שמות 12:2
הַחֹדֶשׁ הַזֶּה לָכֶם רֹאשׁ חֳדָשִׁים רִאשׁוֹן הוּא לָכֶם לְחָדְשֵׁי הַשָּׁנָה
Rashi, citing the Mechilta, explains that Moses received a lesson in lunar astronomy:
רש׳י, שם
החדש הזה. הֶרְאָהוּ לְבָנָה בְּחִדּוּשָׁהּ וְאָמַר לוֹ כְּשֶׁהַיָּרֵחַ מִתְחַדֵּשׁ יִהְיֶה לְךָ רֹאשׁ חֹדֶשׁ (מכילתא)
החדש הזה — He showed him the moon in the first stage of its renewal, and He said to him, “This stage of renewal (חדש) shall be the moment of beginning the months.”
Apparently, Moses was a visual learner, so God pointed out the way the moon would look at various times in the month:
רש׳י, שם
נִתְקַשָּׁה מֹשֶׁה עַל מוֹלַד הַלְּבָנָה, בְּאֵיזוֹ שִׁעוּר תֵּרָאֶה וְתִהְיֶה רְאוּיָה לְקַדֵּשׁ, וְהֶרְאָה לוֹ בְּאֶצְבַּע אֶת הַלְּבָנָה בָּרָקִיעַ וְאָמַר לוֹ כָּזֶה רְאֵה וְקַדֵּשׁ (שם). .. סָמוּךְ לִשְׁקִיעַת הַחַמָּה נֶאֶמְרָה לוֹ פָרָשָׁה זוֹ וְהֶרְאָהוּ עִם חֲשֵׁכָה
הזה THIS [STAGE OF RENEWAL] — Moses was in perplexity regarding the Molad of (the exact moment when begins) the new moon — how much of it must be visible before it is proper to consecrate it as new moon: He therefore pointed it out to him in the sky with the finger and said to him, “Behold it like this, and consecrate it” (i. e., when you see the moon in a stage of renewal similar to this which you now behold you may proclaim that a new month has begun). … This chapter was spoken to him close to sunset and He pointed it out to him at nightfall.
The moon is the defining celestial object for the Jewish People, dictating the rhythms of the calendar and its cycle of special events. This week on Talmudology, we will focus therefore on one crucial aspect of this calendar: how long is a Jewish lunar month?
The Talmud addresses this question in (where else but) Masechet Rosh Hashanah:
ראש השנה כה, א
תָּנוּ רַבָּנַן: פַּעַם אַחַת נִתְקַשְּׁרוּ שָׁמַיִם בְּעָבִים, וְנִרְאֵית דְּמוּת לְבָנָה בְּעֶשְׂרִים וְתִשְׁעָה לַחֹדֶשׁ. כִּסְבוּרִים הָעָם לוֹמַר רֹאשׁ חֹדֶשׁ, וּבִקְּשׁוּ בֵּית דִּין לְקַדְּשׁוֹ. אָמַר לָהֶם רַבָּן גַּמְלִיאֵל: כָּךְ מְקוּבְּלַנִי מִבֵּית אֲבִי אַבָּא — אֵין חִדּוּשָׁהּ שֶׁל לְבָנָה פְּחוּתָה מֵעֶשְׂרִים וְתִשְׁעָה יוֹם וּמֶחֱצָה וּשְׁנֵי שְׁלִישֵׁי שָׁעָה וְשִׁבְעִים וּשְׁלֹשָׁה חֲלָקִים
The Sages taught in a baraita: Once the sky was covered with clouds, and the form of the moon was visible on the twenty-ninth of the month. The people thought to say that the day was the New Moon, and the court sought to sanctify it. However, Rabban Gamliel said to them: This is the tradition that I received from the house of my father’s father: The monthly cycle of the renewal of the moon takes no less than twenty-nine and a half days, plus two-thirds of an hour, plus seventy-three of the 1,080 subsections of an hour.
Rabban Gamliel had a tradition that a lunar month cannot be shorter than 29 days, 12 hours and 792 chalakim (where one chelek is 1/1080 parts of an hour). Therefore, if witnesses claim to have seen a new moon before this time has elapsed after the previous new moon, they must be mistaken. But according to the medieval commentator Menachem ben Solomon (1249–1315) known as the Meiri, this period is also the longest period for a lunar month.
How the Lunar Month varies
The average length of a lunar month, that is, the period between two new moons, is 29.53059 days, which is 29 days 12 hours and 44 minutes. But this is an average, and the actual length of the month varies. This is because the moon’s rotation around the earth is not uniform. When the moon is closest to the earth (called the lunar perigee) it speeds up, and when it is furthest from the earth (at the lunar apogee) it slows down, though only by a little in each case.
From here.
Take a look at the lengths of the lunar months for this calendar year, 2024. Note the longest lunar month marked in red, and the shortest lunar month, shown in green. They differ by eight hours and fifty-seven minutes!
| Lunar Calendar 2024 | ||
|---|---|---|
| Lunar Month Start* | Lunar Month End* | Lunar Month Length |
| Jan 11, 11:57 | Feb 9, 22:59 | 29 days, 11 hours, 2 min |
| Feb 9, 22:59 | Mar 10, 09:00 | 29 days, 10 hours, 1 min |
| Mar 10, 09:00 | Apr 8, 18:20 | 29 days, 9 hours, 20 min |
| Apr 8, 18:20 | May 8, 03:21 | 29 days, 9 hours, 1 min |
| May 8, 03:21 | Jun 6, 12:37 | 29 days, 9 hours, 16 min |
| Jun 6, 12:37 | Jul 5, 22:57 | 29 days, 10 hours, 20 min |
| Jul 5, 22:57 | Aug 4, 11:13 | 29 days, 12 hours, 16 min |
| Aug 4, 11:13 | Sep 3, 01:55 | 29 days, 14 hours, 42 min |
| Sep 3, 01:55 | Oct 2, 18:49 | 29 days, 16 hours, 54 min |
| Oct 2, 18:49 | Nov 1, 12:47 | 29 days, 17 hours, 58 min |
| Nov 1, 12:47 | Dec 1, 06:21 | 29 days, 17 hours, 34 min |
| Dec 1, 06:21 | Dec 30, 22:26 | 29 days, 16 hours, 5 min |
| *all times are UTC, which may or may not be the same as GMT | ||
The corrupted text in the Talmud
In his book Calendar and Community, the British scholar Sacha Stern pointed out that the period of the lunar moth, called a lunation, is exactly the same as in the present day rabbinic calendar. “However, the phrase אֵין חִדּוּשָׁהּ שֶׁל לְבָנָה פְּחוּתָה (‘not …less than’) which implies a minimal value, is inappropriate for what should represent a fixed value.” He continues:
Moreover, the mean lunation is totally out of context in this passage. The context of this passage is the Mishnaic, empirical calendar, which is based on the appearance of the new moon; calculation of the molad is therefore irrelevant. R. Gamliel was only establishing that the moon could not have been sighted before the 29th day of the previous month. All he could have stated, therefore, was the minimal number of days in an empirical lunar month.
Other scholars like David Gans (1743), Hayyim Slonimsky (1852) and Hayyim Yehiel Bornstein (1904) also recognized this problem. Stern therefore suggests that the text we have in our Talmud is a later addition.
Originally the text would have read: אֵין חִדּוּשָׁהּ שֶׁל לְבָנָה פְּחוּתָה מֵעֶשְׂרִים וְתִשְׁעָה יוֹם (‘not after less than 29 days’) - and no more. The interpolation שְׁנֵי שְׁלִישֵׁי שָׁעָה וְשִׁבְעִים וּשְׁלֹשָׁה חֲלָקִים (‘and a half, two-thirds of an hour and 73 parts’) would have been made by an editor who thought that the mean lunation - not the minimal number of days in the month - was meant in this passage. The absence of manuscript evidence does not undermine this argument; it only suggests that the interpolation must have been made relatively early, perhaps in the late Geonic period.
The origin of 29-12-793
If Professor Stern and his intellectual predecessors are correct, the origin of the 29-12-793 period for a lunation is not in fact in the Talmud. So where does it come from? In the twelfth century Rabbi Avraham bar Hiyya acknowledged that the calculation is identical to that found in the Almagest, a Greek language compendium on mathematics and astronomy which was composed by Ptolemy in the second century. In that book Ptolemy gives the lunation in the standard Babylonian sexagesimal system as 29d, 31i, 50ii and 20iv, (where one i=1/60 of the day, one ii is a sixtieth part of that and so on). It is exactly the same length as the rabbinic lunation. Rabbi Avraham bar Hiyya claimed that Hipparchus (the second century B.C.E scholar who Ptolemy used as his source) had taken this value from the Jewish sages - the ancestors of Rabban Gamliel referred to on today’s page of Talmud. But, as Sacha Stern noted, “it seems far more plausible to assume on the contrary, that it was the rabbis who borrowed their lunation from Ptolemy.” This assumption led a number of Jewish scholars to conclude that the molad calculation of 29- 12-793 could not have been instituted before the ninth century.
This is because Ptolemy’s Almagest was not known to astronomers in the Near East before its translation into Arabic in the early ninth century…It is likely that Ptolemy’s calculation of the conjunction was only then transmitted to the Jews, who soon incorporated it into the fixed rabbinic calendar. Although somewhat conjectural, this theory remains completely plausible, particularly as evidence of the present day molad calculation only begins to emerge in the ninth century.
Stern also admits that it is also possible that rabbinic calendar makers took their lunation period of 29-12-793 directly from the Babylonians, without resorting to Ptolemy’s Almagest. If that happened, “the rabbinic lunation could have been adopted long before the ninth century.” Either way, we got it from the Babylonians.
“Whether the molad calculation was borrowed from Babylonian astronomers, or from an Arabic translation of Ptolemy’s Almagest that would have been made at the ninth century Abbasid capital of Baghdad, in the heartland of Babylonia, the geographical origins of this molad would have been the same. It was in Babylonia, indeed, that this molad would have become known to the Jews and incorporated into the present-day rabbinic calendar. ”
Where does that 1/1080 measure come from?
In 1989, shortly before his death, Otto Neugebauer (d. 1990), who was described as “the most original and productive scholar of the history of the exact sciences, perhaps of the history of science, of our age” published a paper that reviewed the transmission of the standard Babylonian value for the lunation. In it, he noted that in the third century B.C.E (!) in Mesopotamia, there existed a small unit of measure called “barleycorn” which represented a fraction of 1/6 of a finger breadth. The finger breadth is in turn a faction of a palm, and the palm of the cubit, so that 1 cubit = 180 barleycorns. But, noted Neugebauer, “measures can lose their specific meaning and become terms for fractional parts in general….Similarly, the barleycorn, embedded in a sequence of sexagesimally arranged units, retains only its fractional significance as 18 units of 60ths, ie 1/1080.” And so the Babylonians used this measure, which we inherited as halakim (parts). representing 1/1080 of an hour.
The Babylonians also discovered the nineteen year cycle around 600 B.C.E. which today is known as the Metonic cycle. It is is the period after which the phases of the moon recur at the same time of the year. They kept careful records of the time for a number of lunar cycles, and used these to calculate the average lunation. These were later adopted by the Romans. And by us.
No, It’s not a miracle
Some organizations, keen to spread the word about the beauty of Judaism, have looked to Rabban Gamliel and his knowledge about the length of the lunar month as proof of the divine origins of the oral law. Here is an excerpt from the Aish Hatorah Discovery Book:
So just how long is a lunar month, according to the reckoning of the Talmudic sages? The Talmud in Rosh Hashanah 25a tells us: Rabban Gamliel said...I have it on the authority of my father’s father that the renewal of the moon takes place after not less than twenty-nine and a half days, two-thirds of an hour and seventy-three parts of an hour.
Okay, class, you do the math. Two-thirds of an hour remembering that an hour is divided into 1,080 parts equals 720 parts. Add to that another 73 parts and you have 793 parts. So that according to the ancient calculation of the Sages of the Talmud, a lunar month is 29 and days plus 793 out of 1,080 parts of an hour. 793 out of 1,080 equals 0.734259 hours, which equals 0,03059 days. Add to that 29.5 days, and the average length of the lunar month according to the Rabbis is 29.53059 days.
What is so incredibly amazing about all this is the fact that, in our own times, the scientists and researchers at NASA have spent years of research using satellites, hairline telescopes, laser beams and supercomputers and all this in order to determine the exact length of the synodic (lunar) month. And the calculation they came up is that the length of the lunar month is 29.530588 days. The difference between this figure and that used by the Sages is .0000006, or one sixth millionth of a day!!!
Incredible! How could the Sages of millennia ago have been able to calculate the exact length of the lunar month with such incredible precision, enabling them to accurately and successfully balance the solar and lunar cycles for so many thousands of years?! With absolutely no modern technological tools and equipment, how could the Rabbis of old have had access to such accurate information way ahead of their time?! [Can you say G-d?]
We actually have a tradition, based on an ancient Midrash, that when G-d commanded Moses regarding the establishment of the calendar and the Jewish holidays based on the sanctification of the New Moon, He also gave to Moses all the secrets and vital information necessary to accurately calculate and balance the solar and lunar cycles.
Maybe accepting the Torah as G-d’s truth doesn’t require such a leap of faith after all?
There may be lots of good reasons to follow traditional Jewish practice, but, contra Aish Hatorah, the knowledge of the length of the lunar month is not one of them. It was an inheritance we took from the Babylonians, and unless Aish is suggesting that God revealed the average length of the lunar month to them, knowing the history of the Jewish lunation reveals something else and just as impressive. It is the ingenuity of the human mind.
