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Using data from the following book one can estimate the visible phases of the Moon and the dates and time.Calendar Converter
Hebrew Calendar
The Hebrew (or Jewish) calendar attempts to simultaneously maintain alignment between the months and the seasons and synchronise months with the Moon—it is thus deemed a “luni-solar calendar”. In addition, there are constraints on which days of the week on which a year can begin and to shift otherwise required extra days to prior years to keep the length of the year within the prescribed bounds. This isn't easy, and the computations required are correspondingly intricate.
Years are classified as common (normal) or embolismic (leap) years which occur in a 19 year cycle in years 3, 6, 8, 11, 14, 17, and 19. In an embolismic (leap) year, an extra month of 29 days, “Veadar” or “Adar II”, is added to the end of the year after the month “Adar”, which is designated “Adar I” in such years. Further, years may be deficient, regular, or complete, having respectively 353, 354, or 355 days in a common year and 383, 384, or 385 days in embolismic years. Days are defined as beginning at sunset, and the calendar begins at sunset the night before Monday, October 7, 3761 b.c.e. in the Julian calendar, or Julian day 347995.5. Days are numbered with Sunday as day 1, through Saturday: day 7.
The average length of a month is 29.530594 days, extremely close to the mean synodic month (time from new Moon to next new Moon) of 29.530588 days. Such is the accuracy that more than 13,800 years elapse before a single day discrepancy between the calendar's average reckoning of the start of months and the mean time of the new Moon. Alignment with the solar year is better than the Julian calendar, but inferior to the Gregorian. The average length of a year is 365.2468 days compared to the actual solar tropical year (time from equinox to equinox) of 365.24219 days, so the calendar accumulates one day of error with respect to the solar year every 216 years.
http://assets.cambridge.org/97805211/46548/frontmatter/9780521146548_frontmatter.pdf
I had calculated Thursday April 26 31AD for 15th of Nisan, but proved to be the followiing month of Iyyar. Sr Isaac Newton had made a simular error for 34AD Friday April 23.
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