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Hebrew calendar

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The Hebrew calendar (Hebrew: הלוח העברי‎) or Jewish calendar is a lunisolar calendar used by Jews for predominantly religious purposes. It is used to reckon the Jewish New Year and dates for Jewish holidays, and also to determine appropriate public reading of Torah portions, Yahrzeits (dates to commemorate the death of a relative), and daily Psalm reading, among many ceremonial uses. Originally the Hebrew calendar was used by Jews for all daily purposes, but by the era of the Roman occupation (1st century BCE), Jews followed the imperial civil calendar for all civic matters, such as the payment of taxes and dealings with government officials.

The principles of the Hebrew calendar are found in the Torah, which contains several calendar-related commandments, including God's commandment during the Exodus from Egypt to fix the month of Nisan as the first month of the year. The Babylonian exile in the 6th century BCE influenced the calendar, including the adoption of Babylonian names for the months.

Before the destruction of the Second Temple in 70 CE, the calendar was observational, with the beginning of each month determined by the testimony of witnesses who had observed a new crescent moon. Between 70 and 1178 CE a rule-based fixed-arithmetic lunisolar calendar system was adopted to achieve the same effect. The principles and rules of the current calendar were fully described by Maimonides in 1178 CE in the Mishneh Torah.

Because of the roughly eleven-day difference between twelve lunar months and one solar year, the year lengths of the Hebrew calendar vary in a repeating 19-year Metonic cycle of 235 lunar months, with an intercalary lunar month added every two or three years, for a total of 7 times per 19 years. Seasonal references in the Hebrew calendar reflect its development in the region east of the Mediterranean Sea and the times and climate of the Northern Hemisphere. With respect to the present-day mean solar year, the Hebrew calendar's year is longer by about 6 minutes and 25+25/57 seconds, meaning that every 224 years, the Hebrew calendar will fall a full day behind the modern fixed solar year, and about every 231 years it will fall a full day behind the Gregorian calendar year. This is due to the 0.6 second discrepancy between the calendric " Molad" (lunar conjunction interval), which is fixed by Jewish Law, and the actual mean lunar conjunction interval, which itself is slowly changing over time.

Years in the Hebrew calendar are labeled with the era designation Anno Mundi (Latin: "in the year of the world", abbreviated AM or A.M.) and are numbered from the epoch approximately a year before Creation. The current Hebrew calendar year is 5768.


The Jewish calendar is a lunisolar calendar, or "fixed lunar year," based on twelve lunar months of twenty-nine or thirty days, with an intercalary lunar month added seven times every nineteen years (once every two to three years) to synchronize the twelve lunar cycles with the slightly longer solar year. Each Jewish lunar month starts with the new moon; although originally the new lunar crescent had to be observed and certified by witnesses, the timing of the new moon is now mathematically determined.

Concurrently there is a weekly cycle of seven days, mirroring the seven day period of the Book of Genesis in which the world is created. The names for the days of the week, like those in the Creation story, are simply the day number within the week, with Shabbat being the seventh day. The Jewish day runs from sunset to the next sunset, and accordingly, standard times and time zones have no place in the Jewish calendar.

The twelve regular months are: Nisan (30 days), Iyar (29 days), Sivan (30 days), Tammuz (29 days), Av (30 days), Elul (29 days), Tishrei (30 days), Cheshvan (29 or 30 days), Kislev (29 or 30 days), Tevet (29 days), Shevat (30 days), and Adar (29 days). In the leap years an additional month, Adar I (30 days) is added after Shevat, and the regular Adar is referred to as "Adar II".

The first month of the year is Nisan. The 14th of Nisan is the start of the festival of Pesach, corresponding to the full moon of Nisan. Though it is not expressly prescribed in these terms, Pesach is a spring festival, so the 14th of Nisan is the first full moon after the vernal equinox. Therefore, from the standpoint of determining the annual calendar cycle, the principal problem is that the lunar month/new moon of Nisan must occur before the spring equinox. Since at least the 12th Century, the Hebrew calendar has determined this time mathematically, but prior to this tradition held that the 1st of Nisan does not start (and an intercalary month would be added) until the barley is ripe.

While the bible designates this month (without calling it Nisan) as the first month of the year, Rosh Hashanah, which is literally "The Head of the Year", meaning "The Beginning of the Year", is actually celebrated on the first of the seventh month, currently called Tishrei, so most Jews today view Tishrei as the de facto beginning of the year. Although there are references to this holiday in the Torah, it was not then regarded as the beginning of the year, but more as a Holiday for reflection and remembrance.

Change to a calculated calendar

Observational principles

A stone (2.43x1 m) with Hebrew inscription "To the Trumpeting Place" is believed to be a part of the Second Temple.

In Second Temple times (c. 518 BCE – 70 CE), the Hebrew calendar operated on an observational basis. The beginning of each lunar month was decided on the basis of two eye witnesses testifying to the Sanhedrin to having seen the new lunar crescent at sunset. Patriarch Gamaliel II (c. 100) would ask the witnesses to select the appearance of the moon from a collection of drawings that depicted the crescent in a variety of orientations, only a few of which could be valid in any given month. According to tradition, these observations were compared against calculations made by the Sanhedrin. When thirty days elapsed since the last new moon, the witnesses were readily believed.

At first the beginning of each Jewish month was signaled to the communities of Israel and beyond by fires lit on mountaintops, but after the Samaritans and Boethusians began to light false fires, messengers were sent. The inability of the messengers to reach communities outside Israel before mid-month High Holy Days ( Succot and Passover) led outlying communities to celebrate scriptural festivals for two days rather than one, observing the second feast-day of the Jewish diaspora because of uncertainty of whether the previous month ended after 29 or 30 days.

Transitional period

In Rome the Arch of Titus still stands, depicting the enslaved Judeans and objects from the Temple being brought to Rome.

The destruction of the Second Temple in 70 CE and the general disruption of Jewish communal life after the Jewish-Roman Wars of 66–73, 115–117, and 132–135, caused major disruptions in Jewish life. It also disrupted the calendar. During the third and fourth centuries, Christian sources describe the use of eight, nineteen, and 84 year lunisolar cycles by Jews, all linked to the civil calendars used by various communities of Diaspora Jews, which were effectively isolated from Levant Jews and their calendar. Some assigned major Jewish festivals to fixed solar calendar dates, whereas others used epacts to specify how many days before major civil solar dates Jewish lunar months were to begin. The Talmud notes the irregular intercalation (adding of extra months) performed in three successive years in the early second century. The Ethiopic Christian computus (used to calculate Easter) describes in detail a Jewish calendar which must have been used by Alexandrian Jews near the end of the third century. These Jews formed a relatively new community in the aftermath of the annihilation (by murder or enslavement) of all Alexandrian Jews by Emperor Trajan at the end of the 115–117 Kitos War. Their calendar used the same epacts in nineteen year cycles that were to become canonical in the Easter computus used by almost all medieval Christians, both those in the Latin West and the Hellenist East. Only those churches beyond the eastern border of the Byzantine Empire differed, changing one epact every nineteen years, causing four Easters every 532 years to differ.

The period 70 to 1178 saw a gradual transition from an observation based calendar to a mathematically calculated one. Except for the epoch year number, the calendar rules reached their current form before 820 or 921, with some uncertainty regarding when.

If one back-calculates the moments of the traditional moladot using modern astronomical calculations then the closest that their reference meridian of longitude ever got to Israel was midway between the Nile River and the end of the Euphrates River (about 4° east of Jerusalem), and that was in the era of the Second Temple.

From the times of the Amoraim (third to fifth centuries), calculations were increasingly used, for example by Samuel the astronomer, who stated during the first half of the third century that the year contained 365 ¼ days, and by "calculators of the calendar" circa 300. Jose, an Amora who lived during the second half of the fourth century, stated that the feast of Purim, 14 Adar, could not fall on a Sabbath nor a Monday, lest 10 Tishrei (Yom Kippur) fall on a Friday or a Sunday. This indicates a fixed number of days in all months from Adar to Elul, also implying that the extra month was already a second Adar added before the regular Adar.

Under the patriarchate of Rabbi Judah III (300-330 CE) the testimony of the witnesses with regard to the appearance of the new moon was received as a mere formality, the settlement of the day depending entirely on calculation. This innovation seems to have been viewed with disfavor by some members of the Sanhedrin, particularly Rabbi Jose, who wrote to both the Babylonian and the Alexandrian communities, advising them to follow the customs of their fathers and continue to celebrate two days, an advice which was followed, and is still followed, by the majority of Jews living outside of Israel.

Traditionally, intercalations were determined at meetings of a special calendar commission of the Sanhedrin. But Constantius II, following the precedents of Hadrian, prohibited the holding of such meetings. However, the Jewish community outside the land of Israel depended on the calendar sanctioned by the Judean Sanhedrin for the proper observance of the Jewish holidays. However, danger threatened the participants in that sanction and the messengers who communicated their decisions to distant congregations. Temporarily, to relieve the foreign congregations, Huna ben Abin once advised Rava not to wait for the official intercalation:

When you are convinced that the winter quarter will extend beyond the sixteenth day of Nisan declare the year a leap year, and do not hesitate ( R. H. 21a).

There is a popular tradition, first mentioned by Hai Gaon (d.1038 CE), that as religious persecutions continued, Patriarch Hillel II determined to provide an authorized mathematically-based calendar for all time to come, though by so doing he severed the ties which united the Jews of the diaspora to their mother country and to the patriarchate. It is recorded that the calendar was adopted at a clandestine, and maybe final, meeting of the Sanhedrin in 358, marking the last universal decision made by that body.

This explanation has been questioned. It is noted that the Talmud, which did not reach its final form until c. 500, does not mention the continuous calendar or even anything as mundane as either the nineteen-year cycle or the length of any month, despite discussing the characteristics of earlier calendars, suggesting the final form of the modern calendar was fixed subsequent to the sixth century.

Furthermore, Jewish dates during post-Talmudic times (specifically in 506 and 776) are impossible using modern rules, and all evidence points to the development of the arithmetic rules of the modern calendar in Babylonia during the times of the Geonim (seventh to eighth centuries), under the Abbasid Caliphate. The Babylonian rules required the delay of the first day of Tishrei when the new moon occurred after noon.

Epoch year

One notable difference between the calendar of that era and the modern form was the date of the epoch (the fixed reference point at the beginning of year 1), which at that time was one year later than the epoch of the modern calendar.

Codification of rules

Most of the present rules of the calendar appear to have been in place by about 820, according to a treatise by the Muslim astronomer Muḥammad ibn Mūsā al-Ḵwārizmī (c. 780-850 CE) a Persian polymath noted for his contributions to Islamic mathematics, Islamic astronomy, Islamic astrology and geography. Al-Khwārizmī's study of the Jewish calendar, Risāla fi istikhrāj taʾrīkh al-yahūd "Extraction of the Jewish Era" describes the 19-year intercalation cycle, the rules for determining on what day of the week the first day of the month Tishrī shall fall, the interval between the Jewish era (creation of Adam) and the Seleucid era, and the rules for determining the mean longitude of the sun and the moon using the Jewish calendar.

In 921, Aaron ben Meir proposed changes to the calendar. Though the proposals were rejected, it indicates that all of the rules of the modern calendar (except for the epoch) were in place before that date. In 1000, the Muslim chronologist al-Biruni described all of the modern rules of the Hebrew calendar, except that he specified three different epochs used by various Jewish communities being one, two, or three years later than the modern epoch.

Finally, in 1178, Maimonides, in his work Mishneh Torah, described all of the modern rules and their scriptural basis, including the modern epochal year. Maimonides showed analytically how the scriptural procedure for determining the calendar must be flawed, something he could explain through his faith. He noted that non-Jewish savants had presented mathematically correct methods of calculating the potential visibility of the new crescent, and reasoned that since these methods exist, they must have been used by the Sanhedrin and the record of their use lost.


Measurement of month

Animation of the Moon as it cycles through its phases, as seen from the Northern Hemisphere. The apparent wobbling of the Moon is known as libration.
Synodic month

A synodic month (known in Hebrew as a " molad") is a scientifically defined lunar conjunction based on the position of the moon in the lunar orbit. It equals exactly 765433/25920 days, or 29 days, 12 hours, and 793 parts (44+1/18 minutes) (ie 29.5306 days). This interval matches the mean synodic month determined by the Babylonians before 300 BCE and as adopted by the Greek astronomer Hipparchus and the Alexandrian astronomer Ptolemy. Its remarkable accuracy is thought to have been achieved using records of lunar eclipses from the eighth to fifth centuries BCE, with a reference meridian midway between the Nile River and the end of the Euphrates River, about 4° east of Jerusalem.

Traditional new moon

A "new moon" is the day on which the first visible crescent of the moon is observed. It occurs 29 or 30 days after the preceding visible crescent and traditionally signaled the start of a Jewish lunar month.

Combining the observation method with the scientific lunar month length works as follows. Assume one begins at a particular new month of 29 days. As the mean lunar month is 29.5306 days long, there would be a carry forward into the next month of 0.5306 days (ie 12 hours, 44+1/18 minutes). Adding that carry forward amount to the next month will make it equal 30.0612 days (30 days, 1 hour and 24+2/18 minutes). So the second month would be 30 days long, and 0.0612 days (or 1 hour 24+2/18 minutes) would be carried forward to be added to the next cycle, and so on. Then every 17 lunar months the carry forward amounts would exceed 24 hours (0.0612 x 17 = 1.0404), which would require an additional day to be added to that month. In summary, the progression becomes: year 1 | 29 – 30 – 29 – 30 – 2930 – 29 – 30 – 29 – 30 – 29 – 30 | year 2 | 29 – 30 – 29 – 30 – 3029 – etc.

Pattern of calendar years

The Jewish calendar is based on the Metonic cycle of 19 years, of which 12 are common years (12 months) and 7 leap years (13 months). A Metonic cycle equates to 235 lunar months in each 19-year cycle. This gives an average of 6939 days, 16 hours and 595 parts for each cycle.

But due to the Rosh HaShanah postponement rules (see below), a cycle of 19 Jewish years can be either 6939, 6940, 6941, or 6942 days in duration. Since none of these values is evenly divisible by seven, the Jewish calendar repeats exactly only following 36,288 Metonic cycles, or 689,472 Jewish years. There is a near-repetition every 247 years, except for an excess of 50 minutes (905 parts).

There are 14 different patterns that Jewish years may take. Each of these patterns is called a "keviyah" (Hebrew for "a setting" or "an established thing"), and is distinguished by the day of the week for Rosh Hashanah of that particular year and by that particular year's length.

A Jewish non-leap year can only have 353, 354, or 355 days. A leap year can have 383, 384, or 385 days (always 30 days longer than the non-leap length).

  • A chaserah year (Hebrew for "deficient" or "incomplete") is 353 or 383 days long. Both Kislev and Cheshvan have 29 days. The Hebrew letter ח "het", and the letter for the weekday denotes this pattern.
  • A kesidrah year ("regular" or "in-order") is 354 or 384 days long. Kislev has 29 days and Cheshvan has 30 days. The Hebrew letter כ "kaf", and the letter for the week-day denotes this pattern.
  • A shlemah year ("abundant" or "complete") is 355 or 385 days long. Both Kislev and Cheshvan have 30 days. The Hebrew letter ש "shin", and the letter for the week-day denotes this pattern.

Determining leap years

The Jewish leap years are years 3, 6, 8, 11, 14, 17, and 19 of the Metonic cycle. To determine whether a year is a leap year, find the remainder when dividing the Jewish year number by 19. If the remainder is 3, 6, 8, 11, 14 or 17, the year is a leap year and an extra month, Adar II, is added. If the remainder is zero, the year is also a leap year since year 19 of the Metonic cycle is a year exactly divisible by 19. Another way to check a specific year is to find the remainder in the following calculation: ( 7 x the Jewish year number + 1 ) / 19. If the remainder is less than 7, the year is a leap year.

A mnemonic word in Hebrew is GUCHADZaT "גוחאדז"ט" (the Hebrew letters gimel-vav-het aleph-dalet-zayin-tet, i.e. 3, 6, 8, 1, 4, 7, 9. See Hebrew numerals). A variant of this pattern of naming includes another letter which specifies the day of the week for the first day of Pesach (Passover) in the year.

Another memory aid notes that intervals of the major scale follow the same pattern as do Jewish leap years, with do corresponding to year 19 (or 0): a whole step in the scale corresponds to two common years between consecutive leap years, and a half step to one common year between two leap years.

Special holiday rules

Adjustments are needed to ensure certain holy days and festivals do or do not fall on certain days of the week in the coming year.

Rosh Hashanah postponement rules
Day of week Number of days
Monday 353 355 383 385
Tuesday 354 384
Thursday 354 355 383 385
Saturday 353 355 383 385

Although simple math would calculate 21 patterns for calendar years, there are other limitations which mean that the first day of Rosh Hashanah, Sukkot and Shmini Atzeret (which all occur on the same day of the week in any given year) may only occur on Mondays, Tuesdays, Thursdays, and Saturdays (the "four gates"), according to the table.

That means that the pattern can be varied to ensure that Rosh Hashanah does not fall on the other 3 days. This is to ensure that Yom Kippur does not directly precede or follow Shabbat, which would create practical difficulties, and that Hoshana Rabbah is not on a Shabbat, in which case certain ceremonies would be lost for a year.

Yom Kippur

Yom Kippur, on which no work can be done, can never fall on Friday (the day prior to the Sabbath), or on Sunday (the day after Shabbat) to avoid having the previous day's restrictions still going on at the start of Sabbath, or the restrictions of Shabbat still going on at the start of Yom Kippur. Thus some flexibility has been built in.

Leap years

In leap years, a 30 day month called Adar I is inserted immediately after the month of Shevat, and the regular 29 day month of Adar is called Adar II. This is done to ensure that the months of the Jewish calendar always fall in roughly the same seasons of the solar year, and in particular that Nisan is always in spring. Whether either Chesvan or Kislev both have 29 days, or both have 30 days, or one has 29 days and the other 30 days depends upon the number of days needed in each year. Thus a leap year of 13 months has an average length of 383½ days, so for this reason alone sometimes a leap year needs 383 and sometimes 384 days.

The 265 days from the first day of the 29 day month of Adar (i.e. the twelfth month, but the thirteenth month, Adar II, in leap years) and ending with the 29th day of Heshvan forms a fixed length period that has all of the festivals specified in the Bible, such as Pesach (Nisan 15), Shavuot (Sivan 6), Rosh Hashana (Tishrei 1), Yom Kippur (Tishrei 10), Sukkot (Tishrei 15), and Shemini Atzeret (Tishrei 22).


The festival period from Pesach up to and including Shemini Atzeret is exactly 185 days long. The time from the traditional day of the vernal equinox up to and including the traditional day of the autumnal equinox is also exactly 185 days long. This has caused some unfounded speculation that Pesach should be March 21 and Shemini Atzeret should be September 21, which are the traditional days for the equinoxes. Just as the Hebrew day starts at sunset, the Hebrew year starts in the Autumn (Rosh Hashanah), although the mismatch of solar and lunar years will eventually move it to another season if the modern fixed calendar isn't moved back to its original form of being judged by the Sanhedrin (which requires the Beit Hamikdash)

Days of week of holidays

Purim Passover
(first day)
(first day)
Seventeenth of Tamuz/
Tisha B'Av
Rosh Hashanah/
Shmini Atzeret/
(first day)
Yom Kippur Chanukah
(first day)
Tenth of Tevet Tu B'Shevat

*Postponed to not be held on Shabbat

Measurement of hours

Every hour is divided into 1080 halakim or parts. A part is 3⅓ seconds or 1/18 minute. The ultimate ancestor of the helek was a small Babylonian time period called a barleycorn, itself equal to 1/72 of a Babylonian time degree (1° of celestial rotation). Actually, the barleycorn or she was the name applied to the smallest units of all Babylonian measurements, whether of length, area, volume, weight, angle, or time.

But by the twelfth century that source had been forgotten, causing Maimonides to speculate that there were 1080 parts in an hour because that number was evenly divisible by all numbers from 1 to 10 except 7. But the same statement can be made regarding 360. The weekdays start with Sunday (day 1) and proceed to Saturday (day 7). Since some calculations use division, a remainder of 0 signifies Saturday.

While calculations of days, months and years are based on fixed hours equal to 1/24 of a day, the beginning of each halachic day is based on the local time of sunset. The end of the Shabbat and other Jewish holidays is based on nightfall (Tzeis Hacochavim) which occurs some amount of time, typically 42 to 72 minutes, after sunset. According to Maimonides, nightfall occurs when three medium-sized stars become visible after sunset. By the seventeenth century this had become three second-magnitude stars. The modern definition is when the centre of the sun is 7° below the geometric (airless) horizon, somewhat later than civil twilight at 6°. The beginning of the daytime portion of each day is determined both by dawn and sunrise. Most halachic times are based on some combination of these four times and vary from day to day throughout the year and also vary significantly depending on location. The daytime hours are often divided into Shaos Zemaniyos or "Halachic hours" by taking the time between sunrise and sunset or between dawn and nightfall and dividing it into 12 equal hours. The earliest and latest times for Jewish services, the latest time to eat Chametz on the day before Passover and many other rules are based on Shaos Zemaniyos. For convenience, the day using Shaos Zemaniyos is often discussed as if sunset were at 6:00pm, sunrise at 6:00am and each hour were equal to a fixed hour. For example, halachic noon may be after 1:00pm in some areas during daylight saving time.


Irregularities and "Missing Years"

The traditional dates of events in Jewish history are often used interchangeably with the modern secular dates according to the Gregorian calendar. For example, the traditional Jewish date for the destruction of the First Temple (3338 AM = 423 BCE) differs from the modern scientific date, which is usually expressed using the Gregorian calendar (586 BCE). Implicit in this practice is the view that if all the differences in structure between the Hebrew and Gregorian calendars are taken into consideration, the two dates can be derived from each other. This is not the case. If the traditional dates of events before the Second Temple era are assumed to be using the standard Hebrew calendar, they refer to different objective years than those of the secular dates. The discrepancy is some 165 years.

The conflict does not necessarily imply that either the traditional dates or the secular dates must be objectively wrong. It is possible that the traditional dates did not use a consistent calendar matching the year count of the standard Hebrew calendar. It could be that one or more substantial calendar shifts have occurred, or the years counted might in certain periods have differed from astronomical years. Taking into account the possibility of a changing structure of the Hebrew calendar, theoretically, both the traditional dates and those of secular scholars could be correct. Even so, the account of history in the traditional sourcebook Seder Olam Rabba, and in particular its description of the period of Persian domination, seems to be irrevocably at odds with modern scientific understanding.

Furthermore, the modern Hebrew calendar cannot be used to calculate Biblical dates because new moon dates may be in error by ±2 days and months may be in error by ±2 months. The latter accounts for the irregular intercalation (adding of extra months) that was performed in three successive years in the early second century, according to the Talmud.

Mean year length

The Hebrew calendar mean year is 365.2468 days long, or 365 days, 5 hours 55 minutes, and 25+25/57 seconds (the molad/monthly interval × 235 months per 19-year cycle ÷ 19 years per cycle). As the present-era mean northward equinoctial year is about 365 days 5 hours 49 minutes and zero seconds long, the Hebrew calendar mean year is about 6 minutes and 25+25/57 seconds longer than the modern fixed solar year. This amounts to approximately one day in every 224 years.

In addition, since the mean Gregorian calendar year is 365.2425 days (exactly 365 days 5 hours 49 minutes and 12 seconds) and the mean Hebrew calendar year is 365.2468 days, the Hebrew calendar falls behind the Gregorian calendar by about a day every 231 years.

Molad intervals

The source of the discrepancy is the difference between the molad interval and the actual lunar conjunction cycle. The molad interval is currently about 0.6 seconds too long, and the discrepancy is accumulating at an accelerating rate, since the mean lunation interval is progressively shortening due to gravitational tidal effects. The accumulated "error" since the era of Hillel II is such that the molad moments are now almost 1 hour and 40 minutes late relative to the mean lunar conjunctions at the original reference meridian, which was midway between the Nile River and the end of the Euphrates River. The modern molad moments match the mean solar times of the lunar conjunction moments near the meridian of Kandahar, Afghanistan, more than 30° east of Jerusalem.

In the present era actual lunar conjunction intervals can be as short as 29 days 6 hours and 30 minutes to as long as 29 days and 20 hours, an astonishing variation range of about 13 hours and 30 minutes. Furthermore, due to the eccentricity of Earth's orbit, series of shorter lunations alternate with series of longer lunations, consequently the actual lunar conjunction moments can range from 12 hours earlier than to 16 hours later than the molad moment, in terms of Jerusalem mean solar time (make the conjunction moments 16 minutes earlier if referred to the original molad reference meridian midway between the Nile River and the end of the Euphrates River, about 4° east of Jerusalem). Today, in terms of the mean solar time at the meridian of Qandahar, Afghanistan the actual lunar conjunctions vary ±14 hours relative to the traditional moladot.

Measured on a strictly uniform time scale, such as that provided by an atomic clock, the mean synodic month is becoming gradually longer, but since due to the tides the Earth rotation rate slowing even more the mean synodic month is becoming gradually shorter in terms of mean solar time. The value 29-12-793 was almost exactly correct at the time of Hillel II and is now about 0.6 seconds per month too long. However, it is still the most correct value possible as long as only whole parts (1/18 minute) are used.

Implications for Jewish ritual

This figure, in a detail of a medieval Hebrew calendar, reminded Jews of the palm branch ( Lulav), the myrtle twigs, the willow branches, and the citron ( Etrog) to be held in the hand and to be brought to the synagogue during the holiday of sukkot, near the end of the autumn holiday season.

Although the molad of Tishrei is the only molad moment that is not ritually announced, it is actually the only one that is relevant to the Hebrew calendar, for it determines the provisional date of Rosh HaShanah, subject to the Rosh HaShanah postponement rules. The other monthly molad moments are announced for mystical reasons. With the moladot on average almost 100 minutes late, this means that the molad of Tishrei lands one day later than it ought to in (100 minutes) ÷ (1440 minutes per day) = 5 of 72 years or nearly 7% of years!

Therefore the seemingly small drift of the moladot is already significant enough to affect the date of Rosh HaShanah, which then cascades to many other dates in the calendar year and sometimes, due to the Rosh HaShanah postponement rules, also interacts with the dates of the prior or next year. The molad drift could be corrected by using a progressively shorter molad interval that corresponds to the actual mean lunar conjunction interval at the original molad reference meridian. Furthermore, the molad interval determines the calendar mean year, so using a progressively shorter molad interval would help correct the excessive length of the Hebrew calendar mean year, as well as helping it to "hold onto" the northward equinox for the maximum duration.

If the intention of the calendar is that Passover should fall near the first full moon after the northward equinox, or that the northward equinox should land within one lunation before 16 days after the molad of Nisan, then this is still the case in about 80% of years, but in about 20% of years Passover is a month late by these criteria (as it was in Hebrew year 5765, an 8th year of the 19-year cycle = Gregorian 2005 AD). Presently this occurs after the "premature" insertion of a leap month in years 8, 19, and 11 of each 19-year cycle, which causes the northward equinox to land at exceptionally early moments in such years. This problem will get worse over time, and so beginning in Hebrew year 5817 the 3rd year of each 19-year cycle will also be a month late. Furthermore, the drift will accelerate in the future as perihelion approaches and then passes the northward equinox, and if the calendar is not amended then Passover will start to land on or after the summer solstice around Hebrew year 16652, or about 10885 years from the present. (The exact year when this will begin to occur depends on uncertainties in the future tidal slowing of the Earth rotation rate, and on the accuracy of predictions of precession and Earth axial tilt.)

The seriousness of the spring equinox drift is widely discounted on the grounds that Passover will remain in the spring season for many millennia, and the text of the Torah is generally not interpreted as having specified tight calendrical limits. On the other hand, the mean southward equinoctial year length is considerably shorter, so the Hebrew calendar has been drifting faster with respect to the autumn equinox, and at least part of the harvest festival of Sukkot is already more than a month after the equinox in years 9, 1, 12 and 4 of each 19-year cycle (these are the same year numbers as were mentioned for the spring season in the previous paragraph, except that they get incremented at Rosh HaShanah). This progressively increases the probability that Sukkot will be cold and wet, making it uncomfortable or impractical to dwell in the traditional succah during Sukkot. The first winter seasonal prayer for rain is not recited until Shemini Atzeret, after the end of Sukkot, yet it is becoming increasingly likely that the rainy season in Israel will start before the end of Sukkot.

"Rectifying" the Hebrew calendar

Given the importance in Jewish ritual of establishing the accurate timing of monthly and annual times, some futurist writers and researchers have considered whether a "corrected" system of establishing the Hebrew date is required, due to the small but accelerating changes in the actual lunar cycle interval. Further religious questions include how such a system might be implemented and administered throughout the diverse aspects of the world Jewish community.

It is traditionally held that the fixed arithmetic Hebrew calendar was established on the authority of Hillel ben Yehudah, President of the Sanhedrin in Hebrew year 4119, and therefore only an equal authority (the modern Sanhedrin) or a higher authority (the Messiah) can either amend it or reinstate the observational Hebrew calendar.

A 353-year leap cycle of 4366 months, including 130 leap months, along with use of a progressively shorter molad interval, could keep an amended fixed arithmetic Hebrew calendar from drifting for more than 7 millennia.

Usage in contemporary Israel

Early Zionist pioneers were impressed by the fact that the calendar preserved by Jews over many centuries in far flung diasporas, as a matter of religious ritual, was geared to the climate of their original country: the Jewish New Year marks the moment of transition from the Dry Season to the Rainy one, and major Jewish Holidays such as Sukkot, Passover or Shavuot correspond to major points of the country's agricultural year such as planting and harvest.

Accordingly, in the early 20th Century the Hebrew Calendar was re-interpreted as an agricultural rather than religious calendar. The Kibbutz movement was especially inventive in creating new rituals fitting this interpretation.

With the creation of the State of Israel the Hebrew Calendar was made its official calendar. New holidays and commemorations not derived from previous Jewish tradition invariably were to be defined according to their Hebrew dates — notably the Israeli Independence Day on Iyar 5, Jerusalem Reunification Day on 28 Iyar, and the Holocaust Commemoration Day on Nisan 27 (close to the Hebrew date of the start of the Warsaw Ghetto Uprising).

Nevertheless, since the 1950s the Hebrew calendar steadily declined in importance in Israeli daily life, in favour of the worldwide Gregorian Calendar. At present, Israelis — except for the minority of religiously observant — conduct their private and public life according to the Gregorian Calendar.

The Jewish New Year (Rosh Hashana) is a two-day public holiday in Israel. However, since the 1980s an increasing number of secularist Israelis had taken up the habit of celebrating the Gregorian New Year (usually known as " Sylvester Night" — "ליל סילבסטר") by holding all-night parties on the night between December 31 and January 1. Prominent Rabbis have on several occasions sharply denounced this practice, but with no noticeable effect on the secularist celebrants.

The disparity between the two calendars is especially noticeable with regard to commemoration of the assassinated Prime Minister Yitzchak Rabin. The official Day of Commemoration, instituted by a special Knesset law, is marked according to the Hebrew Calendar - on Heshvan 12. However, left-leaning Israelis, who revere Rabin as a martyr for the cause of peace and who are predominantly secularist, prefer to hold their own mass memorial rallies on November 4. In some years the two competing Rabin Memorial Days are separated by as much as two weeks.

The wall calendars commonly used in Israel are hybrids — organised according to Gregorian rather than Jewish months, but beginning in September, where the Jewish New Year usually falls, and providing the Jewish date in small characters.

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