Luke 1:10-11 is the key to determine Jesus’ date of birth. It contains a story of Gabriel’s visit to Zachariah when whole multitude of Israel people outside the Jerusalem temple, while they were waiting for Zachariah burning incense inside.
10 And the whole multitude of the people were in prayer outside at the hour of the incense offering.
11 And an angel of the Lord appeared to him, standing to the right of the altar of incense. (Luke 1: 10-11)
Phrase “whole multitude of the people” is an initial primary clue to investigate date of Elizabeth’s conception.
Three possible Hebrew major festivals allowed the whole multitude of Israel people gathering outside Jerusalem temple: Sukkot, Yom Kippur, and Shavuot.
By lot, Zachariah served burning incense (Luke 1: 8-9). In contrary, incense burner in Yom Kippur is was by lot and was obligatorily carried out by the High Priest. Hence, Zachariah was not high priest and the fest was not Yom Kippur.
Zachariah was included in the course of Abia.
There was in the days of Herod, the king of Judea, a certain priest named Zachariah, of the course of Abia: and his wife was of the daughters of Aaron, and her name was Elizabeth. (Luke 1: 5)
Course of Abia was the eighth course, while course of Jehoiarib was the first course, which served in second week Av, as determined from Ezra 7: 8-10 and Rabbi Jose ben Halafta’s testimony (± 150 M). Between the first and the eight courses, there were feast of Rosh Hashanah and Yom Kippur in which the whole priest from all courses were in charge together. Then the course of Abia served at week 9 (= 8 + 1) from the second week Av, i.e. 3rd week Tishri, which was the Feast of Sukkot. This will be discussed in more detail in the next posting.
Gabriel visited Zachariah in Sukkot 15th day of Tishri 3756 Hebrew Calendar a.k.a September 26, 6 BC Julian Calendar, instead of Shabuot or Yom Kippur .