3.6 KiB
High-Latitude Handling
The Problem
At latitudes above approximately 48.5°N/S, the Sun never reaches 18° below the horizon during summer months. Above 51.5°N/S, it never reaches 15° below the horizon. During these periods, a fixed-angle method produces no Isha: or computes a sunrise before Fajr, or other nonsensical results.
Even at latitudes where the Sun does reach 18°, the resulting times can be extreme. At 52°N in summer, a 15° Isha occurs around 2–3 AM, making a 4 AM Fajr effectively continuous with Isha. Islamic jurisprudence recognizes this as hardship (haraj) and provides accommodations.
The MSC Approach
The Moonsighting Committee Worldwide algorithm handles this by design. Because it works in minutes rather than angles, it naturally produces reasonable times even when fixed angles would fail:
- The minute offsets grow with latitude but are bounded by the seasonal interpolation
- At very high latitudes, the model applies a "Sab'u lail" (seventh-of-night) rule: divide the night into 7 parts; Isha starts at the end of the first seventh, Fajr ends at the start of the last seventh
This produces the longest practical Isha-Fajr interval allowed by the model, which corresponds roughly to the juristic principle of not making the night shorter than 1/7 of the 24-hour period.
When This Applies
The MSC model is used as the base for the dynamic method. The model transitions to the seventh-of-night rule at approximately latitude 57°N/S (varies slightly by season and longitude). pray-calc inherits this behavior automatically.
For the MSC entry in getTimesAll, the same model is used directly.
Fixed-Angle Methods at High Latitudes
The 13 other methods in getTimesAll use fixed depression angles. For dates and
locations where the Sun never reaches the specified angle, the NREL SPA returns
NaN for that rise/set event. pray-calc propagates NaN unchanged; calcTimesAll
renders it as "N/A".
This is intentional. The Methods map in getTimesAll shows you exactly which methods
are applicable for a given location and date. If ISNA returns N/A for Isha in
London in June, that is the correct answer for that method: it simply doesn't work
there.
Juristic Solutions
Islamic scholars have proposed several approaches for high-latitude regions:
Nearest Latitude (Aqrab al-Bilad)
Use the prayer times of the nearest city where the Sun does reach the required angle, scaled to local midnight.
Nearest Day (Aqrab al-Ayyam)
Use the prayer times from the nearest date in the year when the Sun does reach the required angle at the same location.
Seventh of Night (Sab'u lail)
Divide the 24-hour period (from midnight to midnight, or from Maghrib to Fajr) into 7 equal parts. Isha begins at the end of the first seventh; Fajr begins at the start of the last seventh.
Specific Latitude Cutoff
Many North American institutions use the rule: above 48.5°N, compute times as if the latitude were 48.5°N. This is simple and avoids discontinuities.
Makkah Time
A minority position: use Makkah's times globally. Not widely adopted outside of specific communities.
What pray-calc Does
The dynamic method (getTimes, calcTimes) uses the MSC model as its base.
The MSC model handles high latitudes with the seventh-of-night fallback. This
means getTimes always returns a finite time for all latitudes.
The Methods map in getTimesAll returns NaN for any fixed-angle method that
fails for a given location/date. This allows the caller to detect which methods
are inapplicable and apply their own high-latitude policy.