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84 lines
2.4 KiB
Markdown
84 lines
2.4 KiB
Markdown
# Asr Calculation
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## The Rule
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Asr is the afternoon prayer. Its start time is defined by shadow length, not by
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a solar depression angle.
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The standard definition: Asr begins when an object's shadow equals its height
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**plus** the length of its shadow at solar noon.
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For the Shafi'i, Maliki, and Hanbali schools of law (the majority), the shadow
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multiplier is **1**. For the Hanafi school, the multiplier is **2**.
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In practice, the difference is typically 30–60 minutes, with Hanafi Asr being later.
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## The Math
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Let:
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- φ = observer latitude in radians
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- δ = solar declination in radians at local noon
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- s = shadow factor (1 for Shafi'i, 2 for Hanafi)
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The Sun's altitude when the shadow multiplier condition is met:
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```
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A = arccot(s + tan(|φ - δ|))
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= arctan(1 / (s + tan(|φ - δ|)))
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```
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This altitude corresponds to a specific hour angle H:
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```
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cos(H) = (sin(A) - sin(φ)sin(δ)) / (cos(φ)cos(δ))
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```
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Asr time in local fractional hours:
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```
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asrTime = solarNoon + H / 15 (H in degrees, since 15° = 1 hour)
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```
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If `cos(H) < -1` or `cos(H) > 1`, the Sun never reaches the required altitude,
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and `getAsr` returns `NaN`. This can happen at extreme latitudes when latitude
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and declination are far apart.
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## Implementation
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`getAsr` is a pure math function. It requires:
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1. `solarNoon`: fractional hours (from the SPA output)
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2. `latitude`: decimal degrees
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3. `declination`: solar declination in degrees (from `solarEphemeris`)
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4. `hanafi`: boolean (default `false`)
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```typescript
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import { getAsr } from 'pray-calc';
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const asr = getAsr(
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12.15, // solar noon at ~12:09 local time
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40.7128, // New York latitude
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23.44, // solar declination at summer solstice
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false, // Shafi'i
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);
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```
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## Why Not Use the SPA for Asr?
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Some prayer time libraries solve for Asr by running the SPA with the altitude A
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as the zenith input. This requires an extra SPA call or a second zenith slot in
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the batch call.
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pray-calc computes Asr analytically using the Meeus declination (`solarEphemeris`)
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rather than the SPA's internal declination. This avoids a second SPA call, removes
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any dependency on internal SPA state, and is accurate to well within a minute
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for any realistic use case.
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The SPA uses a more rigorous ephemeris for declination (accurate to ~0.0003°
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vs. Meeus at ~0.01°). For Asr, the difference in δ of 0.01° translates to less
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than 5 seconds of timing error: completely negligible.
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---
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_[Back to Home](Home) | [API Reference](API-Reference) | [Architecture](Architecture)_
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