PCD dynamic algorithm: MSC seasonal base + Earth-Sun distance correction + ecliptic geometry + atmospheric refraction + observer elevation - getTimesAll() batches all 14x2 zenith angles into a single SPA call - getMscFajr() / getMscIsha() expose MSC seasonal reference directly - getAngles() returns the PCD-computed fajrAngle and ishaAngle - High-latitude bounds: angles clipped to [10, 20] above 55N - 106 tests across ESM and CJS (test.mjs + test-cjs.cjs) - CI matrix: Node 20/22/24, typecheck, pack-check - Wiki: 12 reference pages + 6-page research section with global accuracy study, home-territory comparison, observational evidence, and field observation matrix - Moon functions removed (migrated to moon-sighting package) - pnpm-only, Node >=20, sideEffects: false
151 lines
5.8 KiB
Markdown
151 lines
5.8 KiB
Markdown
# Dynamic Twilight Angle Algorithm
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The core differentiator of pray-calc is that it does not use a fixed depression angle
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for Fajr and Isha. Instead, it computes the angle that matches the observable
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astronomical phenomenon for the specific location and date.
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## Why Fixed Angles Fail
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A depression angle is the number of degrees the Sun sits below the horizon. Traditional
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methods hard-code a value: ISNA uses 15°, MWL uses 18°, MUIS uses 20°.
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This works reasonably well near the equator. At 0° latitude, the Sun's path is nearly
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vertical at the horizon, so it passes through any given depression quickly. Twilight is
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short, and the sky becomes astronomically dark (18°) close to when it visually darkens
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for a human observer.
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At higher latitudes, the Sun's path is oblique. It skims below the horizon rather than
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diving through it. Two consequences follow:
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1. **Twilight is extended.** The sky stays illuminated at a given depression longer
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than at the equator.
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2. **The Sun may never reach the required angle.** Above 48.5°N in summer, the Sun
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never reaches 18° depression. Above 51.5°N, it never reaches 15°. A fixed-angle
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method produces no Isha in London for weeks in summer.
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Even at mid-latitudes, observational campaigns show that true Fajr (the visible
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"white thread" of dawn) appears when the Sun is around 14–16° below the horizon, not
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18°. Using 18° makes Fajr 20–30 minutes too early in many regions.
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## Three-Layer Model
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The `getAngles` function computes a depression angle in three layers.
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### Layer 1: MSC Seasonal Base
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The Moonsighting Committee Worldwide (Khalid Shaukat) derived a piecewise-linear
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empirical model by fitting to field observations across a wide range of latitudes.
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The model returns the expected time offset in minutes:
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- Fajr: minutes before astronomical sunrise
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- Isha: minutes after astronomical sunset
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The model uses four seasonal anchor points per latitude (winter solstice, spring
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equinox, summer shoulder, summer solstice) and interpolates between them. The
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offsets grow with latitude and peak near the summer solstice, reflecting the
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astronomical reality of extended twilight.
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pray-calc converts those minute offsets to depression angles using spherical
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trigonometry:
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```
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cos(H) = (sin(a) - sin(φ)sin(δ)) / (cos(φ)cos(δ))
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depression = -a (where a is the altitude solution)
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```
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Where `H` is the hour angle derived from the minute offset, `φ` is latitude,
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`δ` is solar declination.
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### Layer 2: Physics Corrections
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Three corrections are added to the MSC base angle:
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**Earth-Sun distance correction (Δr)**
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The Earth's orbit is elliptical. At perihelion (January 3), r ≈ 0.983 AU; at
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aphelion (July 4), r ≈ 1.017 AU. When the Earth is closer to the Sun, sunlight
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is more intense, and the scattering that produces twilight glow begins at a slightly
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deeper depression. Conversely, at aphelion, the sky stays darker a bit longer.
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```
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Δr = -0.5 × ln(r) (degrees)
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```
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This correction is ±0.015° over the year — small, but included for completeness.
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**Fourier harmonic correction (Δf)**
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A double-harmonic model captures the annual and semi-annual variation in observed
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twilight angle that is not fully explained by MSC's piecewise model. It uses the
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ecliptic longitude (θ, degrees) and absolute latitude (|φ|):
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```
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Δf = 0.1 × (|φ|/45) × sin(θ × π/180)
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+ 0.05 × (|φ|/45) × sin(2θ × π/180)
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```
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This adds up to ±0.15° at 45°N and proportionally less near the equator.
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**Atmospheric refraction**
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Near the horizon, refraction bends light rays by about 34 arcminutes. At twilight
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angles (Sun 14–18° below horizon), refraction is small — a few arcminutes — but
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is still computed via the Bennett/Saemundsson formula for completeness. The current
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atmospheric conditions (pressure, temperature) are used.
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**Elevation dip**
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An observer at elevation `h` meters above sea level sees a horizon that is `d`
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degrees below the geometric horizon:
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```
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d ≈ 1.06 × sqrt(h / 1000) (degrees)
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```
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At 1000 m, this is 1.06° — the effective depression for a given visual phenomenon
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is reduced by this amount. The correction is:
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```
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Δe = -0.3 × 1.06 × sqrt(h / 1000)
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```
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The factor 0.3 reflects that twilight depression is only partially affected by
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horizon dip (the illumination geometry is dominated by the upper atmosphere, not
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the local horizon).
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### Layer 3: Physical Bounds
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The final angle is clipped to [10°, 22°]. Below 10° the sun is high enough that
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no prayer timing convention places a twilight boundary there; above 22° is outside
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the range of any empirical observation of dawn or dusk.
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## Validation
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The dynamic method should stay within the range defined by the full set of
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traditional methods for any given location and date. At equatorial latitudes
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it converges to approximately 18°, matching MWL and Karachi. At 50–55°N in
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summer it typically produces 12–14°, matching the empirical UK observations
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that prompted adjustments from 18° to lower values. At 30–40°N it falls in
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the 15–17° range, consistent with the Egyptian and Saudi observational studies.
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The `calcTimesAll` function returns comparison times for all 14 traditional
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methods alongside the dynamic method, enabling direct comparison.
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## High-Latitude Fallback
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When the MSC minutes function would produce an angle outside [10°, 22°] or
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when the Sun never reaches the computed angle, the bounds clamp the result.
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For extreme latitudes (beyond approximately 57°N/S) in summer, the MSC model
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itself uses a "seventh-of-night" rule as a juristic fallback, which is respected
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here.
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## Code Location
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The implementation is in [src/getAngles.ts](../src/getAngles.ts). The MSC
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piecewise model is in [src/getMSC.ts](../src/getMSC.ts). The solar ephemeris
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(declination, r, ecliptic longitude) is in
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[src/getSolarEphemeris.ts](../src/getSolarEphemeris.ts).
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---
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*[Back to Home](Home) | [Traditional Methods](Traditional-Methods) | [Twilight Physics](Twilight-Physics)*
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