Determining the first day of the calendar
year, Rosh HaShanah, on 1 Tishri:
 1.
 The new year starts on the day
of the new moon that occurs about 354 days (or 384 days if the
previous year was a leap year) after 1 Tishri of the
previous year
 2.
 If the new moon occurs after
noon on that day, delay the new year by one day. (Because in
that case the new crescent moon will not be visible until the
next day.)
 3.
 If this would cause the new
year to start on a Sunday, Wednesday, or Friday, delay it by
one day. (Because we want to avoid that Yom Kippur (10 Tishri)
falls on a Friday or Sunday, and that Hoshanah Rabba (21 Tishri)
falls on a Sabbath (Saturday)).
 4.
 If two consecutive years start
356 days apart (an illegal year length), delay the start of
the first year by two days.
 5.
 If two consecutive years start
382 days apart (an illegal year length), delay the start of
the second year by one day.
Note: Rule 4 can only come into
play if the first year was supposed to start on a Tuesday.
Therefore a two day delay is used rather that a one day delay, as
the year must not start on a Wednesday as stated in rule 3.
When is the new moon?
A calculated new moon is used. In
order to understand the calculations, one must know that an hour
is subdivided into 1080 ``parts''.
The calculations are as follows:
The new moon that started the
year AM 1, occurred 5 hours and 204 parts after sunset (i.e.
just before midnight on Julian date 6 October 3761 BC).
The new moon of any particular
year is calculated by extrapolating from this time, using a
synodic month of 29 days 12 hours and 793 parts.
Note that 18:00 Jerusalem
time (15:39 UTC) is used instead of sunset in all these
calculations.
