7.1 KiB
Twilight Physics
Understanding what Fajr and Isha represent astronomically is essential context for evaluating any prayer time calculation.
The Islamic Definition
Neither the Quran nor Hadith specifies a numeric angle. The required criteria are:
- Fajr: The appearance of Subh Sadiq (true dawn): a broad, horizontal whitening of the eastern sky that stretches from north to south. Distinguished from Subh Kadhib (false dawn), which is a vertical column of zodiacal light that appears and then vanishes before true dawn.
- Isha: The disappearance of Shafaq: the twilight glow remaining in the western sky after sunset. Classical scholars disagreed on which glow: shafaq ahmer (red glow, which fades first) or shafaq abyad (white glow, which persists longer). Shia tradition and the IGUT/Tehran method use shafaq ahmer; Sunni tradition generally uses shafaq abyad.
Any calculation must reproduce these observable cues as closely as possible.
Three Stages of Twilight
Astronomers define twilight by the Sun's depression angle below the true horizon:
| Stage | Sun Depression | Sky Condition |
|---|---|---|
| Civil | 0–6° | Horizon clearly visible; enough light for outdoor work |
| Nautical | 6–12° | Horizon visible at sea; brightest stars visible |
| Astronomical | 12–18° | Sky nearly dark; all but faintest objects visible |
| True night | > 18° | Sky fully dark by most definitions |
Fajr roughly corresponds to the end of astronomical night (transition from true night to astronomical twilight). Isha roughly corresponds to the end of nautical or astronomical twilight, depending on the convention.
Why the Angle Varies
Latitude Effect
The Sun's path intersects the horizon at a shallower angle at higher latitudes. Near the equator, the path is nearly vertical: the Sun passes through 18° of depression quickly. At 55°N in summer, the Sun may skim 5–10° below the horizon before rising again. The geometry forces twilight to persist at much smaller depression angles.
Quantitatively, the hour angle H corresponding to a depression of angle a obeys:
cos(H) = (sin(-a) - sin(φ)sin(δ)) / (cos(φ)cos(δ))
When φ (latitude) is large and δ (declination) has the same sign, the denominator shrinks, and the solution for H spreads out: more time is spent near the horizon.
Seasonal Effect (Declination)
Solar declination δ ranges from -23.45° (December solstice) to +23.45° (June solstice). When δ matches the observer's latitude, the Sun rises and sets at its furthest north (or south), and its path is most oblique to the horizon. This is when extended twilight is most extreme.
Earth-Sun Distance
The Earth's orbit is slightly elliptical (eccentricity ≈ 0.017). At perihelion (~January 3), the Earth is about 3.4% closer to the Sun than at aphelion (~July 4). Closer means more solar flux, which means slightly more intense scattering in the upper atmosphere. The effect on twilight depression is small (~0.03°) but nonzero.
Atmospheric Scattering
Twilight glow is produced by sunlight scattering in the stratosphere and upper troposphere (roughly 20–50 km altitude). At deeper depression angles, only the very top of the atmosphere is illuminated, and the scattered light is fainter. The sky brightness follows roughly an exponential decay with depression angle.
The human eye's threshold for detecting sky illumination above the nighttime background is approximately 0.01–0.015 cd/m². Photometric studies measuring sky surface brightness find this threshold is crossed when the Sun is about 14–16° below the horizon at mid-latitudes (Saudi Arabia, Egypt), and closer to 12–13° at higher latitudes (50–55°N) where the scattering geometry is different.
This is the observational basis for the claim that 18° is too conservative for Fajr at most latitudes: the visual threshold for dawn is reached at a lesser depression.
Observational Evidence
Several major observational campaigns have mapped true Fajr/Isha angles:
| Location | Latitude | Fajr Angle (observed) | Source |
|---|---|---|---|
| Indonesia (multiple sites) | ~6°S–7°S | 16.5° | National Observatory Study |
| Saudi Arabia (desert) | ~27.5°N | 14.0° avg | Hail Campaign |
| Egypt (multiple sites) | ~26–30°N | 14.56° avg | 2015–2019 photometric study |
| UK observations | ~51–53°N | 12–14° (seasonal) | Local community data |
The pattern is clear: the angle decreases as latitude increases, and the equatorial 18° is not universal. At mid-latitudes, empirical Fajr is consistently around 14–15°. The Moonsighting Committee's algorithm was calibrated to these observations.
False Dawn (Zodiacal Light)
The zodiacal light is sunlight scattered by interplanetary dust along the ecliptic plane. It appears as a faint, cone-shaped glow pointing upward from the western horizon after evening twilight, or from the eastern horizon before dawn. It is most prominent at equatorial latitudes in spring (evening) and autumn (morning), and requires very dark skies to see.
False dawn (Subh Kadhib) is the zodiacal light seen in the east before true dawn. Observers have reported it disappearing by around 15–16° Sun depression, after which the genuine horizontal twilight takes over. The distinction matters for Fajr timing: Subh Sadiq (true dawn) is later than any zodiacal light brightening.
Atmospheric Refraction Near the Horizon
At the horizon (0° altitude), atmospheric refraction bends sunlight upward by about 34 arcminutes (0.567°). This is why the Sun appears to sit on the horizon when it is geometrically 34' below it. Standard sunrise/sunset calculations account for this by using an effective solar altitude of -0.833° (0.267° for half-disk + 0.567° for refraction).
At twilight angles (Sun 12–20° below horizon), the refraction is much smaller:
approximately 0.1–0.2 arcminutes. This is negligible for prayer timing purposes but
is still computed by getAngles for completeness.
Shafaq: Red vs. White
After sunset, the western sky transitions through several phases:
- Shafaq ahmer (red glow): The brilliant red/orange color disappears when the Sun is about 4–7° below the horizon: well before astronomical Isha. The Tehran/IGUT method places Isha at 14° depression, reflecting this earlier boundary.
- Shafaq abyad (white glow): The diffuse white luminosity persists longer. Most Sunni calculations use this, placing Isha at 15–18° depression.
The practical difference is 20–40 minutes at mid-latitudes. The pray-calc dynamic method uses the shafaq abyad (white glow) convention by default, consistent with the MSC "general" shafaq mode.