mirror of
https://github.com/acamarata/pray-calc.git
synced 2026-07-01 03:14:28 +00:00
141 lines
7.1 KiB
Markdown
141 lines
7.1 KiB
Markdown
# 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:
|
||
|
||
1. **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.
|
||
2. **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.
|
||
|
||
---
|
||
|
||
_[Back to Home](Home) | [Dynamic Algorithm](Dynamic-Algorithm) | [High-Latitude Handling](High-Latitude)_
|