The list below gives a time which can be used to determine the day the Jewish ecclesiastical (spring) year starts over a period of nineteen years. These are not Nisan
molad times, although the offset necessarily remains constant. (The fractions shown are fractions of a minute.) :17:49 Wednesday, 22 March 2023 :15:21 \tfrac{13}{18} Tuesday, 9 April 2024 :00:10 \tfrac{7}{18} Sunday, 30 March 2025 :08:59 \tfrac{1}{18} Thursday, 19 March 2026 :06:31 \tfrac{14}{18} Wednesday, 7 April 2027 :15:20 \tfrac{8}{18} Sunday, 26 March 2028 :00:09 \tfrac{2}{18} Friday, 16 March 2029 :21:41 \tfrac{15}{18} Wednesday, 3 April 2030 :06:30 \tfrac{9}{18} Monday, 24 March 2031 :15:19 \tfrac{3}{18} Friday, 12 March 2032 :12:51 \tfrac{16}{18} Thursday, 31 March 2033 :21:40 \tfrac{10}{18} Monday, 20 March 2034 :19:13 \tfrac{5}{18} Sunday, 8 April 2035 :04:01 \tfrac{17}{18} Friday, 28 March 2036 :12:50 \tfrac{11}{18} Tuesday, 17 March 2037 :10:23 \tfrac{6}{18} Monday, 5 April 2038 :19:12 Friday, 25 March 2039 :04:00 \tfrac{12}{18} Wednesday, 14 March 2040 :01:33 \tfrac{7}{18} Tuesday, 2 April 2041 Every nineteen years this time is 2 days, 16 hours, 33 1/18 minutes later in the week. That is either the same or the previous day in the civil calendar, depending on whether the difference in the day of the week is three or two days. If 29 February is included fewer than five times in the nineteen – year period the date will be later by the number of days which corresponds to the difference between the actual number of insertions and five. If the year is due to start on Sunday, it actually begins on the following Tuesday if the following year is due to start on Friday morning. If due to start on Monday, Wednesday or Friday it actually begins on the following day. If due to start on Saturday, it actually begins on the following day if the previous year was due to begin on Monday morning. The table below lists, for a Jewish year commencing on 23 March, the civil date of the first day of each month. If the year does not begin on 23 March, each month's first day will differ from the date shown by the number of days that the start of the year differs from 23 March. The correct column is the one which shows the correct starting date for the following year in the last row. If 29 February falls within a Jewish month the first day of later months will be a day earlier than shown. For long period calculations, dates should be reduced to the
Julian calendar and converted back to the civil calendar at the end of the calculation. The civil calendar used here (Exigian) is correct to one day in 44,000 years and omits the leap day in centennial years which do not give remainder 200 or 700 when divided by 900. It is identical to the Gregorian calendar between 15 October 1582 CE and 28 February 2400 CE (both dates inclusive). To find how many days the civil calendar is ahead of the Julian in any year from 301 BCE (the calendar is proleptic [assumed] up to 1582 CE) add 300 to the year, multiply the hundreds by 7, divide by 9 and subtract 4. Ignore any fraction of a day. When the difference between the calendars changes the calculated value applies on and from 1 March (civil date) for conversions to Julian. For earlier dates reduce the calculated value by one. For conversions to the civil date the calculated value applies on and from 29 February (Julian date). Again, for earlier dates reduce the calculated value by one. The difference is applied to the calendar one is converting
into. A negative value indicates that the Julian date is ahead of the civil date. In this case it is important to remember that when calculating the civil equivalent of 29 February (Julian), 29 February is discounted. Thus if the calculated value is −4 the civil equivalent of this date is 24 February. Before 1 CE use astronomical years rather than years BCE. The astronomical year is (year BCE) – 1. Up to the 4th century CE, these tables give the day of the Jewish month to within a day or so and the number of the month to within a month or so. From the 4th century, the number of the month is given exactly and from the 9th century the day of the month is given exactly as well. In the Julian calendar, every 76 years the Jewish year is due to start 5h 47 14/18m earlier, and 3d 18h 12 4/18m later in the week. ;Example calculation On what civil date does the eighth month begin in CE 20874–5? 20874=2026+(248×76). In (248×76) Julian years the Jewish year is due to start (248×3d 18h 12 4/18m) later in the week, which is 932d 2h 31 2/18m or 1d 2h 31 2/18m later after removing complete weeks. Allowing for the current difference of thirteen days between the civil and Julian calendars, the Julian date is 13+(248×0d 5h 47 4/18m) earlier, which is 72d 21h 28 16/18m earlier. Convert back to the civil calendar by applying the formula. :20874+300=21174 :211×7=1477 :1477/9=164 remainder 1 :164−4=160. :160d−72d 21h 28 16/18m=87d 2h 31 2/18m. So, in 20874 CE, the Jewish year is due to begin 87d 2h 31 2/18m later than in 2026 CE and 1d 2h 31 2/18m later in the week. In 20874 CE, therefore, the Jewish year is due to begin at 11.30 3/18 am on Friday, 14 June. Because of the displacements, it actually begins on Saturday, 15 June. Odd months have 30 days and even months 29, so the starting dates are 2, 15 July; 3, 13 August; 4, 12 September; 5, 11 October; 6, 10 November; 7, 9 December, and 8, 8 January. The rules are based on the theory that Maimonides explains in his book
Rabbinical Astronomy. The times in the list are those calculated by
Gauss with an offset of −14 days as his calculation gives the civil date of Passover rather than the start of the month. Gauss's calculation has been rigorously proved. == Other uses ==