The Moon, the Molad, and the Math of Rosh Hashanah

Parshat Nitzavim-Vayeilech

This coming Shabbat, September 4-5, is the 23rd of Elul 5786. When the 23rd of a Jewish month is on Shabbat, it usually means that we bentch Rosh Chodesh, which will be on the following Shabbat (or Shabbat and Sunday). The other possible dates for Shabbat M’vorchim are the 24th, 25th, 26th, 27th, 28th, and 29th of the month. When Shabbat is the 29th, we have Machar Chodesh in addition to bentching Rosh Chodesh.

But this month we do not announce Rosh Chodesh Tishrei. This is because Rosh Chodesh Tishrei is overshadowed by Rosh Hashanah and Rosh Hashanah is itself astronomically obscured by the fact that the Moon is hardly visible. It is the only holy day observed when the Moon is hidden.

Ironically, the molad of Tishrei, the only molad of the year that does not get announced in public, is the most important molad for our fixed calendar.

The first mitzva given to Bnei Yisrael – shortly before we became a nation – was the mitzva to set up our own calendar. It consists of two plans: Plan A is for when we have a Sanhedrin. Plan B is for when we (temporarily) don’t.

The mitzva consists of three parts: setting months based on the cycle of the Moon’s phases, adding an extra month periodically to keep Pesach in the spring, and knowing how the whole thing works. The requirement to know about the Sun, Earth, and Moon, about their rotations and orbits, falls on judges of the Sanhedrin. But because the Torah emphasizes that the Jewish Calendar is a gift from G-d to us – the word “lachem,” to you, is used twice in the pasuk of “HaChodesh hazeh lachem” – I have always felt that knowing at least some of the workings of the Calendar, both Plan A and Plan B, is part of the spirit of the mitzva.

So bear with me as I get into some detail concerning the upcoming Rosh Hashanah and the new year, 5787, Hei-Tav-Shin-Pei-Zayin.

This knowledge is not necessary for us to know when Rosh Hashanah is. Anyone can buy or download a ready-made calendar and see that this year, Rosh Hashanah 5787 is on Shabbat and Sunday, the first and second of Tishrei, September 12-13.

But our knowing the workings of the Calendar – both when we have a Sanhedrin and when we don’t – shows an appreciation to HaKadosh Baruch Hu for the gift He gave Am Yisrael right at the birth of the nation.

With that said, let’s look at how, with our current calendar, Rosh Hashanah is fixed.

We start with the molad, the New Moon of Tishrei. To do that, we have to see what Rambam writes in his Hilchot Kiddush HaChodesh. First, the definition of the molad is the instant that the Sun and the Moon are aligned as seen from Earth. That moment is considered the beginning of the cycle of the Moon through its phases – from no moon to crescent moon to waxing half to full moon (known as the nigud, opposition) to waning half to crescent to no moon once again.

That cycle varies from month to month (due to Kepler’s Second Law of Planetary Motion – which I like to call G-d’s Second Law of Planetary Motion that Kepler discovered) by up to several hours, but the average length of a lunation (the time from one molad to the next) is 29 days (d), 12 hours (h), 44 minutes (m), and 1 cheilek, or part (p) (with 18 chalakim in a minute, a cheilek is three-and-a-third seconds). The length of the lunation Plan B uses is extremely close to the 29.530589 found on the internet.

Rambam establishes the molad of Creation, and from that point he basically adds the aforementioned 29:12:44:1 for every month thereafter until the molad of the month being calculated. Actually, he breaks that time down to 28 days plus 1d 12h 44m 1p, which is the remainder after taking away four full weeks. The result is that the molad of any month is 1d 12h 44m 1p after the previous month’s molad. He calculates the remainders for a full year, both a 12-month and a 13-month year. Then he finds the remainder of a 19-year lunar cycle which allows the calculation of the molad of Tishrei for the first year of a cycle.

The next step is to determine what year of a lunar cycle we want. We take the year’s number – 5787 in our case – and divide it by 19. The result is 304 remainder 11. This means that 304 lunar (19-year) cycles have been completed since Creation, and that 5787 is the 11th year of the current cycle, which is the 305th one.

This tells us the status of the coming year. Years 3, 6, 8, 11, 14, 17, and 19 of a cycle are shana m’uberet – that is, 13-month years with two Adars.

Back to the molad of Tishrei 5787. It will be on Friday night (Leil Rosh Hashanah) at 20h 59m 1p (corresponding to 9:35 p.m. Israel Summer Time).

The molad of Tishrei will determine when the first of Tishrei (the first day of Rosh Hashanah) is. The rule is that Rosh Hashanah is the day of the molad of Tishrei – unless one of four situations exists.

If the molad is after noon (which 9:35 p.m. on Friday definitely is), then Rosh Hashanah is on the following day. This fits our situation exactly. If the molad is after chatzot (midnight), then Rosh Hashanah is the following day – Shabbat.

Also note that even had the molad been before noon, another “push” would have taken effect. Namely, when the molad of Tishrei is on a Sunday, Wednesday, or Friday, then Rosh Hashanah is pushed to the following day.

Bottom line: Rosh Hashanah 5787 is Shabbat (and Sunday).

Let’s finish with another detail of the 5787 calendar. Knowing that it is a 13-month year, the molad of the following year’s Tishrei will be on a Thursday, 18h 31m 14p. The molad’s being after noon on Thursday pushes Rosh Hashanah to Friday, and then it gets pushed a second time because of LO ADU ROSH – Rosh Hashanah is not set for a Sunday, a Wednesday, or a Friday.

So Rosh Hashanah 5788 is scheduled to also be Shabbat-Sunday.

Last step: To go from Shabbat Rosh Hashanah 5787 to Shabbat Rosh Hashanah 5788 requires that 5787 have 385 days. In order for that to happen, Marcheshvan 5787 needs to be shaleim – that is, it must have a 30th day.

The coming year 5787 is coded Mem-Zayin-Shin. Mem is for m’uberet – meaning a year with two Adars (the other option is Pei, for p’shuta). Zayin is for Shabbat (Day 7, or Zayin), the first day of Rosh Hashanah. Shin is for shaleim, as both Marcheshvan and Kislev will have 30 days.

Buying a calendar or downloading one is easier. But this (for some people) is more fun, as well as reflecting the twice-used word “lachem” in the Torah’s presentation of the mitzva. The calendar, says Hashem, is yours. Use it, know it, and realize how special it makes Am Yisrael.

* * * * *

Sources tell us that Nitzavim is always the sedra we read on the last Shabbat of the year, the Shabbat before Rosh Hashanah. Sometimes we read it by itself and sometimes combined with Vayeilech.

To be specific, LO ADU ROSH means that the first day of Rosh Hashanah cannot be on a Sunday, a Wednesday, or a Friday. It follows, then, that Rosh Hashanah can begin on a Monday, Tuesday, Thursday, or Shabbat.

When Rosh Hashanah is Monday-Tuesday, the following Shabbat is Shabbat Shuva, Yom Kippur is on Wednesday, and there is a Shabbat between Yom Kippur and Sukkot, which is the following Monday.

When Rosh Hashanah is Tuesday-Wednesday, Yom Kippur is on Thursday, Sukkot is the following Tuesday, and there is a Shabbat between Yom Kippur and Sukkot.

But when Rosh Hashanah is Thursday-Friday, Shabbat Shuva will be the next day and Yom Kippur will be the following Shabbat. And there will not be a Shabbat between Yom Kippur and Sukkot.

Similarly, in years like this one, Rosh Hashanah is Shabbat-Sunday; then comes Shabbat Shuva, followed by Yom Kippur on a Monday; and Sukkot begins on the following Shabbat.

There is always a Shabbat between Rosh Hashanah and Yom Kippur – Shabbat Shuva. But there isn’t always a Shabbat between Yom Kippur and Sukkot. When there is, that Shabbat is Parshat Ha’azinu and the previous Shabbat is Parshat Vayeilech and Shabbat Shuva. And the Shabbat before that will have been Nitzavim by itself.

When there is no Shabbat between Yom Kippur and Sukkot, then Ha’azinu is Shabbat Shuva and the previous week is Nitzavim-Vayeilech combined.

One way or the other, Nitzavim will be read on the last Shabbat of every year.

So what’s the big deal about that? The explanation given is that Ki Tavo, with its harsh Tochacha, the longest aliya of the Torah (63 p’sukim, more than half of Ki Tavo), should not be the Shabbat that brings us into Rosh Hashanah and the Yamim Nora’im.

OK, I get that. But then take a look at Nitzavim – the sedra that is purposely chosen to usher us toward Rosh Hashanah.

“Perhaps there is among you a man, woman, family, or tribe, whose heart strays this day from the L-rd, our G-d, to go and worship the deities of those nations... HaShem will not be willing to forgive him; rather, then, the L-rd’s fury and His zeal will fume against that man, and the entire curse written in this book will rest upon him, and HaShem will obliterate his name from beneath the heavens... And a later generation, your descendants, who will rise after you, along with the foreigner who comes from a distant land, will say, upon seeing the plagues of that land and the diseases with which HaShem struck it: Sulfur and salt have burned up its entire land! It cannot be sown, nor can it grow [anything], not [even] any grass will sprout upon it. It is like the overturning of Sodom... And all the nations will say, Why did G-d do so to this land?... Then they will say, It is because they abandoned the covenant of G-d, the G-d of their fathers, [the covenant] which He made with them when He took them out of the land of Egypt, For they went and served other deities...” (D’varim 29:17-27).

Even without the text that I did not include here, this certainly sounds like tochacha – harsh rebuke. So why is Nitzavim used to separate Ki Tavo from Rosh Hashanah?

This can be answered in one word: T’shuva. Repentance. The Tochacha in Parshat B’chukotai and the one in last week’s sedra, Ki Tavo, are harsh rebukes, warnings, and – sadly – prophetic. But neither of those two harsh portions gives us the feeling that there is a way back. They just warn us what will happen if we are not faithful to G-d. If we sink that low, is there a way back?

But Nitzavim has the answer. No matter how low we, as a people and as individuals, may fall, there is t’shuva. Nitzavim also shows us the concept of free will. And other passages from Nitzavim give us a good feeling to carry into the new year.

There is more, so much more, but for now...

Shabbat Shalom.