A question we can examine

Begin with a passage, without rewriting it.

Qur’an 10:5 connects the sun, moon, phases and reckoning years. Read the full wording, translation and notes at QuranEnc, Rowwad translation, 10:5. This is a passage reference and project paraphrase, not a new translation or a claim that the verse specifies our formula.

State a narrow claim.

Do twelve average lunar phase cycles have the same duration as a seasonal year? If they are shorter, dates in a twelve-month lunar calendar should move through the seasons over successive years.

Choose the quantities and the sources.

NASA’s Moon Fact Sheet lists a mean synodic period of 29.53 days. The U.S. Naval Observatory gives approximately 365.2422 days for a tropical year. A phase cycle is the synodic month; it differs from the Moon’s roughly 27.3-day orbit relative to the stars.

NASA Moon Fact Sheet · USNO: tropical year · NASA: phases

Run the comparison.

The editable values let you test sensitivity. Changing a value does not change the published source. The calculation compares mean durations, rather than predicting any particular month’s crescent visibility.

Compare the prediction with observations.

Record successive lunar phases and the dates of seasonal markers, or compare published observation series. Keep location, observation method and uncertainty. Revisit the calculation if the evidence differs from your prediction. No new observational experiment has been conducted by QuranML for this example.

Keep the conclusion within its scope.

The arithmetic explains why twelve mean lunations do not stay aligned with a seasonal year. It does not establish the divine origin of a text, settle its interpretation or determine religious observance. USNO’s calendar introduction explains how solar, lunar and lunisolar systems handle these different cycles.