Modern scientific accuracy in the Bible?
The new moon signifies the start of every Jewish month. The calendar is lunisolar calendar, measuring months defined in lunar cycles as well as years measured in solar cycles. The calendar is calculated based on mathematical rules handed down from God to Moses at the moment the command was given to make sure that Passover always falls in the springtime.
Months are calculated at 29.530594 days, following the cycle of the moon. This practice is based on the Talmud (Rosh Hashanah 25a). The most accurate scientific method yields a value of 29.530589 days. The difference between the Biblical value written down in Babylonian times and the latest scientific value is only 0.0000005, which adds up to about only 4 hours since Babylonian times.
Coincidence or Divine revelation?
The Roadmap to the End of Days describes this calendar in more detail and shows that all of history follows a divine plan in a particular pattern that matches past and current events and a final destination that illuminates what we can expect in the near future Messianic times.