The dates of Jewish holidays only seem to change from year to 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 Gregorian calendar used by most of the western world, so the date shifts on the Gregorian calendar.
The Jewish calendar is primarily lunar, with each month beginning on the new moon, when the first sliver of moon becomes visible after the invisibility of the moon. In ancient times, the new months used to be determined by observation. When people observed the new moon, they would notify the Sanhedrin. 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 loses about 11 days every year and a 13-month lunar gains about 19 days every year. The months on such a calendar "drift" relative to the solar year. On a 12-month calendar, the month of Nisan, which is supposed to occur in the Spring, occurs 11 days earlier each year, eventually occurring in the Winter, the Fall, the Summer, and then the Spring again. To compensate for this drift, an extra month is occasionally added: an extra month of Adar. The month of Nisan would occur 11 days earlier for two or three years, and then would jump forward 29 or 30 days, balancing out the drift.
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. An extra month of Adar is added in the 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years of the cycle. Jewish year 5758 (beginning October 2, 1997) is the first year of the current cycle.
In addition, Yom Kippur should not fall adjacent to a Sabbath, because this would cause difficulties in coordinating the fast with the Sabbath, and Hoshanah Rabba should not fall on Sabbath because it would interfere with the holiday's observances. A day is added to the month of Cheshvan or subtracted from the month of Kislev of the previous year to prevent these things from happening.
The year number on the Jewish calendar represents the number of years since creation, as calculated by adding up the ages of people in the Bible back to the time of creation. However, it is important to note that this date is not necessarily supposed to represent a scientific fact. For example, many Orthodox Jews will readily acknowledge that the seven "days" of creation are not necessarily 24-hour days (indeed, a 24-hour day would be meaningless until the creation of the sun on the fourth "day").
Jews do not generally use the words "A.D." and "B.C." to refer to the years on the Gregorian calendar. "A.D." means the year of the Lord, and we know that Jesus is not the LORD. Instead, we use the abbreviations C.E. (Common or Christian Era) and B.C.E. (Before the Common Era).
The first month of the Biblical Jewish calendar is the month of Nisan, in the spring, when Passover occurs. However, the regular Jewish New Year is in Tishri, the seventh month in the Biblical calendar, and that is when the year number is increased. This concept of different starting points for a year is not as strange as it might seem at first glance. The US "new year" starts in January, but the new "school year" starts in September, and many businesses and governmental institutions have "fiscal years" that start at various times of the year. Similarly, the Jewish calendar has different starting points for different purposes.
The Jewish calendar has the following months:
|Cheshvan||29 or 30 days||October-November|
|Kislev||30 or 29 days||November-December|
|Adar||29 or 30 days||February-March|
|Adar II||29 days||March-April|
In leap years, Adar I has 30 days; in non-leap years, Adar has 29 days.
Note that the number of days between Nisan and Tishri is always the same. Because of this, the time from the first major Biblical festival (Passover in Nisan) to the last major Biblical festival (Sukkot in Tishri) is always the same.
There are plenty of easily accessible computer programs that will calculate the Jewish calendar for any year one needs.
For an excellent detailed explanation of these matters, see Hebrew Calendar Science and Myths.
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