Halachah 1 – Calculations Do Not Guarantee Actual Visibility
Even when the astronomical calculations show that the moon should be visible, it may still not be seen. Clouds may cover it, mountains may obstruct the horizon, or observers may be located in a valley. Therefore, the calculations determine whether visibility is possible, not whether the moon will actually be observed.
Halachah 2 – Geography Affects Visibility
A person standing in a low place may fail to see the moon, while someone standing on a high mountain may see it clearly. Likewise, observers on a seashore or on ships often see the new moon more easily because their western horizon is less obstructed.
Halachah 3 – Seasonal Weather Makes a Difference
Visibility is generally better during clear winter weather than during summer. In winter the atmosphere is cleaner and contains less dust, making the sky more transparent. In summer, airborne dust and haze reduce visibility, especially when the crescent is very small.
Halachah 4 – The Importance of the Arc of Visibility
When the arc of visibility and the first longitude are only barely within the minimum thresholds, the moon will be extremely small and difficult to see. Such a crescent may be visible only from especially favorable locations.
When those values greatly exceed the minimum requirements, the crescent becomes larger and easier to observe.
Halachah 5 – Why Beit Din Asked About Location
Because visibility depends on local conditions, Beit Din questioned witnesses carefully about where they saw the moon. If the calculations indicated a very difficult sighting but witnesses claimed to have seen it from a poor location, their testimony required especially careful examination.
If, however, the sighting occurred during favorable weather or from an elevated location, the testimony was more plausible.
Halachah 6 – The Problem of Consecutive Thirty-Day Months
The Rambam discusses a practical problem. Suppose one month was sanctified through witnesses, but in the following month no witnesses arrived and Beit Din declared a thirty-day month.
If this process continued repeatedly, one might theoretically make month after month thirty days long, eventually creating absurd results in which the moon could appear long before the calendar predicted it should.
Halachah 7 – This Situation Is Not Merely Theoretical
The Rambam stresses that such situations are realistic. Long periods of cloudy weather can prevent sightings for many months. Sometimes the moon could have been seen but was hidden by clouds; other times it was simply too small to be noticed.
Therefore, Beit Din could not rely on observation alone without the guidance of calculation.
Halachah 8 – The Tradition Received from Moshe Rabbeinu
The sages possessed a tradition tracing back to Moshe Rabbeinu. When the moon was not seen month after month, Beit Din alternated between full and deficient months according to calculation. These determinations were made by calendar fixing (kevi’ah), not by sanctification through witnesses (kiddush), because sanctification requires actual testimony.
At times Beit Din would make several consecutive full months or several consecutive deficient months, whenever calculation required it.
Halachah 9 – The Goal of These Calculations
Beit Din arranged the calendar so that whenever the moon could next be seen, it would appear at the proper time, either on the expected night or on the night following. The calculations explained in the previous chapters reveal when visibility is possible and when it is impossible.
The court therefore relied on these calculations when deciding whether to make months full or deficient.
Halachah 10 – Limits on Full Months
The Rambam notes that in a year there can never be fewer than four full months nor more than eight full months. Even months established by calculation rather than visibility were treated seriously, and the traditional meal associated with declaring a leap month would still be observed.
Halachah 11 – Understanding Talmudic References
Many passages in the Talmud appear to show that Beit Din relied on calculation. The Rambam explains that these statements refer to situations where the moon was not seen at the proper time. In those cases Beit Din had authority, based on tradition, to determine the calendar through calculation.
Similarly, when the sages spoke of adjusting months “for necessity,” they referred to these calculated arrangements.
However, whenever the moon was actually seen at the first possible opportunity, Beit Din would always sanctify the month based on the testimony of witnesses.
Halachah 12 – The Difference Between Then and Now
Everything discussed in these chapters applied when a functioning Beit Din existed and the calendar depended on witnesses. In later generations, when that system ceased, the Jewish people relied entirely on the fixed calendar calculation described earlier in Hilchot Kiddush HaChodesh.
Halachah 13 – Visibility West of Eretz Yisrael
Astronomical science shows that if the moon is visible in Eretz Yisrael, it may also be visible in lands directly west of it.
However, if the moon is seen in a western country, that does not prove that it was visible in Eretz Yisrael.
Halachah 14 – When Western Visibility Gives Certainty
If the moon cannot be seen even from high mountains in a country directly west of Eretz Yisrael, then it certainly was not visible in Eretz Yisrael either.
Halachah 15 – Visibility East of Eretz Yisrael
The opposite rule applies in the east.
If the moon is not visible in Eretz Yisrael, it certainly will not be visible in lands directly east of it.
But if the moon is seen in an eastern country, that is proof that it was visible in Eretz Yisrael as well.
Halachah 16 – Final Principle: Authority Belongs to Eretz Yisrael
These comparisons between eastern and western lands apply only to places located on roughly the same latitude as Eretz Yisrael.
The Rambam concludes by emphasizing that this discussion is only for understanding the laws of moon visibility. The calendar never depended on observations made outside Eretz Yisrael. The determining factor was always the sanctification performed by the Beit Din in Eretz Yisrael.
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