interesting calendar phenomenon

So Pesach will tell us all other holidays, see SA O’CH 428,3 by using reverse aleph beis א’ת, ב’ש, ג’ד, ד’ק, ה’צ, ו’פ and פל’ג.

IyH b’karov (seems like pieces are falling into place)

Yabia Omer, the interesting phenomenon is this: There are 4 possible days of the week that the first day of Pesach can fall out on. 2022 – 2025 will be a four- year span where we have Pesach occurring on each of the four possible days.
It’s interesting to note that we had the same phenomenon during the years 2021 – 2024.
After 2025, the first day of Pesach won’t occur on Sunday again for approximately 20 years.

Reb Eliezer, that’s almost right.
When the first day of Pesach is on Shabbos, Shavuos will begin on a Sunday, not on a Tuesday.

Goldilocks, thank you for your correction. Shavuos is the day after Pesach (ב’ש) and not after Rosh Hashana.

During a non-leap year, Asara B’Teves will fall on the same day of the week as Purim.
During a leap year, Asara B’Teves will fall on the same day as the following Simchas Torah.

The climate changes through the seasons determined by the sun whereas Jewish holidays are determined through the moon. Pesach is spring and Sukkos fall time causes a Jewish leap year 7 times in 19 years in order that lunar year having normally 354 days and the solar year 365 1/4 days even itself out. The mnemonic is guchadzut, 3, 6, 8, 11, 14, 17, 19 year in 19 years becomes a Jewish leap year. A calendar is available in the Tur after siman 428 which enumerates each of the 19 years determined by Cheshvan and Kislev if they are deficient, both 29 days, full, both 30 days or even one 29 days and the other 30 days. The rest of the months cycle between 29 and 30 days. 6×29 + 6×30 = 174 + 180 = 354 days. The variation of the two months above causes the movement of Rosh Hashanah as Adu lo Rosh, the Rosh Hashanah cannot fall on Wednesday or Friday. Rosh Hashanah cannot be on a Sunday in order Hashanah Rabba should not fall on a shabbos eliminating the knocking off the hashanas and Yom Kippur should not be next to shabbos in order that there should not be two consecutive days where work is not allowed.

RE

“The variation of the two months above causes the movement of Rosh Hashanah as Adu lo Rosh”

Phrasing is backwards, Lo Adu Rosh (along with the other dechuyos) causes the variation of the two months.

ubi, you are right.

Goldilocks

Today you are!

It is all spelled out in Rambam Kidddush Hachodesh 7 wit hmefarshim there as well as end of hilchos Rosh chodesh in OC

first Tuesday- it is more common and a bit easier

The time between one molad and the next is 29 days 12 hours and 793 chalakim ( a chelek is 1/1080 of an hour which equal 3 and 1/3 seconds)

Since 28 days is 4 full weeks One month’s molad will occur 1 day 12 hours and 793 chalakim later in the week.
A regular year is of course 12 months, if you multiple 1 day 12 hours 793 by chalakim and remove full weeks)
You end up wit h4 days 8 hours 876 chalakim

Thus for example the molad Of Tishrei 5781 Was Thursday 20 hours 701 chalakim
If you add 4 days 8 hours 876 Chalaikm
you get molad tishrei 5782 which was Tuesday 5 hours 497 chalakim

Rosh Hashana 5781 was pushed off to Shabbos, since Molad occured after 18 hours (noon) and cant be Friday becasue Lo Adu Rosh
Rosh Hashana of this year 5782 was not pushed off and was on Tuesday, the day of the molad

However if the molad occurs on a tuesday after 9 hrs 204 chalakim (G”T”RD gimmel is 3 for tues tes 9 for 9 hours 204 chalakim) Then Rosh Hashana That year would be Tuesday
The next molad occurs 4 days 8 hours 876 Chalaikm later in the week Whci his Shabbos, 18 hours 0 chalaikm. This is molad Zaken pushed to Sunday then Pushed to Monday Because of the first 2 dechuyos)
A Year that begins on Tuesday and whose final day is Sunday is 356 days long this is too long (options are 354 if all months alternate 29/30, 353 if bot h chesvan Kislev have 29 and 355 if both have 30)
So we push off Rosh Hashana from Tuesday thursday

The monday Dechiya is rarer still, in fact it will not occur again until after 6000
The idea is the same except it comesu p after leap years

the difference between molad Tishrei before a leap year and after is 13 x (1-12-793) = 5 days 21 hrs 589 Chalakim

As mentioned Molad tishrei 5782 was Tuesday 5 hours 497 chalakim
NExt Year’s molad tishrei 5782 will be Monday 3 hrs 6 chalakim

However if Molad of year after leap year is on Monday 15 hrs 589 chalakim or later
The previous years’ molad was 5 days 21 hrs 589 Chalakim earlier whci his Tuesday 18 hours.

That Rosh hashana gets pushed off because molad zaken then lo adu Rosh to Thursday. If we keep the year after leap year on Monday the year is 382 days long this is too short options for leap year are 383 384 385 (regular year + 30) so we push off the year after leap year to tuesday

hope this helps

That is an 1/1080 of an hour.

answer to question 2 had some mistakes this is correct:

2) “Why can’t Chanukah start on Tuesday?”

for Chanuka to start on Tuesday You would need Rosh Hashana on Tuesday and the year “shalem” meaning that cheshvan and Kislev both have 30 days* In such a year 1 Kislev would be Shabbos 22 Kislev would be 3 week late on Shabbos, 23 sunday, 24 Monday 25 Tuesday.

However such a year is impossible a shalem year has 355 days if regular and 385 days for leap year
For a regular year Rosh Hashana would occur 355 days later ie 50 weeks and 5 days, which means Rosh Hashana would be Sunday – an impossibility
For a leap year Rosh Hashana would occur 385 days later ie after exactly 55 weeks. That would mean Rosh Hashana on Tuesday, while this is THEORETICLY possible, in reality it isnt becasue 2 Tuesdays back to back are impossible see Question 1

*It doesn’t matter how many days Kiselv has for this , but the choices are 29 for both Cheshvan and Kislev 29 for Cheshvan and 30 for Kislev or 30 for both. there is no possibility of 30 for Cheshvan and 29 for Kislev

@participant

Chanukah never falls out on Monday night going into Tuesday. It’s the only time it can never fall out.

Participant.

The Rambam at the end of Perek 7 of Kiddush Hachodesh writes that the reason for Lo Adu Rosh, is because the the calculated molad is an average and often the real molad falls later. The make up for this discrepency We keep one day and push off one day.

The Raavad argues and says the reason for Lo Adu Rosh is the morecoomnly given reason to avoid Y”K o sunday/Friday and hoshana Rabbah on shabbos. This is not mentioned by the Rambam.

R’ Chaim Kanievesky in his Shekel Hakodesh explains that the Rambam doesnt disagree that those are why Ad”u were the days chosen to push off. He is just explaining why it is pushed off at all. If the calculated molad was the real molad there would never be any dechuyos, since it is an average and is not accurate which requires occasional adjustments, we push off for these other reasons. Though still not arbitrary.

I don’t understand why maintaining a 29 day month is important? and what would be the driving factor to determine whether to keep 29 days or not? if every year was always 354 days alternating 29/30 It would quickly fall away from the molad ( the average molad is not 29.5 days it is 793 chalakim longer) and even from the seasons as the 19 year cycle wouldn’t fit either