The Hebrew Calendar uses what is called postponement rules not only to maintain its accuracy but also to prevent Yom Kippur (the Day of Atonement) from falling on certain days.
Calendar (postponement) rules determine when Tishri 1, the first day of the first month of the Hebrew civil year, occurs. Once the first day of the civil year is calculated then other guidelines are used to determine how many days are in each month as well as how many months occur within the year. Tishri 1 is also the day the Feast of Trumpets (Rosh Hashanah) is celebrated.
A Hebrew postponement rule is a one or two-day adjustment to the calculation of the Molad of Tishri. A Molad is the calculation of the average conjunction of the moon with the earth and the sun. It is based on the mean or average length of the lunar month, which is 29.53059 days.
The Molad is not the astronomical conjunction. These adjustments enable the process of calculating the Molad to consistently achieve the greatest degree of accuracy in relationship to the cycle of the moon. After calculating the Molad of Tishri the following postponement calendar rules are applied to declare Tishri 1.
The postponement rules
Postponement Rule 1 is invoked when Tishri's Molad or advancement occurs on a Sunday, Wednesday, or Friday. The declaration of Tishri 1 is advanced one day to a Monday, Thursday or Saturday (Sabbath) respectively.
Rule number 1 prevents the Day of Atonement (Yom Kippur), which must be celebrated on Tishri 10 (sunset on Tishri 9 to sunset on the 10th) from falling on a Friday or Sunday. Atonement is a complete day of fasting that requires absolutely no work be done on it.
Rule #1 mercifully prevents Atonement from occurring just before the weekly Sabbath, which is a "feasting" day that starts at sunset each Friday and requires preparation. It also prevents Atonement from occurring right after the weekly Sabbath (preventing a feasting day to come just before a fast).
Rule 2 is invoked when Tishri's Molad happens at or after noon (18 hours 0 parts). The counting of Hebrew hours begins at sunset each day which is fixed at 6 pm. The declaration of Tishri 1 is delayed to the following Hebrew day.
Rule 3 is invoked when Tishri's Molad of a common year occurs on a Tuesday (on or after 9 hours and 204 parts). The declaration of Tishri 1 is moved to the next day (Wednesday). Then, because of the above listed Rule One, the day declared as Tishri 1 is moved to Thursday.
Rule 4 is used when Tishri's Molad of a common year (a year with twelve months) comes right after an intercalary year (a leap year which has thirteen months) occurs on a Monday, at or after 15 hours and 589 parts. The declaration of Tishri 1 on the Hebrew calendar is advanced to Tuesday. This rule applies roughly once every 186 years.
If none of the postponement rules apply for a particular year then Tishri 1 is declared to occur on the same day as the Molad. Below are a couple of examples of using postponements for determining the first day of the Hebrew civil calendar.