Editing Hebrew calendar (section)

==Accuracy==
===Molad interval===
A "[[new moon]]" (astronomically called a [[lunar conjunction]] and, in Hebrew, a [[molad]]) is the moment at which the sun and moon have the same [[Ecliptic coordinate system|ecliptic longitude]] (i.e. they are aligned horizontally with respect to a north–south line). The period between two new moons is a [[synodic month]]. The actual length of a synodic month varies from about 29 days 6 hours and 30 minutes (29.27 days) to about 29 days and 20 hours (29.83 days), a variation range of about 13 hours and 30 minutes. Accordingly, for convenience, the Hebrew calendar uses a long-term average month length, known as the '''molad interval''', which equals the [[Lunar month#Synodic month|mean synodic month]] of ancient times. The molad interval is 29 days, 12 hours, and 793 "parts" (1 "part" = <sup>1</sup>/<sub>18</sub> minute = 3<sup>1</sup>/<sub>3</sub> seconds) (i.e., 29.530594 days), and is the same value determined by the Babylonians in their [[Babylonian mathematics|System B]] about 300 BCE<ref name=Neugebauer2>Neugebauer, ''Astronomical cuneiform texts'', Vol 1, pp. 271–273</ref> and was adopted by [[Hipparchus]] (2nd century BCE) and by [[Ptolemy]] in the ''[[Almagest]]'' (2nd century CE). Its remarkable accuracy (less than one second from the current true value) is thought to have been achieved using records of lunar eclipses from the 8th to 5th centuries BCE.<ref>[[G. J. Toomer]], Hipparchus' Empirical Basis for his Lunar Mean Motions, ''Centaurus'', Vol 24, 1980, pp. 97–109</ref> In the Talmudic era, when the mean synodic month was slightly shorter than at present, the molad interval was even more accurate, being "essentially a perfect fit" for the mean synodic month at the time.<ref name=molad/>

Currently, the accumulated drift in the moladot since the Talmudic era has reached a total of approximately 97 minutes.<ref name=molad/> This means that the molad of Tishrei lands one day later than it ought to in (97 minutes) ÷ (1440 minutes per day) = 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 rate of calendar drift is increasing with time, since the mean synodic month is progressively shortening due to gravitational [[tide|tidal]] effects. 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 the tides slow Earth's rotation rate even more, the mean synodic month is becoming gradually shorter in terms of mean solar time.<ref name=molad/>

===Metonic cycle drift===
A larger source of error is the inaccuracy of the Metonic cycle. Nineteen Jewish years average 6939d 16h 33m 03{{fraction|1|3}}s, compared to the 6939d 14h 26m 15s of nineteen mean solar years.<ref name=weinberg>Weinberg, I., [http://adsabs.harvard.edu/full/1956MNSSA..15...86W Astronomical Aspects of the Jewish Calendar], Monthly Notes of the Astronomical Society of South Africa, Vol. 15, p. 86.</ref> Thus, the Hebrew calendar drifts by just over 2 hours every 19 years, or approximately one day every 216 years.<ref name="richards">{{cite book| publisher = Oxford University Press| isbn = 978-0-19-286205-1| last = Richards| first = E. G| title = Mapping time: the calendar and its history| page = 224| url = https://archive.org/details/mappingtimecalen00rich| url-access = registration| date = 1998}}</ref><ref name=aviv>[https://www.daat.ac.il/he-il/hagim/luach_ivri/הלוח-העברי/נספחים/aviv.htm למועד חודש האביב]</ref> Due to accumulation of this discrepancy, the earliest date on which Passover can fall has drifted by roughly eight days since the 4th century, and the 15th of Nisan now falls only on or after 26 March (the date in 2013), five days after the actual equinox on 21 March. In the distant future, this drift is projected to move Passover much further in the year.<ref name=aviv/> If the calendar is not amended, then Passover will start to land on or after the summer solstice around approximately AM 16652 (12892 CE).{{efn|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.}}

===Implications for Jewish ritual===
When the calendar was fixed in the 4th century, the earliest Passover (in year 16 of the Metonic cycle) began on the first full moon after the [[March equinox]].{{efn|reference=That is to say, Passover began within a day or so of the full moon}} This is still the case in about 80% of years; but, in about 20% of years, Passover is a month late by this criterion.{{efn|reference=As it was in AM 5765, 5768 and 5776, the 8th, 11th and 19th years of the 19-year cycle = Gregorian 2005, 2008 and 2016 CE.}} Presently, this occurs after the "premature" insertion of a leap month in years 8, 11, and 19 of each 19-year cycle, which causes Passover to fall especially far after the March equinox in such years. Calendar drift also impacts the observance of [[Sukkot]], which will shift into Israel's winter rainy season, making dwelling in the [[sukkah]] less practical. It also affects the logic of the [[Shemini Atzeret]] prayer for rain, which will be more often recited once rains are already underway.

Modern scholars have debated at which point the drift could become ritually problematic, and proposed adjustments to the fixed calendar to keep Passover in its proper season.<ref name=aviv/> The seriousness of the calendar drift is discounted by many, on the grounds that Passover will remain in the spring season for many millennia, and the Torah is generally not interpreted as having specified tight calendrical limits. However, some writers and researchers have proposed "corrected" calendars (with modifications to the leap year cycle, molad interval, or both) which would compensate for these issues:

*Irv Bromberg has suggested a 353-year cycle of 4,366 months, which would include 130 leap months, along with use of a progressively shorter ''molad'' interval, which would keep an amended fixed arithmetic Hebrew calendar from drifting for more than seven millennia.<ref name=irv353>{{Cite web|first=Irv|last=Bromberg|title=The Rectified Hebrew Calendar.|url=http://individual.utoronto.ca/kalendis/hebrew/rect.htm|work= University of Toronto |access-date=13 May 2011 }}</ref> The 353 years would consist of 18 Metonic cycles, as well as an 11-year period in which the last 8 years of the Metonic cycle are omitted.<ref name=irv353/>
*Other authors have proposed to use cycles of 334 or 687 years.<ref name=aviv/>
*Another suggestion is to delay the [[leap years]] gradually so that a whole intercalary month is taken out at the end of Iggul 26; while also changing the [[synodic month]] to be the more accurate 29.53058868 days. Thus, the length of the year would be {{nowrap|(235 × 13 × 26 − 1)/(19 × 13 × 26) {{=}} 365.2422 days,}} very close to the actual [[tropical year]]. The result is the "Hebrew Calendar" in the program CalMaster2000.<ref>A. O. Scheffler and P. P. Scheffler, "Calmaster2000: Dates, Holidays, Astronomical Events". Pittsburgh, PA: Zephyr Services.</ref>

Religious questions abound about how such a system might be implemented and administered throughout the diverse aspects of the world Jewish community.<ref>{{cite web|url=http://www.thesanhedrin.org/en/index.php/Committee_concerning_the_fixing_of_the_Calendar|title=Committee concerning the fixing of the Calendar |work= The Sanhedrin }}</ref>