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Jewish Calendar
Introduction
The Jewish calendar is a lunisolar calendar. Hence, in regular intervals a thirteenth lunar month has to be inserted in order to keep the lunar calendar aligned with the solar year. Until the Mishnaic period (10 - 220 CE) the calendar was based on observations with an additional month added whenever observation of agriculture-related events deemed this necessary. A new month started when the lunar crescent could be observed for the first time after new moon. Consequently, a new day began at the end of civil twilight. Starting with the Amoraic period (220 - 500 CE), this system was gradually replaced by a calendar scheme that is still used today. Maimonides (12th century CE) in his work Mishneh Torah gives all necessary rules for the computation of the scheme. He introduced the counting of the years starting with creation called Anno Mundi (AM). The epoch AM 1, Tishri 1 equals October 7th, 3761 BCE of the Julian calendar.
For synchronisation with the solar year, the 19-year Metonic cycle is used. Leap years occur in years 3, 6, 8, 11, 14, 17 and 19 of a cycle. The Jewish month has either 29 or 30 days, and the year consists of 12 or 13 months. Both types of years - called common and embolismic years - can vary in three ways due to the additional rule, that a new Jewish year cannot start on wednesday, friday or saturday. Hence, a Jewish common year may contain 353, 354 or 355 days, and an embolismic year 383, 384 or 385 days. The following table lists the length of the months for all six cases[1].
| Month | Common Year | Embolismic Year | ||||
|---|---|---|---|---|---|---|
| Deficient | Regular | Complete | Deficient | Regular | Complete | |
| Tishri (1) | 30 | 30 | 30 | 30 | 30 | 30 |
| Heshvan (2) | 29 | 29 | 30 | 29 | 29 | 30 |
| Kislev (3) | 29 | 30 | 30 | 29 | 30 | 30 |
| Tevet (4) | 29 | 29 | 29 | 29 | 29 | 29 |
| Shevat (5) | 30 | 30 | 30 | 30 | 30 | 30 |
| Adar (6) | 29 | 29 | 29 | 30 | 30 | 30 |
| Veadar (6.2) | - | - | - | 29 | 29 | 29 |
| Nisan (7) | 30 | 30 | 30 | 30 | 30 | 30 |
| Iyar (8) | 29 | 29 | 29 | 29 | 29 | 29 |
| Sivan (9) | 30 | 30 | 30 | 30 | 30 | 30 |
| Tammuz (10) | 29 | 29 | 29 | 29 | 29 | 29 |
| Av (11) | 30 | 30 | 30 | 30 | 30 | 30 |
| Elul (12) | 29 | 29 | 29 | 29 | 29 | 29 |
| Sum | 353 | 354 | 355 | 383 | 384 | 385 |
Calculations
The calculation of first visibility of the lunar crescent after new Moon for times far in the past is subject to several uncertainties:
- Earth's rate of rotation decreases with time. The resulting time difference, called ΔT must be accounted for.
- Today, astronomers are still working on the problem of refining the prediciton criteria for a successful first sighting of the lunar crescent. Here Yallop's criterion is used, but only the zones A and B were considered [2].
New Moon epochs and last/first visibility of the lunar crescent before/after New Moon were calculated between 600 and 2000 AD. Concerning the lunar and solar ephemerides the longterm DE406 ephemerides of the Jet Propulsion Laboratory were used, which enable the calculation of the positions of the Sun, the Moon and of all planets between 3001 BC and 3000 AD [3]. The uncertainty in ΔT was accounted for. More details about the calculations can be found here.
For the computation of the corresponding Jewish calendar date, the fact was used that Jewish Easter, Pesach, always falls on day 15 in the month of Nisan (7). The Easter formulae of Gauss allow to determine the date of the Pesach. Adding 163 days to the Pesach date results in the date of the beginning (day 1 of Tishri) of the next Jewish year. Then the character (kebioth) of the year in question can be determined with the help of the Slonimski formula[4]. Once the type and exact number of days of the respective year is known, Jewish dates can be easily converted to Julian or Gregorian dates and vice versa.
Data download
If you download the following data and use them in a publication, please mention the adress of this website and the following paper as origin of the data: R. Gautschy & J. Thomann, Dating historical Arabic observations, Astronomy in Focus Volume 1, 2018, 163-166. You can download the paper here.
For Jerusalem tables were created, containing - for a mean value of ΔT - epochs of New Moon and first or last visibility of the lunar crescent in the Julian/Gregorian Calendar and the Jewish Calendar according to observation. For better comparison with actual data and earlier work, the weekday is given too as well as the Jewish date according to the calendar scheme. If there arose any difference in the date when the uncertainty of ΔT was accounted for, it is marked accordingly in the tables. In such cases one cannot say exactly on which day the last or first visibility occured.
In the following table, the downloadable data contain in the column "download data last (first)" for each site:
- The date of the last/first visibility in the Julian (after 1582, the Gregorian) Calendar,
- the time in Greenwich mean time when the lunar crescent could be observed best (to obtain local time simply add the number of hours given in the last column of the table),
- the value of ΔT in seconds,
- the value of the uncertainty of ΔT in seconds,
- the date of the last/first visibility in the Jewish Calendar (year, month, day) according to the calendar scheme,
- the weekday,
- the date of the last/first visibility in the Jewish Calendar (year, month, day) according to observation,
- the time of surise in Greenwich mean time in case of last visibility, resp. time of sunset in Greenwich mean time in case of first visibility (to obtain local time simply add the number of hours given in the last column of the table),
- the time of moonset in Greenwich mean time in case of last visibility, resp. time of moonrise in Greenwich mean time in case of first visibility (to obtain local time simply add the number of hours given in the last column of the table),
- the value of the Yallop criterion if the lunar crescent falls into zone B,
- a code if there arose a difference in the date in positive direction (+1) or in negative direction (-1) when the uncertainty of ΔT was accounted for,
- the date of (geocentric) New Moon in the Julian (after 1582, the Gregorian) Calendar,
- the time in Greenwich mean time of New Moon (to obtain local time simply add the number of hours given in the last column of the table).
| Place | download data first | download data last | correction to obtain local time in tables [hours] |
|---|---|---|---|
| Jerusalem | here | here | +2.35 |
Important:
The date in the Jewish Calendar in the tables changes at midnight like the Julian/Gregorian date.
This must be taken into account when real and computed data are compared!
Bibliography
- 1 J. Meeus, Astronomical Algorithms, 1998, 72.
- 2 B. D. Yallop, A Method for Predicting the First Sighting of the New Crescent Moon, NAO Technical Note No. 69, 1997.
- 3 E. M. Standish, JPL Planetary and Lunar Ephemerides, DE405/LE405, Jet Propulsion Laboratory Interoffice Memorandum 312.F, 1998.
- 4 Slonimski formula.