Molad
Encyclopedia
Molad 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.
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, so that in the present era the molad interval is about 3/5 of a second too long.
The traditional epoch
of the cycle was 5 hours 11 minutes and 20 seconds after the mean sunset (considered to be 6 hours before midnight) at the epoch of the Hebrew calendar (first eve of Tishrei of Hebrew year 1).
Historically, the original molad reference meridian
of longitude
was halfway between the Nile
river and the end of the Euphrates
river, but the excess length of the molad interval causes it to drift progressively eastward at an accelerating rate — in the present era it is at a meridian that passes near Qandahar, Afghanistan
!
The molad interval as an exact fraction is 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, so 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.
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 18ths of a minute 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
.
+ 2h 20m 56s 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.
Molad Emtzai (Average Molad)
The molad emtzai (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 after the previous molad moment. This interval is numerically exactly the same as the length of the mean synodic month that was published by PtolemyPtolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
in the Almagest
Almagest
The Almagest is a 2nd-century mathematical and astronomical treatise on the apparent motions of the stars and planetary paths. Written in Greek by Claudius Ptolemy, a Roman era scholar of Egypt,...
, who cited Hipparchus
Hipparchus (astronomer)
Hipparchus, or more correctly Hipparchos , was a Greek astrologer, astronomer, geographer, and mathematician of the Hellenistic period. He is considered the founder of trigonometry....
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, so that in the present era the molad interval is about 3/5 of a second too long.
The traditional epoch
Epoch (reference date)
In the fields of chronology and periodization, an epoch is an instance in time chosen as the origin of a particular era. The "epoch" then serves as a reference point from which time is measured...
of the cycle was 5 hours 11 minutes and 20 seconds after the mean sunset (considered to be 6 hours before midnight) at the epoch of the Hebrew calendar (first eve of Tishrei of Hebrew year 1).
Historically, the original molad reference meridian
Meridian (geography)
A meridian is an imaginary line on the Earth's surface from the North Pole to the South Pole that connects all locations along it with a given longitude. The position of a point along the meridian is given by its latitude. Each meridian is perpendicular to all circles of latitude...
of longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
was halfway between the Nile
Nile
The Nile is a major north-flowing river in North Africa, generally regarded as the longest river in the world. It is long. It runs through the ten countries of Sudan, South Sudan, Burundi, Rwanda, Democratic Republic of the Congo, Tanzania, Kenya, Ethiopia, Uganda and Egypt.The Nile has two major...
river and the end of the Euphrates
Euphrates
The Euphrates is the longest and one of the most historically important rivers of Western Asia. Together with the Tigris, it is one of the two defining rivers of Mesopotamia...
river, but the excess length of the molad interval causes it to drift progressively eastward at an accelerating rate — in the present era it is at a meridian that passes near Qandahar, Afghanistan
Afghanistan
Afghanistan , officially the Islamic Republic of Afghanistan, is a landlocked country located in the centre of Asia, forming South Asia, Central Asia and the Middle East. With a population of about 29 million, it has an area of , making it the 42nd most populous and 41st largest nation in the world...
!
The molad interval as an exact fraction is 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, so 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.
Although the moment of the traditional Hebrew calendar molad is announced in synagogues
Synagogue
A synagogue is a Jewish house of prayer. This use of the Greek term synagogue originates in the Septuagint where it sometimes translates the Hebrew word for assembly, kahal...
on the Shabbat
Shabbat
Shabbat is the seventh day of the Jewish week and a day of rest in Judaism. Shabbat is observed from a few minutes before sunset on Friday evening until a few minutes after when one would expect to be able to see three stars in the sky on Saturday night. The exact times, therefore, differ from...
prior to each month (except before Tishrei
Tishrei
Tishrei or Tishri , Tiberian: ; from Akkadian "Beginning", from "To begin") is the first month of the civil year and the seventh month of the ecclesiastical year in the Hebrew calendar. The name of the month is Babylonian. It is an autumn month of 30 days...
), its only relevance to the present day fixed arithmetic lunisolar Hebrew calendar
Hebrew calendar
The Hebrew calendar , or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits , and daily Psalm reading, among many ceremonial uses...
is that the molad of the month of Tishrei
Tishrei
Tishrei or Tishri , Tiberian: ; from Akkadian "Beginning", from "To begin") is the first month of the civil year and the seventh month of the ecclesiastical year in the Hebrew calendar. The name of the month is Babylonian. It is an autumn month of 30 days...
determines the date of the New Year Day (Rosh Hashanah
Rosh Hashanah
Rosh Hashanah , , is the Jewish New Year. It is the first of the High Holy Days or Yamim Nora'im which occur in the autumn...
), 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 18ths of a minute elapsed from mean sunset, because Hebrew calendar
Hebrew calendar
The Hebrew calendar , or Jewish calendar, is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits , and daily Psalm reading, among many ceremonial uses...
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
Tishrei
Tishrei or Tishri , Tiberian: ; from Akkadian "Beginning", from "To begin") is the first month of the civil year and the seventh month of the ecclesiastical year in the Hebrew calendar. The name of the month is Babylonian. It is an autumn month of 30 days...
and thus could imply an erroneous date for Rosh Hashanah
Rosh Hashanah
Rosh Hashanah , , is the Jewish New Year. It is the first of the High Holy Days or Yamim Nora'im which occur in the autumn...
.
Molad Amiti (True Molad)
The molad amiti (true 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 TimeUniversal Time
Universal Time is a time scale based on the rotation of the Earth. It is a modern continuation of Greenwich Mean Time , i.e., the mean solar time on the Prime Meridian at Greenwich, and GMT is sometimes used loosely as a synonym for UTC...
+ 2h 20m 56s or simply + 2h 21m) or as the clock time in Israel
Israel
The State of Israel is a parliamentary republic located in the Middle East, along the eastern shore of the Mediterranean Sea...
. 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.
External links
- Molad times until 2010 and further description
- The Molad of the Hebrew Calendar (astronomical analysis)
- The Kalendis Calendar Calculator (freeware — zmanim and moladot for any year)
- Molad for mobile phones (freeware)
- The Length of the Lunar Cycle (numerical integration analysis)
- The Purpose of the Hebrew Calendar Rosh HaShanah Dehiyyot (Postponements of the First Day of Tishrei)
- Why Divide Hours into 1080 Parts?
- Hebrew Calendar Dates and Holydays (Diaspora or Israel)
- Molad times for 6000 Years (Multilingual)