Weekly Question Archive 11 - 20

Weekly Question Archive 11 - 20

by Remy Landau

Question 11

In which year or years of the 19 year Hebrew calendar cycle is Rosh Hashannah most likely to occur at its earliest point in the Gregorian year?


The clue to the answer can be found under the topic of the Calendar Drift in the Additional Notes.

The first Rosh Hashannah shown is that for 17H corresponding to Monday 11 August -3744g. The table also indicates that it was also the last occurrence of Rosh Hashannah on that date until 77,491H corresponding to Saturday 11 August 73,731g.

Closer to our times, the earliest Rosh Hashannah cannot occur any earlier than September 5. This coincidence last occurred for the year 5660H corresponding to Tuesday 5 September 1899g. It won't happen again until 5774H corresponding to Thursday 5 September 2013g. The whole of the 20th century missed out on a September 5 Rosh Hashannah!

Common to all these Hebrew years is that they are the 17th year of the 19 year cycle. In point of fact, it is the 17th year of the 19 year cycle that will most likely host the earliest possible Rosh Hashannah's. However, not all of those 17th years will see the earliest possible Gregorian date for the festival.

The Hebrew calendar cycle has a known repetition cycle that spans 689,472 years. Hence the molad of any one month is garanteed to occur on exactly the same year, month and day of the 19 year cycle exactly 689,472 years later. However, this does not imply that the time of any molad will not reoccur until then.

Question 12

What is the repetition cycle of the moladot?


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 most famous of the moladot, 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).

Question 13

After the molad of Tevet 29,340H when next will BaHaRaD occur?


There are 181,440 months in the cycle of the moladot.

Hence, the third cycle will require the elapsed time of

               181,440 * 3 = 544,320 months

There are 235 months in every cycle of 19 Hebrew years.

Hence there are 544,320 / 235 = 2316 cycles of 19 years in those moladot.

2316 * 235 = 544,260 months which is 60 short of the total.

Also, 2316 * 19 = 44004 years.

Consequently, the molad after the 3rd molad cycle will begin 60 months after Tishrei 44005H
(Mon 17 Mar 40245g).

Since 44005H is the first year in a 19 year cycle, we count the remaning months as follows

12 + 12 + 12 + 13 + 12 = 49 months with 11 left over.

This means that the molad following immediately after the 3rd molad cycle will be at the the end of the 11th month in the year 44009H.

Since 44009H is not a leap year, the date of the molad we are looking for is

the molad of Elul 44009H (Mon 21 Jan 42050g).

Question 14

At least what 3 calendar features do the years 5758H (1997/8g) and 5759H (1998/9g) have in common?

L'Shannah Tovah!

1. 5758H and 5759H are years 1 and 2 respectively of the current 304th 19 year cycle. Hence, these two years are both non-leap years. 5758H was 354 days long (regular) and 5759H is 355 days long (abundant).

2. The molad of Tishrei 5758H was at 5d 4h 129p. The molad of Tishrei 5759H
was at 2d 12h 1005p. Hence, neither of these two years had their starting day postponed.

3. The first day of Nisan 5758H fell on Sat 28 Mar 1998g while the first day of Nisan 5759H will fall on Thu 18 Mar 1999g. Since the first day of Nisan for both these years is in March, both these years exhibit the phenomenon of the Nisan Descent. The Nisan Descent is explained in the Additional Notes.

4. Both 5758H and 5759H started after the 16th day of September.

Question 15

What is the significance of September 16th to the Hebrew calendar?

L'Shannah Tovah!


At the present time the earliest that Rosh Hashannah can occur in the Gregorian calendar is September 5. The latest that Rosh Hashannah can occur in the Gregorian calendar is October 5.

In this interval, September 16 is the separating date between the Hebrew years that are leap and non-leap. Any Hebrew year that begins prior to September 16 is a leap year, that is a year of 13 months. Any Hebrew year that begins after September 16 is a non-leap year consisting of 12 months.

This great separating date is also subject to the Calendar Drift, which topic is discussed in the Additional Notes. So that, when Rosh Hashannah will begin no earlier than September 6, the separating date between the leap years and the non-leap years will become September 17. However, that won't actually happen for another 90 years or so.

The table below shows the Gregorian dates for Rosh Hashannah between the 60 years 5751H (1990g) and 5811H (2050g), and is ordered by day and month.

                5774H Thu  5 Sep 2013g =385d
                5755H Tue  6 Sep 1994g =384d
                5793H Mon  6 Sep 2032g =383d
                5763H Sat  7 Sep 2002g =385d
                5782H Tue  7 Sep 2021g =384d
                5801H Sat  8 Sep 2040g =383d
                5809H Tue  8 Sep 2048g =384d
                5752H Mon  9 Sep 1991g =385d
                5771H Thu  9 Sep 2010g =385d
                5779H Mon 10 Sep 2018g =385d
                5790H Mon 10 Sep 2029g =383d
                5798H Thu 10 Sep 2037g =385d
                5760H Sat 11 Sep 1999g =385d
                5787H Sat 12 Sep 2026g =385d
                5806H Tue 12 Sep 2045g =384d
                5768H Thu 13 Sep 2007g =383d
                5757H Sat 14 Sep 1996g =383d
                5776H Mon 14 Sep 2015g =385d
                5795H Thu 14 Sep 2034g =385d
                5803H Mon 15 Sep 2042g =385d
                5773H Mon 17 Sep 2012g =353d
                5811H Sat 17 Sep 2050g =355d
                5762H Tue 18 Sep 2001g =354d
                5792H Thu 18 Sep 2031g =354d
                5770H Sat 19 Sep 2009g =355d
                5781H Sat 19 Sep 2020g =353d
                5800H Mon 19 Sep 2039g =355d
                5751H Thu 20 Sep 1990g =354d
                5759H Mon 21 Sep 1998g =355d
                5778H Thu 21 Sep 2017g =354d
                5789H Thu 21 Sep 2028g =354d
                5808H Sat 21 Sep 2047g =353d
                5797H Mon 22 Sep 2036g =353d
                5805H Thu 22 Sep 2044g =355d
                5767H Sat 23 Sep 2006g =355d
                5786H Tue 23 Sep 2025g =354d
                5794H Sat 24 Sep 2033g =355d
                5756H Mon 25 Sep 1995g =355d
                5775H Thu 25 Sep 2014g =354d
                5783H Mon 26 Sep 2022g =355d
                5802H Thu 26 Sep 2041g =354d
                5764H Sat 27 Sep 2003g =355d
                5810H Mon 27 Sep 2049g =355d
                5753H Mon 28 Sep 1992g =353d
                5791H Sat 28 Sep 2030g =355d
                5772H Thu 29 Sep 2011g =354d
                5750H Sat 30 Sep 1989g =355d
                5761H Sat 30 Sep 2000g =353d
                5769H Tue 30 Sep 2008g =354d
                5780H Mon 30 Sep 2019g =355d
                5799H Thu 30 Sep 2038g =354d
                5807H Mon  1 Oct 2046g =355d
                5758H Thu  2 Oct 1997g =354d
                5788H Sat  2 Oct 2027g =355d
                5777H Mon  3 Oct 2016g =353d
                5785H Thu  3 Oct 2024g =355d
                5766H Tue  4 Oct 2005g =354d
                5796H Thu  4 Oct 2035g =354d
                5804H Mon  5 Oct 2043g =353d

It is to be noted that September 16 is missing from this table.

Question 16

How does September 16th fit into the leap and non-leap year separation pattern?


At the present time the earliest that Rosh Hashannah can occur in the Gregorian calendar is September 5. The latest that Rosh Hashannah can occur in the Gregorian calendar is October 5.

The first time that Rosh Hashannah began on October 5 was in 2089g. The last time that Rosh Hashanah will begin on September 5 will be in 2089g.

For the period extending from 5576H (1815g) to 5850H (2089g) Rosh Hashannah is seen to occur 10 times on September 16. In that time, exactly half the Hebrew years beginning on September 16 are leap years, while the remainder are non-leap years.

It is to be noted that during this period all of the leap years started on September 16 are 383 days long, while none of the common years are 353 days long.

                5583H Mon 16 Sep 1822g =355d
                5602H Thu 16 Sep 1841g =354d
                5632H Sat 16 Sep 1871g =383d
                5670H Thu 16 Sep 1909g =383d
                5746H Mon 16 Sep 1985g =383d
                5754H Thu 16 Sep 1993g =355d
                5765H Thu 16 Sep 2004g =383d
                5784H Sat 16 Sep 2023g =383d
                5830H Mon 16 Sep 2069g =355d
                5849H Thu 16 Sep 2088g =354d

Question 17

If your Hebrew calendar does not tell you the year length, is it possible to determine that length without doing any arithmetic?



There are 3 digits to the year length of which the first is always 3.

The second digit is either 5 or 8. If the calendar shows two months of Adar, then the year is a leap year and the second digit is 8. Otherwise that second digit is 5.

The 3rd digit is either 3, 4, or 5.

If the month of Heshvan has 30 days, then the 3rd digit is 5.

If the month of Kislev has 29 days, then that 3rd digit is 3.

Otherwise, the 3rd digit is 4.

Try this out on this year's calendar. The digits will be 3-5-5, that is, they will indicate a 355 day year, otherwise known as an abundant year.

In our times, we expect each and every Rosh Hashannah to occur in each and every Gregorian year of our lifetime, and possibly beyond.

Question 18

In the foreseeable future, will there ever be a Gregorian year without a Rosh Hashannah?


YES! Although that future will be quite distant!

Assuming that no changes take place to either the Gregorian or the Hebrew calendars, then Rosh Hashannah will NOT be observed during the year 22,335g.

This will be the first time that a Gregorian year will not host such an important holiday.

Rosh Hashannah 26,095H will fall on Thu 13 Dec 22,334g while the immediately following Rosh Hashannah 26,096H will occur on Thu 2 Jan 22,336g.

The topic on The Calendar Drift found in the Additional Notes fully explains why the 1st day of Tishrei eventually lands in the Gregorian month of December.

Question 19

In the foreseable future can 2 consecutive Rosh Hashannot ever begin in the same Gregorian year?


Correspondent Larry Padwa sent in the correct answer and said as follows:

The answer is yes, and it follows immediately from your reply to the previous question.

RH 26,096H falls on 2-Jan 22336g. Since 26096H (mod 19) = 9, 26096H is not a leap year and hence has at most 355 days. 355 days from 2-Jan falls in December of the same year, so RH 26096H and 26097H fall in the same Gregorian year.

Holding constant both the Hebrew and Gregorian calendars, it is possible to discover the occurrence of Gregorian years in which no Rosh Hashannah will occur. It is also possible to discover Gregorian years in which 2 Rosh Hashannot will be observed.

Question 20

In the foreseeable future, can 2 Gregorian years ever see the same Rosh Hashannah?


Correspondent Larry Padwa once again sent in a correct answer. Thank you Larry.

The calendar drift, discussed in the Additional Notes, shows that the Hebrew year moves into the Gregorian calendar at the rate of about one day in every 216 years.

Left unchecked by any changes to either calendar, it is then possible to predict the event of the first day of Rosh Hashannah on December 31. In that instance, the second day of the festivity will occur in the next Gregorian year.

The event of one Rosh Hashannah spanning 2 Gregorian years will then first be seen to occur for Saturday, 1 Tishrei 25716H (31 Dec 21955g).

The next major festival will be Pesach. Some traditions suggest that the Exodus took place on a Thursday in either the year 2448H (-1313g/-1312g) or 2449H (-1312g/-1311g).

For other Additional Notes click here.
For other Archived Weekly Questions click here.
Hebrew Calendar Science and Myths

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Remy Landau

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