Three months into dating site
After many years of blissful ignorance, I finally sat down and worked out the mathematics involved, and I have added a page on The Jewish Calendar: A Closer Look, which may be of interest to those who want a deeper understanding or who want to write a Jewish calendar computer program.
For the rest of us, there are plenty of easily accessible computer programs that will calculate the Jewish calendar for more than a millennium to come. Note that the number of days between Nissan and Tishri is always the same.
In ancient times, the new months used to be determined by observation.
When people observed the new moon, they would notify the Sanhedrin.
Note that Adar II is the "real" Adar, the one in which Purim is celebrated, the one in which yahrzeits for Adar are observed, the one in which a 13-year-old born in Adar becomes a Bar Mitzvah. In the fourth century, Hillel II established a fixed calendar based on mathematical and astronomical calculations.
This calendar, still in use, standardized the length of months and the addition of months over the course of a 19 year cycle, so that the lunar calendar realigns with the solar years.
Years are either 12 or 13 months, corresponding to the 12.4 month solar cycle.
The lunar month on the Jewish calendar begins when the first sliver of moon becomes visible after the dark of the moon.
The Jewish calendar has the following months: The length of Cheshvan and Kislev are determined by complex calculations involving the time of day of the full moon of the following year's Tishri and the day of the week that Tishri would occur in the following year.
When the Sanhedrin heard testimony from two independent, reliable eyewitnesses that the new moon occurred on a certain date, they would declare the rosh chodesh (first of the month) and send out messengers to tell people when the month began.
The problem with strictly lunar calendars is that there are approximately 12.4 lunar months in every solar year, so a 12-month lunar calendar is about 11 days shorter than a solar year and a 13-month lunar is about 19 longer than a solar year.
Holidays are celebrated on the same day of the Jewish calendar every year, but the Jewish year is not the same length as a solar year on the civil calendar used by most of the western world, so the date shifts on the civil calendar.
The Jewish calendar is based on three astronomical phenomena: the rotation of the Earth about its axis (a day); the revolution of the moon about the Earth (a month); and the revolution of the Earth about the sun (a year).
This process is sometimes referred to as "fixing" Rosh Hashanah. However, the Jewish New Year is in Tishri, the seventh month, and that is when the year number is increased.