When did all Rosh Hashannah's beginning on September 11 first become the start of ONLY Hebrew leap years?

The last Rosh Hashannah to coincide with the Gregorian date September 11 will begin on Tuesday 7142H (3381g).

Until then, all of the Rosh Hashannah's coinciding with the Gregorian date September 11 will mark the start of a Hebrew leap year.

The first time that a Hebrew leap year began on the Gregorian date of September 11 was Rosh Hashannah 4511H (750g).

But it wasn't until Rosh Hashannah 4614H (853g) that ONLY Hebrew leap years could begin on the Gregorian date of September 11.

The Saturday which immediately precedes the observance of Rosh Hodesh is known as
Shabbat M'Vorchim. On that particular Shabbat, during the synagogue services, it is customary to announce not only the coming of the new month, but also the specific time of the new month's molad.

Can the time of a molad precede the Shabbat M'Vorchim on which it is to be announced?

YES!

The Saturday which immediately precedes the observance of Rosh Hodesh is known as
Shabbat M'Vorchim. On that particular Shabbat, during the synagogue services, it is customary to announce not only the coming of the new month, but also the specific time of the new month's molad.

Correspondent Larry Padwa guessed at the correct answer based on the following opinion:-

I'm guessing on this one.

I believe that the answer is yes.

If Rosh Hashannah is postponed by two days from the Molad of Tishrei (because of the Dehiyyot), then the remaining months of the year are likely to begin a day or two following their Molad.

It should therefore be possible for a Rosh Hodesh which falls on a Sunday to have its Molad on the previous Friday (two days earlier). In this event, the Shabbat M'vorchim would refer to a Molad on the preceding day.

Thank you Larry Padwa for your response, which leads to the next question.

Is it nececessary that Rosh Hashannah be postponed so as to have a molad precede the Shabbat M'Vorchim on which its month is announced?

NO!

The Saturday which immediately precedes the observance of Rosh Hodesh is known as
Shabbat M'Vorchim. On that particular Shabbat, during the synagogue services, it is customary to announce not only the coming of the new month, but also the specific time of the new month's molad.

A molad can precede the Shabbat M'Vorchim on which its month is announced even though Rosh Hashannah is not postponed for that year. This particular phenomenon occurs in 1.18% of all the Hebrew years.

The most recent molad to occur prior to Shabbat M'Vorchim for a year in which Rosh Hashannah was not postponed was the molad of Sivan 5689H (Fri 7 Jun 1929g).

That molad arrived at 6d 19h 724p.

Rosh Hashannah 5760H will begin on Shabbat 11 September 1999g.

The molad of Tishrei 5760H is 6d 21h 801p, making that molad shy of a Shabbat arrival by 2h 279p.

The year 5760H will be a leap year consisting of 385 days. As a result, the following year 5761H will also begin on Shabbat!

What are at least 2 other Hebrew calendar phenomenae that will take place in the year 5760H?

1. Although it is the third year of the 304th mahzor katan (19 year cycle) the new Hebrew year 5760H is the FIRST LEAP year of that current mahzor katan.

2. The new year 5760H is also the FIRST Hebrew year in a set of 5 consecutive years
of which 4 begin on Shabbat.

3. The molad of Sivan 5760H will occur on Friday 2 Jun 2000g at 16h 21m 0hl, which is PRIOR to the Shabbat M'Vorchim announcing the month of Sivan whose first day will coincide with Sunday 4 Jun 2000g.

When next will 5 consecutive Hebrew years have 4 Rosh Hashannah's begin on Shabbat?

The next pattern of of 5 consecutive Hebrew years in which 4 out of 5 begin on Shabbat will not occur until Rosh Hashannah 5936H (Saturday 16 Sep 2175g).

The 5 Rosh Hashannah's are

5936H corresponding to Sat 16 Sep 2175g
5937H                  Sat  5 Oct 2176g
5938H                  Tue 23 Sep 2177g
5939H                  Sat 12 Sep 2178g
5940H                  Sat  2 Oct 2179g

Correspondent Winfried Gerum sent the following correct answer:

The next period with 4 out of 5 years beginning on Shabbat are the years 5936 through 5940.

Three consecutive years cannot all commence on Shabbat. Therefore, periods with 4 out of 5 years starting on Shabbat must have their 3rd year starting on some day other than Shabbat.

Thank you very much Winfried Gerum for sharing these observations with us.

Correspondent Larry Padwa also sent the following correct answer:

The next occurence of this will be in about 175 years. RH 5936 (Saturday 16-September 2175G) begins the next cycle.

Correspondent Dwight D. Blevins also noted that 247 years separated the last such occurrence from the next one.

[Nearest to 5760H] When will 4 out of 5 consecutive Yom Kippur's be observed on Shabbat?

These are the nearest 5 consecutive Yom Kippur's in which 4 are to be observed on Shabbat:-

5771H corresponding to Sat 18 Sep 2010g
5772H                  Sat  8 Oct 2011g
5773H                  Wed 26 Sep 2012g
5774H                  Sat 14 Sep 2013g
5775H                  Sat  4 Oct 2014g

It is to be noted that Yom Kippur 5774H (2013g) will be observed on the earliest possible Gregorian date now available to the holiday.

In the full Hebrew calendar cycle of 689472 years, which molad of Tishrei will be the first to be repeated as a molad of Tishrei?

The time of any molad is usually given as day, hour, minute and part.

There are 24*60*1080 = 25,920 parts in one day.

Hence there are 7*25920 = 181,440 parts in one week.

Since there are no common factors between 7 and 25920 we must go for 7*25920 = 181,440 months before the time of a given molad is repeated.

For example, the molad of Tishrei 1H, BaHaRad, will return as the molad of Sivan 14,670H (Mon 23 Jun 10,910g) and again 181,440 months later as the molad of Tevet 29,340H (Mon 7 Apr 25,580g).

BaHaRad will not be repeated as a molad of Tishrei until 117,358H (Mon 4 Jan 113,599g) .

By one of these delightful coincidences, in the full Hebrew calendar cycle of 689472 years, BaHaRad is also the very first molad of Tishrei that will be repeated as a molad of Tishrei.

In the full Hebrew calendar cycle of 689472 years, how often do the moladot of Tishrei repeat themselves?

The time of any molad is usually given as day, hour, minute and part.

There are 24*60*1080 = 25,920 parts in one day.

Hence there are 7*25,920 = 181,440 parts in one week.

Since there are no common factors between 7 and 25,920 we must go for 7*25920 = 181,440 months before the time of a given molad is repeated.

Since there are only 181,440 possible values for the moladot, the average number of times that any molad of Tishrei can be repeated is 689,472 / 181,440 = 3.8 repetitions.

In the full Hebrew calendar cycle of 689472 years, any molad of Tishrei is repeated either exactly 3 times or exactly 4 times.

For example, the molad of Tishrei 1H, BaHaRad, (Monday, September 7, -3760g) is repeated 4 times in the full Hebrew calendar cycle. That molad will next occur for the following Hebrew years

What fraction of the moladot of Tishrei are repeated exactly 3 times in the full Hebrew calendar cycle of 689,472 years?

The moladot of Tishrei can be repeated either exactly 3 times or exactly 4 times in the full Hebrew calendar cycle of 689,472 years.

There are 181,440 possible values for the moladot of Tishrei and all are represented at least 3 times in the full Hebrew calendar cycle.

Let T = the number of moladot that are repeated exactly 3 times
Let F = the number of moladot that are repeated exactly 4 times
Then

  T +   F = 181,440 (the total number of possible moladot)
3*T + 4*F = 689,472 (the number of moladot of Tishrei in the full cycle)

Hence,   T = 36,288 which = 1/19 of 689,472
And    3*T = 98,064 which = 3/19 of 689,472

Correspondent Moshe Alfred Silberman sent the following very interesting observations.

I enjoy your page dealing with the calendar very much.

I have a question regarding your statement about the Molad always occurring
prior to the second of the month. I will present the following assumptions
and calculations and please tell me where I am wrong.

1. Rosh Hashana is Thursday/Friday.
2. Molad is on Thursday @ 17:59 Jewish time (which is 11:59AM according to
our clocks). This would be the latest that it can occur befor Dechiya # 2
kicks in.
3. Year has 354 days and runs regular.

1.	Tishrei                 	Rosh Chodesh = Thu
Molad = Thu   @ 18 + 000   Chalakim (- 1 minute)
2.     MarCheshvan		Rosh Chodesh = Fri / Sat	Molad = Sat
@ 06 + 793   Chalakim (- 1 minute)
3.	Kislev			Rosh Chodesh = Sun		Molad = Sun
@ 19 + 506   Chalakim (- 1 minute)
4.	Teves			Rosh Chodesh = Mon / Tue	Molad = Tue
@ 08 + 219   Chalakim (- 1 minute)
5.	Shevat			Rosh Chodesh = Wed		Molad = Wed
@ 20 + 1012 Chalakim (- 1 minute)
6.	Adar				Rosh Chodesh = Thu / Fri
Molad = Fri     @ 09 +725    Chalakim (- 1 minute)
7.	Nissan			Rosh Chodesh = Sat		Molad = Sat
@ 22 + 438   Chalakim (- 1 minute)
8.	Iyar				Rosh Chodesh = Sun / Mon
Molad = Mon   @ 11 + 151  Chalakim (- 1 minute)
9.	Sivan			Rosh Chodesh = Tue		Molad = Tue
@ 23 + 944   Chalakim (- 1 minute)
10.	Tammuz			Rosh Chodesh = Wed / Thu	Molad = Thu
@ 12 + 657   Chalakim (- 1 minute)
 11.     Av                              Rosh Chodesh = Fri
Molad = Fri     @ 25 + 370   Chalakim (- 1 minute) 
12.	Elul				Rosh Chodesh = Sat / Sun
Molad = Sun  @ 14 + 83     Chalakim (- 1 minute)

Correspondent Moshe Alfred Silberman has put forward a very good paradox which appears to refute the fact that Dehiyyah Molad Zaqen solves the Overpost Problem.

How does Silberman's Paradox fail to disprove the fact that Dehiyyah Molad Zaqen solves the Overpost Problem?

Correspondent Moshe Alfred Silberman sent the following very interesting observations.

1. Rosh Hashana is Thursday/Friday.
2. Molad is on Thursday @ 17:59 Jewish time (which is 11:59AM according to
our clocks). This would be the latest that it can occur befor Dechiya # 2
kicks in.
3. Year has 354 days and runs regular.

1.	Tishrei                 	Rosh Chodesh = Thu
Molad = Thu   @ 18 + 000   Chalakim (- 1 minute)
2.     MarCheshvan		Rosh Chodesh = Fri / Sat	Molad = Sat
@ 06 + 793   Chalakim (- 1 minute)
3.	Kislev			Rosh Chodesh = Sun		Molad = Sun
@ 19 + 506   Chalakim (- 1 minute)
4.	Teves			Rosh Chodesh = Mon / Tue	Molad = Tue
@ 08 + 219   Chalakim (- 1 minute)
5.	Shevat			Rosh Chodesh = Wed		Molad = Wed
@ 20 + 1012 Chalakim (- 1 minute)
6.	Adar				Rosh Chodesh = Thu / Fri
Molad = Fri     @ 09 +725    Chalakim (- 1 minute)
7.	Nissan			Rosh Chodesh = Sat		Molad = Sat
@ 22 + 438   Chalakim (- 1 minute)
8.	Iyar				Rosh Chodesh = Sun / Mon
Molad = Mon   @ 11 + 151  Chalakim (- 1 minute)
9.	Sivan			Rosh Chodesh = Tue		Molad = Tue
@ 23 + 944   Chalakim (- 1 minute)
10.	Tammuz			Rosh Chodesh = Wed / Thu	Molad = Thu
@ 12 + 657   Chalakim (- 1 minute)
 11.     Av                              Rosh Chodesh = Fri
Molad = Fri     @ 25 + 370   Chalakim (- 1 minute) 
12.	Elul				Rosh Chodesh = Sat / Sun
Molad = Sun  @ 14 + 83     Chalakim (- 1 minute)

Correspondent Moshe Alfred Silberman has put forward a very good paradox which appears to refute the fact that Dehiyyah Molad Zakein solves the Overpost Problem.

However, the weakness of the demonstration lies in the fact that the molad of Tishrei of any 354 day year cannot be more than 9h 203p on either Tuesday or Thursday.

Let R = start day of Rosh Hashannah for Hebrew year H
Let R' = start day of Rosh Hashannah for Hebrew year H + 1
Then R' - R = 354 days

Let t = time of molad of Tishrei for year H
Let t' = time of molad of Tishrei for year H + 1

Then R + t + 354d 8h 876p = R' + t'
     t = R' - R - (354d 8h 876p) + t'
     t = t' - (8h 876p)

Since the maximum value for t' is 17h 1079p on day R'
the maximum value for t = (17h 1079p) - (8h 876p) = 9h 203p

Some correspondents did not see the coincidence, and suggested this result to be a perfectly logical consequence of the fact that BaHaRaD is the first molad of Tishrei in the full Hebrew calendar cycle.

If that is the case, then the 2nd molad of Tishrei in the full Hebrew calendar cycle should be the 2nd molad of Tishrei to be repeated.

 First  Begun 21 Jun 1998 
First  Paged  5 Nov 2004
Next Revised  5 Nov 2004