Solar Position & NREL SPA

Every prayer time is defined by a specific position of the Sun relative to the observer. Getting that position wrong by even a fraction of a degree shifts prayer times by minutes.

Why solar position matters

Islamic prayer times are tied directly to solar events:

• Fajr — Sun is at a specific depression angle below the horizon before sunrise
• Sunrise (Shuruq) — upper limb of the Sun crosses the geometric horizon
• Dhuhr — Sun transits the meridian (true solar noon)
• Asr — shadow length equals one or two times the object height
• Maghrib — upper limb of the Sun sets below the horizon
• Isha — Sun reaches a specific depression angle after sunset

Each of these requires knowing the Sun's altitude (angle above or below the horizon) and, for Qibla direction, its azimuth (compass bearing). The precision of these calculations directly determines the accuracy of prayer times.

The NREL SPA algorithm

The National Renewable Energy Laboratory's Solar Position Algorithm (Reda & Andreas, 2008, NREL/TP-560-34302) is the gold standard for solar position computation. It derives the Sun's position using:

1. Julian Ephemeris Day — a continuous timescale from January 1, 4713 BC
2. Heliocentric longitude and latitude — Earth's position relative to the Sun in the ecliptic plane, computed as a Fourier series with 2,500+ terms
3. Geocentric coordinates — converting from heliocentric to Earth-centered frame
4. Nutation and aberration — corrections for Earth's wobble and the finite speed of light
5. Apparent right ascension and declination — equatorial coordinates corrected for true obliquity and aberration
6. Local hour angle — the Sun's position relative to the observer's meridian
7. Topocentric correction — parallax shift because the observer is on Earth's surface, not its center (~8.79 arcseconds at zenith)
8. Atmospheric refraction — bending of light through the atmosphere (Bennett's formula or pressure/temperature model)

The result is the Sun's topocentric altitude and topocentric azimuth — the angle above the horizon and compass direction as seen from the observer's exact location.

Inputs and outputs

The algorithm takes six inputs:

ΔT is the difference between Terrestrial Time (TT) and Universal Time (UT1). It accounts for irregular variations in Earth's rotation rate. For current dates, ΔT ≈ 69 seconds. For historical or future dates, use published ΔT tables from IERS.

The algorithm produces:

Accuracy

NREL SPA achieves ±0.0003° (about 1 arcsecond) over the years −2000 to +6000. For prayer time purposes, this corresponds to timing errors of less than one second — far below the precision needed for any practical application.

Older algorithms such as Jean Meeus's simplified series (from Astronomical Algorithms, 1991) achieve ±0.01°, which translates to roughly 30-second timing errors. For most latitudes and seasons this is acceptable, but at high latitudes near solstices the errors compound.

Using nrel-spa

import { computeSolarPosition } from 'nrel-spa'

const pos = computeSolarPosition({
  date: new Date('2025-06-21T12:00:00Z'),
  latitude: 41.4993,
  longitude: -81.6944,
  elevation: 200,
  pressure: 1013.25,
  temperature: 20,
  deltaT: 69.18,
})

// Sun's position as seen from Cleveland, OH at solar noon on the summer solstice
console.log(pos.topocentricAltitude)  // ~71.9° (high summer sun)
console.log(pos.topocentricAzimuth)   // ~180.0° (due south at noon)
console.log(pos.declination)          // ~23.44° (maximum, summer solstice)

import { computeSolarPosition } from 'nrel-spa'

function findSunrise(date: Date, lat: number, lng: number): Date {
  // Binary search between midnight and noon for altitude = -0.8333°
  // (-0.8333° accounts for the Sun's semi-diameter and standard refraction)
  let lo = new Date(date)
  lo.setUTCHours(0, 0, 0, 0)
  let hi = new Date(date)
  hi.setUTCHours(12, 0, 0, 0)

  for (let i = 0; i < 50; i++) {
    const mid = new Date((lo.getTime() + hi.getTime()) / 2)
    const pos = computeSolarPosition({ date: mid, latitude: lat, longitude: lng })
    if (pos.topocentricAltitude < -0.8333) {
      lo = mid
    } else {
      hi = mid
    }
  }
  return new Date((lo.getTime() + hi.getTime()) / 2)
}

The pray-calc package uses this binary search approach for all six prayer times, with the target altitude varying by prayer and calculation method.