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Arakhin 9 for kids: Counting Moon Months

ערכין ט׳

🌙 This daf asks how many months in a year can have 29 days or 30 days. The sages also count how those choices affect Rosh HaShana and the length of a lunar year.

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In the app: the Gemara with Rashi and Tosafot, the printed page, games made from this daf, play coins and treasure chests.

Stories from Arakhin 9

Words to know

Rashi and Tosafot on Arakhin 9 in simple English

Rashi on Arakhin 9a, in English Tab translation (8)
  1. The new moon arrives early — It appears three days before Rosh HaShana: the lunar conjunction is on Wednesday, but Rosh HaShana is on Saturday. People would then accuse the Sages of setting the date however they pleased.
  2. As Rav Mesharshiyya says — He says later, in a discussion of Shavuot, that the case involves a leap year. Here too, the year before this one was a leap year.
  3. The added month of a leap year — We may make that month either full or deficient. We made last year’s added month deficient, bringing last Tishrei forward relative to the lunar conjunction by the difference between a full and a deficient month. We can therefore delay this Tishrei by that same amount. This is what the Gemara means by offsetting a full month against a deficient one.
  4. But there is still one day — Although the difference is a day and a half, the Gemara calls it one day. It could also have answered that this year was a leap year, making eight full months seem reasonable. It instead speaks of the previous year because the mishna cannot refer to a leap year: it says that four full months suffice, but in a thirteen-month year that would leave nine deficient months. According to both Rav Huna and Ulla, even eight deficient months require a leap-year explanation; nine cannot be explained in either an ordinary or a leap year, as discussed below.
  5. People do not notice — A difference of one day does not surprise people or cause them to complain.
  6. The moon lingers — The old moon remains visible for three days after Rosh HaShana. As explained, lunar months ordinarily alternate between full and deficient; making three additional months deficient advances Rosh HaShana by three days.
  7. The year before was a leap year — Last year’s added month had thirty days, though a lunar month is only twenty-nine and a half days. This delays Rosh HaShana by half a day, leaving a difference of only one and a half days. Because that is less than two full days, the Gemara calls it one day and asks, ‘But there is still one day.’
  8. It was visible — The new moon was visible to the court, but we did not make the effort to look for it. People therefore will not complain.
Tosafot on Arakhin 9a, in English Tab translation (4)
  1. Here too, when the preceding year was a leap year — We are discussing the year with eight full months, so why not say that this year was a leap year? The phrase means that the year before this eight-full-month year was a leap year. Without that leap year, if last year Rosh HaShana and the conjunction fell on Saturday, then with months in their usual order this year they would fall on Wednesday. Each additional full month would move Rosh HaShana a day later, eventually to Saturday. With the preceding leap year, however, the conjunction would occur on Thursday at the twenty-first hour and the moon would not be visible until Friday. It would therefore precede Rosh HaShana by only one day.
  2. People do not notice a one-day difference — This implies that eight full months may be established when the moon precedes Rosh HaShana by only one day. But in our present calendar, we postpone Rosh HaShana when the conjunction falls on Tuesday at nine hours and 204 parts, because otherwise the following year’s conjunction would fall on Saturday at eighteen hours and Rosh HaShana would be set on Monday, a six-day interval between the two Rosh HaShana dates. The postponement produces two additional full months, yet the discrepancy is still only one day. We must say that those who established our rules for leap years and Rosh HaShana dates did not want any year to have more than seven full months.
  3. Why not three deficient months? — With months in their usual order, Rosh HaShana falls on Wednesday, the day of the conjunction. Three additional deficient months shorten the year by three days, setting Rosh HaShana on Sunday while the moon appears on Wednesday. Two additional deficient months likewise leave a two-day gap, setting Rosh HaShana on Monday.
  4. When the preceding year was a leap year — Its added month had thirty days. With eight deficient months, Rosh HaShana would otherwise have fallen on Monday; the added month moves it two days later, to Wednesday, while the conjunction falls on Thursday at the twenty-first hour. This explains the Gemara’s question that a one-day gap remains. One might object that the gap is really two days: the moon is hidden for six hours and will not be visible until Friday. The answer is that last year’s conjunction occurred five hours into the day before Rosh HaShana. Adding five days, twenty-one hours, and 589 parts places this year’s conjunction nine hours into Thursday, so it can be seen that day in the Land of Israel. It is thus only one day later than Rosh HaShana. But if last year’s conjunction occurred at the start of the day, this year’s would occur on Thursday at the twenty-first hour and would not be visible until Friday. In that case, eight deficient months would not be established, since the moon would lag two days. One might ask: According to Rav Huna, the mishna’s latter clause permits eight full months only after a leap year when the moon is not visible until Friday. But to explain its opening clause, ‘no fewer than four full months,’ he must follow Ulla’s reading, which permits eight deficient months when the moon is visible on Thursday because last year’s conjunction preceded Rosh HaShana. Would the two clauses then concern different circumstances? The answer is that the mishna teaches every possible departure from the usual order of months: its opening clause permits eight deficient months in the latter circumstance, and its closing clause permits eight full months when last year’s conjunction did not precede Rosh HaShana. Under the explanation given above, however, both clauses apply to the same circumstances.
Rashi on Arakhin 9b, in English Tab translation (21)
  1. What do they disagree about? — Rav Huna reads the mishna as making two points. He follows Rabban Shimon ben Gamliel, who allows the added month in a leap year to have either twenty-nine or thirty days. The mishna permits eight deficient months when that added month has thirty days, and eight full months when it has twenty-nine. Ulla follows the first tanna, who always gives the added month thirty days. He therefore reads the mishna as permitting eight deficient months but not eight full ones, which would put the calendar two days ahead of the moon.
  2. Only on the day of waving — Shavuot falls on the same day of the week as the sixteenth of Nisan, when the fifty-day count begins: day forty-nine ends the seventh week, and day fifty begins a new week.
  3. And Rosh HaShana … or on the night of its intercalation — This means the day of the week on which the thirty-first of Nisan would fall. If the first of Nisan is Sunday, that day is Tuesday. It is called the night of intercalation because making the thirty-first day the new moon makes the preceding month full.
  4. Both are deficient — Kislev and Sivan are made deficient, leaving four deficient months in winter and four in summer. Normally the summer months alternate in length, and Rosh HaShana falls on the weekday of the third day of Passover—the day after the waving. Making one more summer month deficient moves it back to the weekday of the waving. But Rav Huna also permits four full summer months, which would move Rosh HaShana forward to the weekday of the fourth day of Passover.
  5. But we may make seven — Even Ulla permits seven full months; he rules out eight because they would put the calendar two days ahead of the moon. If the extra full month falls in summer rather than winter, there will be four full summer months, and Rosh HaShana will likewise fall on the weekday of the fourth day of Passover.
  6. Rather — The teaching that Rosh HaShana falls no later than the weekday after the waving follows Aḥerim. They allow neither extra full nor extra deficient months; all months alternate in length.
  7. Only four days — If Rosh HaShana falls on Sunday, the next Rosh HaShana falls on Thursday. This follows from the months alternating in length.
  8. You cannot find it on the day of waving — When the months alternate in length, Rosh HaShana falls on the weekday after the waving.
  9. Subtract a month — Make a summer month deficient to offset the full month added in intercalation. Just as Shevat and the first Adar are both full, make Nisan and Iyar both deficient. Otherwise, adding a thirty-day month would move the next Rosh HaShana six weekdays later, rather than the five taught for a leap year. This gives four deficient summer months, so Rosh HaShana falls on the weekday of the waving.
  10. Did Aḥerim come to teach us a count? — If they hold that months alternate in length, the four-day difference is obvious. They should instead have said that a month is not made full for a particular need; the four-day difference would follow.
  11. This is what it teaches us — Had Aḥerim said only that a month is not made full for a particular need, one might have limited that rule to a month whose new moon was seen on time. If no witnesses came on the thirtieth day, one might think the month had to be made full because there is a mitzva to sanctify it on the basis of witnesses.
  12. It teaches us — Keep the four-day difference as your rule, even if the moon was not seen.
  13. But there is the day from the hours — Even if Aḥerim follow the moon’s cycles, there are times when successive Passovers in ordinary years fall five weekdays apart. Between corresponding new moons of successive years there are four days, eight hours, and 876 parts of an hour; over three years, the eight hours alone add up to another day.
  14. And the day from thirty years — The 876 parts each year also accumulate. Taking 864 parts per year, thirty years yield twenty-four hours—another day.
  15. And Shmuel, too, agrees with Rav Huna — Eight full months may be established in a year.
  16. Both are full — If two normally deficient months, such as Marḥeshvan and Iyar, are made full, the year has two more days than an alternating-month year: 356 days.
  17. Both are deficient — If two normally full months, such as Kislev and Sivan, are made deficient, the year has two fewer days than an alternating-month year: 352 rather than 354. The case of 356 days shows that eight full months may be established.
  18. I am a nazirite for the days of the solar year — Or if he says, for the number of days in the solar year, he counts 365 terms of naziriteship.
  19. And Rabbi Yehuda, too, agrees with Rav Huna — Eight full months may be established.
  20. And the new moon was seen — The moon of Tishrei was seen on its proper day, the date fixed for Rosh HaShana.
  21. And Rabbi Yehuda was puzzled — The moon appeared three days late, because the date fixed for the new month had been advanced by three days.
Tosafot on Arakhin 9b, in English Tab translation (3)
  1. Two deficient months: on the day of the waving — That is, the sixteenth of Nisan. With one full month and one deficient month, Rosh HaShana falls on the night after the added day—that is, on the weekday of the thirty-first of Nisan, the same weekday as the seventeenth of Nisan, the third day of Passover.
  2. Ultimately, according to Aḥerim, it cannot fall on the day of the waving — It can if the year was a leap year and its added month had thirty days. Because we added a thirty-day month, we must make one of the full summer months deficient. Thus Rosh HaShana can fall on the weekday of the waving.
  3. Rabbi once made nine months deficient, and the new moon was seen at its proper time — The molad of Tishrei occurred on the day set for Rosh HaShana. Rabbi was surprised: he thought that the previous year’s molad and Rosh HaShana had both been on Saturday. After nine deficient months, Rosh HaShana was set on Sunday, but he expected the moon not to be seen until Wednesday. His son Rabbi Shimon suggested that this was a leap year with a thirty-day added month, and that the previous year two months had been made full. In effect, the three extra deficient months offset the three added days. On that account, the previous year’s molad preceded its Rosh HaShana by two days, falling on Tuesday; adding the leap year’s molad interval of five days, twenty-one hours, and 589 parts could put this year’s molad on Sunday, the day set for Rosh HaShana. But this is difficult: how could the previous year have had eight full months if its molad preceded Rosh HaShana by two days? We concluded above that eight full months are allowed only in a leap year when the moon’s appearance precedes Rosh HaShana by no more than one day. If the previous year’s molad was on Tuesday after eighteen hours, so that the moon was not seen until Wednesday, adding that interval puts this year’s molad on Monday after fifteen hours—not on Sunday. Even if, as explained above, a molad counts as preceding Rosh HaShana only when it occurs before the day’s final eighteen hours, and the previous year’s molad was on Tuesday after six hours but was not seen in Babylonia until Wednesday, this year’s molad would still be on Monday after three hours. Perhaps ‘seen at its proper time’ is not exact: even a sighting on the day after Rosh HaShana is called ‘at its proper time,’ since people do not notice a one-day gap between the molad and the day set for Rosh HaShana.

Sources

Kid summary and story cards written by Tab from the William Davidson Edition English (Sefaria, CC BY-NC 4.0).

Tab translation (machine-assisted) of Rashi and Tosafot, from the Vilna Edition Hebrew (public domain) on Sefaria. May contain mistakes.

In the app, the Gemara text comes from Sefaria (William Davidson Edition, CC BY-NC 4.0; Hebrew/Aramaic Vilna Edition). Rashi and Tosafot Hebrew: Vilna Edition (public domain) via Sefaria.

Also spelled: Arachin, Erchin 9.