Today is St John the Baptist's day in the calendar of several denominations. And one thing I want to focus on is his dad, Zechariah. We don't know much about him, but he was of the priestly order of Abijah (Luke 1:5). Moreover, as vv.8-17 tell us, it was his turn to be on duty when an angel appeared to him.
I remember once hearing that we can then calculate approximate dates - at best months - from this encounter. His wife, Elizabeth, became pregnant (v.24), and 5 to 6 months later, the angel Gabriel appeared to her kinswoman Mary to tell her that she too was going to have a Son (vv.26-33).
So, what have we actually got here? 5 to 7 months (after all, give Elizabeth time to become pregnant) after Zechariah has his encounter with the angel, Mary meets Gabriel. Assuming she becomes pregnant within a month, then she becomes pregnant between 5 and 8 months after Zechariah meets the angel.
Hence, Jesus is born between 1 year 2 months and 1 year 5 months after Zechariah was on duty.
King David organised the priests into the sort of rota so beloved by churches (I Chron. 24) and we see that the division of Abijah was 8th on a rota of 24 (v.10).
So, does that narrow it down? 24 divisions, 12 months, so the priestly divisions each serving a half-month?
Well, it sounds logical. But firstly, the Bible doesn't tell us how long they serve for. Could be a week, could be a month.
And secondly, you can't say "priestly division X served in the first/second half of month Y", as the calendar shifts. The synodic month - which, despite its name, is not set by the Church of England's General Synod - is 29.530589 days, while the tropical year is 365.2421897 days.
19 tropical years is 6,939.6016043 days.
235 synodic months is 6,939.688415 days.
Hence, there is a difference of 2 hours 5 minutes.
235 months works out as 12 years of 12 months and 7 years of 13 months in a 19-year cycle.
And this is what the Jewish calendar uses, so even if the priestly divisions used a 12-month cycle, this would shift through the year.
And to add to this, the Jews were sent into exile, and when they returned only the divisions of Jediah, Immer, Pashhur and Harim returned (Ezra 2:36-39). Logically, if the division of Abijah didn't return with the exiles, then some of them must have returned later. It does sound reasonable then that the system David drew up collapsed (as only a handful of priestly divisions returned) and presumably, when Ezra restored the Temple worship, he drew up a new system which doesn't appear in the Bible.
It's a nice idea that we can date the time of the year Jesus was born from Luke 1, but it doesn't stand up to scrutiny.