Fiqh & astronomy

The polar problem — where local sighting reaches its limit

Above the Arctic Circle the sun does not set for weeks in summer. Without a sunset there is no evening sky — and without an evening sky no hilāl sighting. Anyone who ties the start of the month strictly to their own local sighting faces an unsolvable problem there: the new month would never begin.

The same problem as with prayer times

The legal logic is identical to the polar problem of prayer times (the “Jokkmokk problem” this app solves via taqdīr): the obligation (taklīf) remains, but the physical sign (sabab) — here the visible crescent, there the twilight angle — disappears. The classical answer is taqdīr: estimation takes the place of the sign.

Regarding the “day like a year”, the companions asked: will the prayers of a single day suffice? He ﷺ answered: “No — estimate its measure for it.” (uqdurū lahu qadrahu)

Ṣaḥīḥ Muslim (the Dajjāl narration) — the textual basis of taqdīr. Fiqh councils rely on it both for polar prayer times and for the polar start of the month.

Why the Arctic Circle refutes strict localism

Classically the schools of law debate the reach of a sighting (ikhtilāf al-maṭāliʿ): does it apply only locally (the Shāfiʿī view) or does one sighting bind all Muslims (the majority and Ḥanafī view)? The polar case sharpens this debate into an existential question: a rule that is in principle unfulfillable for entire regions cannot be a universal rule — mā lā yuṭāqu lā yukallafu bihi: the impossible is not imposed.

The asymmetry is striking: during midnight sun, sighting is impossible because the sky never gets dark. During polar night the sky is permanently dark — yet the “evening” and “sunset” on which the sighting ritually depends are missing. So the answer is not “look harder”, but taqdīr.

Four recognised solutions

What this means for this app

The world map of hilāl visibility makes the problem visible: the dark-red polar cap is the zone where local sighting is impossible in principle — and the transition band shows where the nearest visibility begins (aqrab al-bilād). The Hijri correction (±2 days) in the calendar lets every community follow its own authority; the app does not dogmatically pre-decide any position.

From the workshop: validation against UKHO/HMNAO — and a subtlety we found

The visibility map in this app implements the Yallop criterion (HMNAO Technical Note 69) and is continually validated against the official UKHO/HMNAO publications. In June 2026 this turned up a genuine subtlety: our engine initially computed the moon–sun altitude difference (ARCV) topocentrically — that is, including the moon’s parallax of ~0.9° — and with refraction. Yallop’s q formula, however, is calibrated to geocentric, unrefracted quantities. The result: q was systematically ~0.2 too low, and the visibility zones slightly too small.

The proof came from two anchors on the HMNAO map for May 2026 (the moon’s age at the point of first visibility: telescope 11.45 h, naked eye 14.77 h): in the old convention our computation was off by a good three hours; in the TN 69 convention it hits the telescope anchor exactly. Borderline cities such as Dhaka (17 May 2026, UKHO: “visible in perfect conditions”) now land precisely in the right code. The lesson — very much in the spirit of tamkīn (→ article 5): a correction is not right or wrong in itself; what matters is which convention a criterion was calibrated to. Parallax belongs in the sunset computation — but not in Yallop’s q.

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

More from the knowledge section

Thuluth al-layl — the third-of-the-night method and its justification · Where do 18° and 17° come from? — Twelve centuries of the angle debate · 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