Molad

''Molad'' (מולד, plural ''Moladot'', מולדות) is a Hebrew word meaning "birth" that also generically refers to the time at which the New Moon is "born". The word is ambiguous, however, because depending on the context, it could refer to the actual or mean astronomical lunar conjunction (calculated by a specified method, for a specified time zone), or the ''molad'' of the traditional Hebrew calendar (or another specified calendar), or at a specified locale the first visibility of the new lunar crescent after a lunar conjunction.

Other than its usage connected with the lunar cycle, ''מולד'' is also the word used in the Hebrew term for Christmas, ''חג המולד'' (literally “Holiday of the Birth” or “Holiday of the Nativity”).

The Traditional ''Molad'' Interval

The ''molad emtza'i'' (מולד אמצעי, average ''molad'', used for the traditional Hebrew calendar) is based on a constant interval cycle that is widely but incorrectly regarded as an approximation of the time in Jerusalem of the mean lunar conjunction. Each ''molad'' moment occurs exactly 29 days 12 hours 44 minutes and 3+¹/₃ seconds (or, equivalently, 29 days 12 hours and 44+¹/₁₈ minutes) after the previous ''molad'' moment. This interval is numerically exactly the same as the length of the mean synodic month that was published by Ptolemy in the Almagest, who cited Hipparchus as its source. Although in the era of Hipparchus (2nd century BC) this interval was equal to the average time between lunar conjunctions, mean lunation intervals get progressively shorter due to tidal transfer of angular momentum from Earth to Moon, consequently in the present era the ''molad'' interval is about ³/₅ of a second too long.

The ''molad'' interval as an exact improper fraction = 29+¹²/₂₄+⁴⁴/₁₄₄₀+^(10/3)/₈₆₄₀₀ = ⁷⁶⁵⁴³³/₂₅₉₂₀ days, where the denominator 25920 is the number of parts per day (each part equals ¹/₁₈ minute or ¹⁰/₃ seconds) and one can alternatively write the numerator in the interesting descending sequence 765432+1. As a mixed fraction this reduces to 29+¹³⁷⁵³/₂₅₉₂₀ days, which implies an underlying fixed arithmetic lunar cycle of 25920 months in which 13753 months have 30 days and the remaining 25920 – 13753 = 12167 months have 29 days, spread as smoothly as possible. In any such lunar cycle, which must have an integer number of days, 30-day months must occur slightly more frequently than 29-day months, such that 2 consecutive 30-day months occur at intervals of either 17 or 15 months, where the 17-month interval is approximately twice as common as the 15-month interval.

This typical mean lunar cycle pattern becomes clearly evident if one computes the ''molad'' moment, adds ¹/₄ day to account for the ''molad zakein'' postponement rule, keeps only the integer part of the result to compute the ''molad'' day, calculates the difference from the previous ''molad'' day (will be either 30 days = "F" for full, or 29 days = "D" for deficient), and then lists the sequence with the insertion of one space in the middle of every FF pair and starting a new line at the end of every 15-month interval. For example, for the period from the ''molad'' of ''Nisan'' 5726 until the ''molad'' of ''Elul'' 5818 inclusive the pattern obtained is:

FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDFDF FDFDFDFDFDFDFDF
FDFDFDFDFDFDFDFDF

In the above partial sequence, which spans just one ''era'' of the ''molad'' cycle, it is obvious that there are twice as many 17-month groups as there are 15-month groups (23 repeats of a 17+17+15=49 month sequence), except for the stand-alone 17-month group at the end of the era, yielding a total of 1144 months in the era. Another era type, which occurs half as frequently (8<15), has only 22 repeats of the 49 month sequence before the 17-month end group, yielding a total of 1095 months in the era.

The ''Molad'' Epoch

The traditional epoch of the cycle was 5 hours 11 minutes and 20 seconds after the mean sunset (considered to be 6 hours before mean midnight) at the epoch of the Hebrew calendar (first eve of ''Tishrei'' of Hebrew year 1). The traditional source for this moment is as follows:

* Adam, the first man, was considered to have seen the first lunar crescent at the start of the 9th hour of the daytime on the 6th day of Creation (20 hours from the sunset that started that date), when God commanded him never to eat from the Tree of Knowledge. The days of Creation are traditionally considered to have been the final days of Hebrew year 1, so this observation sanctified the month of ''Tishrei'' of year 2.
* Traditionally, assuming that the lunar conjunction was 6 hours earlier, the moment of the ''molad'' of the month of ''Tishrei'' of Hebrew year 2 was at the start of the 3rd hour of the daytime on Friday (14 hours from the sunset that started that date).
* The ''molad'' of ''Tishrei'' of Hebrew year 1 was considered to have occurred 12 lunar months earlier, where each lunar month equals the traditional ''molad'' interval.
* A single ''molad'' interval is 1 day 12 hours 793 parts in excess of a whole number of weeks, so the excess from 12 ''molad'' intervals is 4 days 8 hours 876 parts.
* Therefore the ''molad'' epoch was on (6 days 14 hours) – (4 days 8 hours 876 parts) = 2nd day 5 hours 204 parts.

The ''molad'' epoch is known by the name ''BeHaRad'', which is an acronym based on the Hebrew letters ''beit'' = 2 for the 2nd day, ''hey'' = 5 for the 5th hour, and ''resh daled'' = 200 + 4 = 204 parts.

Announcing the ''Molad'' Moment

Although the moment of the traditional Hebrew calendar ''molad'' is announced in synagogues on the ''Shabbat'' prior to each month (except before ''Tishrei''), its only relevance to the present day fixed arithmetic lunisolar Hebrew calendar is that the ''molad'' of the month of ''Tishrei'' determines the date of the New Year Day (''Rosh Hashanah''), subject to possible postponements of 0, 1 or 2 days (depending on certain postponement rules, also see external link).

Traditionally the announced or printed ''molad'' moment is quoted in terms of the hours, minutes, and 18^ths of a minute (parts) elapsed from mean sunset, because Hebrew calendar days begin at sunset. Some printed sources subtract 6 hours to convert the ''molad'' moment to "civil" time, but doing so causes the Hebrew weekday to be wrong 25% of the time (whenever the ''molad'' moment is between sunset and midnight). Also, some printed sources even add an hour during the summertime for "daylight saving", or attempt to apply conversions to the local time zone, but those are also mistakes because they would affect the ''molad'' of ''Tishrei'' and thus could imply an erroneous date for ''Rosh Hashanah''.

Yaaqov Loewinger of Tel Aviv, Israel, published a Hebrew essay that thoroughly reviewed the multiple widespread improper ways as well as the single proper way to publish and announce the ''molad'' moment."על הכרזת המולד בבתי הכנסת" (On the Announcement of the Molad in Synagogues), Hakirah (חקירה, Investigation), The Flatbush Journal of Jewish Law and Thought, Summer 2008, volume 6, http://www.hakirah.org/Vol%206%20Loewinger.pdf Loewinger also showed how the practice of announcing the ''molad'' moment is itself a very recent innovation in Jewish practice, practically unheard of before the 20th century.

''Molad Amiti'' (מולד אמתי, Real ''Molad'')

The ''molad amiti'' (real ''molad''), which has no relevance to the Hebrew calendar, is the time at which the actual astronomical lunar conjunction occurs, often expressed either as the mean solar time in Jerusalem (Universal Time + 2h 20m 56.9s or simply + 2h 21m) or as the clock time in Israel. If the moment is desired for ritual or social purposes then it may be best to express it in terms of the local clock time.

On average the traditional ''molad'' of the Hebrew calendar is currently >2 hours late, and there are substantial periodic variations in the astronomical lunar cycle length, such that in the present era it varies over a 28-hour span ranging from 12 hours early to 16 hours late, compared to the Jerusalem mean solar time ''molad amiti'', if all months are included in the evaluation. If the evaluation is limited to a single Hebrew month, however, for example ''Tishrei'', then the portion of the variations that are due to Earth orbital eccentricity are for the most part eliminated and the average has an offset that is month-specific, such that presently the ''molad'' of ''Tishrei'' varies over about a 20-hour span ranging from 4 hours early to 16 hours late.

See also

* Hebrew calendar
* Month
* Orbit of the Moon

References

{{Reflist

External links

TorahCalc: Molad Calculator

Hebrew calendar

he:מולד הלבנה