Editing Hebrew calendar (section)

===Rosh Hashanah postponement rules===
Besides the adding of leap months, the year length is sometimes adjusted by adding one day to the month of Marcheshvan, or removing one day from the month of Kislev. Because each calendar year begins with [[Rosh Hashanah]], adjusting the year length is equivalent to moving the day of the next Rosh Hashanah. Several rules are used to determine when this is performed.

To calculate the day on which Rosh Hashanah of a given year will fall, the expected [[molad]] (moment of [[lunar conjunction]] or [[new moon]]) of Tishrei in that year is calculated. The molad is calculated by multiplying the number of months that will have elapsed since some (preceding) molad (whose weekday is known) by the mean length of a (synodic) lunar month, which is 29 days, 12 hours, and 793 parts (there are 1080 "parts" in an hour, so that one part is equal to {{frac|3|1|3}} seconds). The very first molad, the [[#Anno Mundi|molad tohu]], fell on Sunday evening at 11:11:20&nbsp;pm in the local time of [[Jerusalem]],<ref name=Tondering>{{cite web |url=https://www.tondering.dk/claus/cal/hebrew.php#newmoon |title=Calendar FAQ: the Hebrew calendar: New moon |first1=Trine |last1=Tøndering |first2= Claus |last2=Tøndering}}</ref>{{efn|UTC+02:20:56.9}} 6 October 3761 BCE ([[Proleptic Julian calendar]]) 20:50:23.1 [[Coordinated Universal Time|UTC]], or in Jewish terms Day 2, 5 hours, and 204 parts. The exact time of a molad in terms of days after midnight between 29 and 30 December 1899 (the form used by many spreadsheets for date and time) is
:-2067022+(23+34/3/60)/24+(29.5+793/1080/24)*''N''
where ''N'' is the number of lunar months since the beginning. ({{nowrap|''N'' {{=}} 71440}} for the beginning of the 305th Machzor Katan on 1 October 2016.) Adding 0.25 to this converts it to the Jewish system in which the day begins at 6&nbsp;pm.

In calculating the number of months that will have passed since the known molad that one uses as the starting point, one must remember to include any leap months that falls within the elapsed interval, according to the cycle of leap years. A 19-year cycle of 235 synodic months has 991 weeks 2 days 16 hours 595 parts, a common year of 12 synodic months has 50 weeks 4 days 8 hours 876 parts, while a leap year of 13 synodic months has 54 weeks 5 days 21 hours 589 parts.

Four conditions are considered to determine whether the date of Rosh Hashanah must be postponed. These are called the Rosh Hashanah postponement rules, or {{lang|he-Latn|deḥiyyot}}.<ref name=Ibbur>{{cite book|title=Sefer ha-Ibbur |volume= 2|chapter= 9,10 |author=R. Avraham bar Chiya ha-nasi |oclc=729982627 |date=1851 |language=he |location=London}}</ref><ref name=Tur>{{cite book|title=Tur, Orach Chaim ''(section 428)''|url=https://he.wikisource.org/wiki/%D7%98%D7%95%D7%A8_%D7%90%D7%95%D7%A8%D7%97_%D7%97%D7%99%D7%99%D7%9D_%D7%AA%D7%9B%D7%97}}</ref><ref name=HKC>{{cite book|author=Rambam|title=Hilchos Kiddush ha-Chodesh (chapters 6, 7, 8)|url=https://he.wikisource.org/wiki/%D7%A8%D7%9E%D7%91%22%D7%9D_%D7%94%D7%9C%D7%9B%D7%95%D7%AA_%D7%A7%D7%99%D7%93%D7%95%D7%A9_%D7%94%D7%97%D7%95%D7%93%D7%A9_%D7%95}}</ref><ref name=Feldman>{{cite book|author=W. M. Feldman|title=Rabbinical Mathematics and Astronomy|edition=2nd|publisher=Hermon Press|date=1965|chapter=Chapter 17: The Fixed Calendar}}</ref><ref name=Mandelbaum>{{cite book|author=Hugo Mandelbaum|chapter=Introduction: Elements of the Calendar Calculations|editor=Arthur Spier|title=The Comprehensive Hebrew Calendar|edition=3rd|date=1986}}</ref> The two most important conditions are:

*If the molad occurs at or later than noon, Rosh Hashanah is postponed a day. This is called {{lang|he-Latn|deḥiyyat molad zaken}} ({{lang|he|דְחִיַּת מוֹלָד זָקֵן}}, literally, "old birth", i.e., late new moon). This rule is mentioned in the Talmud,<ref name="epstein"/> and is used nowadays to prevent the molad falling on the second day of the month.<ref>{{cite web|last=Landau|first=Remy|url=http://hebrewcalendar.tripod.com/#25|title=Hebrew Calendar Science and Myth: 'The Debatable Dehiyah Molad Zaquen'|access-date=7 February 2015}}</ref> This ensures that the long-term average month length is 29.530594 days (equal to the molad interval), rather than the 29.5 days implied by the standard alternation between 29- and 30-day months.
*If the molad occurs on a Sunday, Wednesday, or Friday, Rosh Hashanah is postponed a day. If the application of {{lang|he-Latn|deḥiyyah molad zaken}} would place Rosh Hashanah on one of these days, then it must be postponed a second day. This is called {{lang|he-Latn|deḥiyyat lo ADU}} ({{lang|he|דְחִיַּת לֹא אד״ו}}), an acronym that means "not [weekday] one, four, or six".
:This rule is applied for religious reasons, so that [[Yom Kippur]] does not fall on a Friday or Sunday, and [[Hoshana Rabbah]] does not fall on [[Shabbat]].{{efn|This is the reason given by most [[halachic]] authorities, based on the [[Talmud]], Rosh Hashanah 20b and Sukkah 43b. [[Maimonides]] ([[Mishneh Torah]], Kiddush Hachodesh 7:7), however, writes that the arrangement was made (possible days alternating with impossible ones) in order to average out the difference between the mean and true [[lunar conjunction]]s.}} Since Shabbat restrictions also apply to Yom Kippur, if either day falls immediately before the other, it would not be possible to make necessary preparations for the second day (such as [[Shabbat candles|candle lighting]]).{{efn|The Talmud (Rosh Hashanah 20b) puts it differently: over two consecutive days of full Shabbat restrictions, vegetables would wilt (since they can't be cooked), and unburied corpses would putrefy.}} Additionally, the laws of Shabbat override those of Hoshana Rabbah, so that if Hoshana Rabbah were to fall on Shabbat, the Hoshana Rabbah ''aravah'' ritual could not be performed.<ref>Yerushalmi, [https://www.sefaria.org/Jerusalem_Talmud_Sukkah.4.1.3 Sukkah 4:1] (18a, 54b)</ref>
:Thus Rosh Hashanah can only fall on Monday, Tuesday, Thursday, and Saturday. The ''kevi'ah'' uses the letters ה ,ג ,ב and ז (representing 2, 3, 5, and 7, for Monday, Tuesday, Thursday, and Saturday) to denote the starting day of Rosh Hashana and the year.

Another two rules are applied much less frequently and serve to prevent impermissible year lengths. Their names are Hebrew acronyms that refer to the ways they are calculated:
* If the molad in a common year falls on a Tuesday, on or after 9 hours and 204 parts, Rosh Hashanah is postponed to Thursday. This is {{lang|he-Latn|deḥiyyat GaTaRaD}} ({{lang|he|דְחִיַּת גטר״ד}}, where the acronym stands for "3 [Tuesday], 9, 204").
* If the molad following a leap year falls on a Monday, on or after 15 hours and 589 parts after the Hebrew day began (for calculation purposes, this is taken to be 6&nbsp;pm Sunday), Rosh Hashanah is postponed to Tuesday. This is {{lang|he-Latn|deḥiyyat BeTUTeKaPoT}} ({{lang|he|דְחִיַּת בט״ו תקפ״ט}}), where the acronym stands for "2 [Monday], 15, 589".