Parshat Re’eh - The Jewish Calendar

Let’s talk about the Jewish calendar.

As you know, when the Sanhedrin existed, the start of each new month was fixed by the testimony of two eyewitnesses who had been present at the moment a new moon appeared.  Witnesses who saw the new moon would come to the Beis Din in Jerusalem and report it, and at least two such witnesses were required.  Once there, they would be interrogated in great detail—and if their responses were convincing, the Beis Din would declare it to be Rosh Chodesh, the New Month.

On the other hand, the Talmud (Tractate Rosh Hashanah 25a) tells us: “Once it happened that the heavens were thick with clouds and the form of the moon was seen on the 29th of the month [of Elul], so that the people thought that New Year’s Day should be then proclaimed, and they [the Beis Din] were about to declare it.  Rabban Gamliel said to them: ‘Thus it has been handed down to me by tradition, from the house of my grandfather, that the declaration of the new moon cannot take place at a time less than twenty-nine-and-a-half days and 793 Chalakim [of an hour] [since the last new-moon declaration].  On that self-same day the mother of Ben Zaza died and Rabban Gamliel delivered a great funeral oration; not because she specially deserved it, but in order that the people might know that the new moon had not yet been declared by the Beis Din.”

Rabban Gamliel clearly invoked a “tradition from the house of my grandfather.”  But how did his grandfather, and the ancestors of his grandfather, know that?  The answer is that they knew it from Moshe Rabbeinu—and Moshe Rabbeinu heard it directly from the Almighty.

So, we have the established tradition that the moon makes one revolution around the Earth every 29 days, 12 hours, 44 minutes and 3.3 seconds.  [Editor’s note: The Halachic time unit of the Cheilek (plural: Chalakim) is roughly 3.3 seconds, thus making 793 Chalakim (793 x 3.3 / 60) just under 44 minutes and 3.3 seconds.]

In addition, we also have a tradition in the time it takes for the Earth to complete 19 revolutions around the Sun (that is, 19 solar-calendar years), the Moon will complete 235 revolutions around the Earth (that is, 235 lunar months).  Today, these 19 years are called the Metonic cycle (after Meton of Athens, the Greek scientist who came to that figure as a result of his calculations).

The Jewish calendar is based on these two traditions.

Every 19 years, the solar and lunar cycles coincide; that is, every 19 years, on the same date of the European Gregorian calendar, there is a certain date of the Jewish calendar.

Thus, every 19 years, the first day of the Jewish-calendar month of Tammuz will fall on the 13th of June—as it in fact did in 1953, 1972 and 1991.  (Sometimes there is a one-day shift due to the fact that we constantly operate in fractions of a day.)  For the same reason, both lunar and solar months are of different lengths—not 29 days plus a fraction, but precisely 29 days in one month and 30 in another.

So now, let’s take the 235 orbits of the Moon—meaning, the 235 lunar months—that occur every 19 years, and divide 235 by 19, meaning, 235 months by 19 years.  What do we get?  We get 12 with a remainder of 7.  In other words, by the end of 19 lunar years—of 12 lunar orbits each—we’re seven months behind the current solar year.

In turn, that means that in order to fix the lunar months according to the solar-year seasons, we need to fix 12 of those lunar years as 12-month years—and seven of them as 13-month years.  In other words, seven of those 19 lunar years get that extra 13th month added to them—making them what we all know as leap years.  Put otherwise, we have 144 regular lunar orbits in the 12 regular years, or 12 x 12, and 91 additional lunar orbits in the seven leap years, or 7 x 13—which all adds up to 235 (144 + 91). Thus, across every 19 solar years, we will have 12 lunar regular years and seven lunar leap years.

But now, how do we distribute seven leap years across a 19-year period with minimal margin of error?

The difference between a typical solar year (which is approximately 365 days and 6 hours) and a normal lunar year (which is approximately 354 days) is about 11 days.  In other words, a lunar year ends 11 days before a solar year ends.  But after three years go by, the lunar year will be 33 days—that is, 3 x 11, or just over a month—behind the current solar year.  After six years go by, the lunar year will be 66 days behind the solar year (or, more precisely, just a little over 65 days). And after eight years, the lunar year’s lag behind the solar year is already around 88 days, and so on.

So it is in those lunar years in each 19-year cycle—the 3rd, 6th, 8th, 11th, 14th, 17th and 19th year—when it is most convenient to add a month.  And that is what we Jews did: We turned those years into leap years.  This way, the Pesach month always remains a springtime month.  In fact, I calculated the year 6000 on the Jewish calendar—and everything is in order!  Passover 6000 still falls in the spring!

But if those calculations are so reliably accurate, why would we need witnesses to the appearance of the new moon?

That’s a difficult question which we will not answer now.  We’ll only note that the two processes, observations and calculations, were always carried out in parallel, and the result was approved by the Great Sanhedrin.  In fact, according to the Ramban, the calculated calendar we use today was approved by the last acting Sanhedrin.

By the way, the figure used by Rabban Gamliel to determine the length of the lunar month is approximated, because the interval between two new moons is not always the same.  For several astronomical reasons, it fluctuates between 29.25 and 29.83 days.  No matter how insignificant that difference is, a lot can add up over the millennia! 

This means that to perform calendar and astronomical calculations, one cannot be ignorant of the average length of the lunar month—which we Jews knew all along from our Oral Tradition.

I must note that these values can even be established empirically.  (Of course, simple visual observation of the time of the new moon’s appearance is not suitable here, because its accuracy cannot be vouched for.)  Here’s how: The time of the appearance of the new moon at the time of a total solar eclipse can be specified precisely.

This has in fact actually happened 15 times in history (13 times, no one paid attention to it); the 14th eclipse was predicted by the Greek scholar Thales of Miletus (624-528 BCE), who correctly predicted that it would occur as it did on May 28, 585 BCE.

The 15th eclipse occurred precisely on September 22, 1968—that is, 932,221.9 days (or 31,568 months) after the 14th eclipse on May 28, 585 BCE.

Now if we divide that first number by the second—meaning, those days by those months—we get the average length of a lunar month: 29.53059 days—more specifically, 29 days, 12 hours, 44 minutes and three seconds.

What’s more, if we translate the hours, specified by Rabban Gamliel thousands of years ago, into fractions of a day, we get the figure 29.5305941—which is precisely equal to the figure cited in by S.I. Seleshnikov in his History of Calendar and Chronology  (1977), from which scientists proceeded when calculating a flight to the moon!

Leafing through that book, I was amazed: All peoples, without exception, have “corrected” the calendar from time to time. Only among the Jews, nothing on the calendar has changed for over 3,300 years.  Ours is the only such calendar in the world!

For example, the Romans added the month of Mercedonia, consisting of 23 or 24 days, every three to four years.  This was done arbitrarily and depended on the decision of the priests-pontiffs, based on some of their own interests.  (Of modern calendars, the Gregorian is more or less accurate.)

Meanwhile, here are a few opinions on the Jewish calendar.

In his Kuzari (2:64), Rabbi Yehuda Halevi writes:

“Isn’t this amazing?  The reckoning of time, which was adopted by the house of David and based on the observation of the phases of the moon, has not been changed for over a thousand years.   For the Greek and other systems of calculation, amendments and additions were required every hundred years, but our system remained unchanged, because it is based on prophecy.”

Don Yitzchak Abarbanel, Spain’s finance minister at the end of the 15th century and one the greatest authorities on the Torah (commentary on Shemos 12), writes: “When Ptolemy was told about the Jewish counting of time, he was amazed and said: ‘This proves that the Jews had prophecy.’ ”

By Rabbi Yitzchak Zilber ztk”l