Fiqh & astronomy · from the dissertation

Where do 18° and 17° come from? — Twelve centuries of the angle debate

Every prayer calendar rests on two numbers: the twilight angles for Fajr and ʿIshāʾ. But where do they come from? Acaroğlu’s dissertation reconstructs the answer from more than 1350 manuscripts: the angles are no arbitrary stipulation but the result of twelve centuries of directed observation — from ages without any light pollution.

Three traditions from early Islam

As early as the 9th century three camps stood side by side: al-Khwārizmī — the eponym of the “algorithm” — used 18° for both phenomena; al-Farghānī held an isolated 17°/17°; and the Banū Mūsā, the three brothers at Baghdad’s House of Wisdom, introduced 17° for the disappearance of evening redness and 19° for Fajr. Their tradition was followed by al-Būzjānī, Ibn Yūnus and — as attested by later astronomers — al-Bīrūnī.

How precisely that early age calculated is shown by the recalculation of Ibn Yūnus’ Cairo twilight tables (10th century): the largest error is two arcminutes — eight seconds of time.

I have observed the sun’s depression at the break of true dawn over consecutive years and found that it increases and decreases with the clearness and turbidity of the atmosphere. Yet it never exceeds 20 degrees, nor does it fall below 18 degrees. I found 19 degrees to be correct — the opinion of the experts of this discipline.

Ibn al-Shāṭir (Damascus, d. 777/1375), al-Nafʿ al-ʿāmm — the empirical basis of the 19°/17° standard.

Observation beats school

The breakthrough came through observatories: Naṣīr al-Dīn al-Ṭūsī first held 18°/18° — and after founding the Marāgha observatory (1259) switched to 19°/17° on the basis of new observations; al-ʿUrḍī and al-Shīrāzī followed. Al-Marrākushī’s counter-tradition (20°/16°) remained a brief Cairene episode: its founder himself conceded ±1° of uncertainty — rendering his values compatible with 19°/17° — and later timekeepers discarded it “for the scarcity of its adherents”.

From the 15th century, 19°/17° was the established standard: Sibṭ al-Māridīnī attests the consensus of all timekeepers of his time, his teachers’ time and his teachers’ teachers’ time. Throughout the entire 17th century, not a single astronomer can be identified who used other values.

The statistics — and the latitude question

The histogram of all collected opinions shows an overwhelming majority for 19°/17° — the mean of all statements is, to one decimal place, exactly 19.0° and 17.0°. And the angles are latitude-independent: sightings by Islamic astronomers from 10°S to 45°N and modern measurements up to 65°N show no correlation with geographic latitude whatsoever. Even Evliya Çelebî’s report of persistent evening redness near the Don–Volga region (≈49°N) yields a lower limit of ≳16.5°.

And the modern 18° convention?

Modern astronomy’s “astronomical twilight” ends at 18° — but, as the Astronomical Almanac (USNO/HMNAO) explicitly states, that is a convention, not a measurement. Its trace leads to Johann Heinrich Lambert (Photometria, 1777), who cited “18 to 19 degrees” of “the oldest astronomers” and calculated with the mean of 18.5°; the decimal got lost over time. His source: the Liber de crepusculis of the Andalusian Ibn Muʿādh (11th century, long attributed to Alhazen) — who himself preferred 19°. The modern 18° convention is thus itself rooted in Islamic astronomy.

Lambert’s own Augsburg measurement series (1759), re-regressed, yields 19.4° ± 0.6. Modern observations confirm the window: Jones (US Navy, 1850s) a mean of 19.3°; Gruner and Dorno after 15 years of observation 19°; Schmid (1372 observations, 1903–1927) saw the red second segment at 17–16°; and the Turkish captain Yazıcı, after decades at sea, found 19°/17° — interpreting 18° as the median between the break of dawn and the emergence of redness, exactly as Ibn al-Shāṭir had interpreted the old 18°/18° tradition.

Geometry confirms — and vindicates an Ottoman

Ibn Muʿādh’s geometric model — the uppermost scattering layer of the atmosphere as a mirror — computed with the modern mesopause yields a window of roughly 18.7° to 20.3°, consistent with all observations. The twist: the mesopause alternates bimodally between ~86 km (summer) and ~101 km (winter). This is precisely what Taqī al-Dīn al-Rāṣid, founder of the Istanbul observatory, had conjectured in the 16th century — diverging measurements arise from the varying height of the atmosphere.

What this means for this app

The angles are lower limits, not sharp thresholds: evening redness disappears at the latest at 17° — calculating with it keeps ʿIshāʾ always on the safe side. For Fajr, owing to its dual normativity, the tradition separates two times: imsāk (start of the fast, earliest possible: 19°) and ṣubḥ (start of the prayer, dawn certainly broken: 18°) — an Ottoman practice the dissertation adopts. This app’s 18°/17° (MWL method, as in the IZA calendar) thus correspond to ṣubḥ and evening redness; for bright summer nights, thuluth al-layl takes over (see its own article).

This text is a factual introduction, not a fatwa. Your local scholars and community remain authoritative.

More from the knowledge section

The polar problem — where local sighting reaches its limit · Thuluth al-layl — the third-of-the-night method and its justification · Are the prayers even obligatory then? — The schools’ dispute · Why tamkīn? — A thousand years of precision corrections · Which calendar gets it right? Germany’s prayer-time calendars compared