Core idea

This is a lunisolar calendar, like the Hebrew and Chinese calendars: its months follow the Moon (one month from conjunction to conjunction), but a leap month is periodically inserted so each month stays fixed to its season. This differs from the Hijri calendar, which is purely lunar — its months drift through the seasons.

1 — The astronomical anchor

The calendar is calibrated to a certain astronomical event: the eclipse of 27 January 632 CE (“Muhammad’s eclipse”), which occurred at the death of Ibrahim, the Prophet’s son (pbuh). A solar eclipse can only occur at conjunction, so it is a precisely defined conjunction point per NASA’s computations. The calculation places it in late Shawwal, 10 AH, matching the historical sources.

2 — The time unit

The mean synodic month (conjunction to conjunction):

Each conjunction instant is actually computed with Meeus’ algorithm (Chapter 49), accurate to under one minute even back to the 7th century CE.

3 — Locking the months to the seasons

The year begins at the conjunction nearest the moment the Sun reaches the same ecliptic longitude it had at 1 Muharram 1 AH. The Sun’s position is computed with Meeus’ algorithm (Chapter 25), keeping the new year tied to a fixed season.

4 — Intercalation via the Metonic cycle

It rests on the astronomical fact:

• 19 × 12 = 228 ordinary months, but the reality is 235 — an excess of 7 months.
• These seven months (“Nasi’”) are inserted, distributed across every 19 years.
• The logic uses no fixed table; it counts actual conjunctions: if a year spans 13 conjunctions it is a leap year.
• The resulting seasonal drift is under two days every 19 years.

5 — The two crescent-impossibility thresholds

Only impossibility is judged (never possibility) at sunset at the visitor’s location:

• Time threshold: crescent age < 15 hours after conjunction.
• Danjon limit: elongation (Sun–Moon angle) < 7°.

The Sun and Moon positions and the sunset instant are computed astronomically for the visitor’s coordinates. Passing both thresholds does not imply visibility — that depends on the horizon, atmosphere, and eyesight.

References

• NASA / Fred Espenak — eclipse catalogue and lunar phases.
• U.S. Naval Observatory — lunar phase timings.
• Jean Meeus — “Astronomical Algorithms” (conjunction & Sun algorithms).
• Yallop & Odeh criteria and the ICOP project — crescent-visibility models.

On the nature and purpose of this tool

We offer this tool as an aid to enthusiasts, students, and researchers in astronomy, calendars, and history — a means of exploration and of comparing calendars and understanding the relationship between astronomical and historical events.

It is not a substitute for any adopted calendar, carries no religious authority for acts of worship such as fasting, Hajj, or festivals, and holds no official academic standing to be cited like peer-reviewed sources. Worship timings are determined by the competent religious authorities and recognised crescent sighting; scholarly research refers to its primary sources.

What this tool provides is an independent, verifiable astronomical computation — to be consulted, not invoked as proof, and corrected whenever an error is shown.