Luke tells us that Mary made haste to visit Elizabeth (Luke 1:39). Therefore, she didn’t wait around in Nazareth unnecessarily, but journeyed to Judea at the earliest opportunity. She was anxious to see Elizabeth and prove the angel’s words one way or another. The problem is that a young girl wouldn’t make such a journey alone. It would be assumed by all in first century culture that respectable women never traveled alone. Luke presents Mary’s safe visit to Elizabeth and her safe return home by assuming a Jewish context of safety. That is, he implies the use of the Jewish annual festivals and of Mary’s using pilgrimages with friends and relatives to journey to and from Judea.
If we are going to understand when Mary left Nazareth for the hill country of Judea, we need to keep in mind that Zacharias was a priest of the course of Abijah. Understanding that his time of service was either the third or fourth week of Iyar, the second calendar month of the Jews (his first week of biannual service), or during the second or third week of Marcheshvan, the eighth month in the Jewish calendar. It was possible for Mary to have made such the journey to Judea weather Zacharias was serving during his first or second ministry that year, because six months after a mid-June pregnancy for Elizabeth would have the angel visiting Mary in Kislev, the ninth month, and permit Mary to journey to Judea at that time for Hanukkah, which was an 8-day minor festival, beginning on the 25th of Kislev. If, on the other hand Zacharias was serving in the middle of Marcheshvan, the 8th month, six months later would allow Mary to visit Elizabeth with friends and relatives during their pilgrimage for Pentecost. Nevertheless, there would then be a problem for Mary’s return journey, if Elizabeth’s pregnancy occurred in the month of Marcheshvan, and Luke is correct concerning the length of Mary’s stay.
Luke tells us that Mary stayed with Elizabeth for about 3 months (Luke 1:56). If Mary arrived late in Iyar, the second calendar month of the Jewish year or even during the first week of the third month, she would have had to wait until Tabernacles was over, late in Tishrei, the seventh calendar month, before returning home. That would have been nearly 5 months before she was able to return to Nazareth with friends and relatives. Nevertheless, if Mary journeyed to Judea for Hanukkah, she could have returned with friends and relatives about three months later after the Feast of Purim (the 14th of Adar, the 12th month), just as Luke records.
No other reckoning fits the Scriptures. Therefore, it is my understanding that Elizabeth’s pregnancy took place near Pentecost, and Mary’s near Hanukkah. This would place John the Baptist’s birth near Passover and Jesus’ birth in or near the 7th month of the Jewish calendar. I place it on the Feast of Trumpets, or Rosh Hashana, the Jewish New Year.
 The course of Abijah could serve in the Temple during the 3rd or 4th week of the Iyar (2nd calendar month, corresponding to our April-May). Which week it served depended upon what date in which the first Sabbath fell in Nissan (1st calendar month – corresponding to our March-April). Temple service was not reckoned from the first day of the calendar year but from the first Sabbath of the calendar year. If the first Sabbath of the year fell upon either the 1st or 2nd of Nissan, the course of Abijah served during the 3rd week (Sabbath to Sabbath) of the month of Iyar. If the first Sabbath of the year fell upon the 3rd to the 7th of Nissan, then the course of Abijah would serve in the Temple during the fourth week of the month of Iyar. Correspondingly, if the course of Abijah fell in the 3rd week of Iyar, then its second week of service would fall in the 2nd week (Sabbath to Sabbath) of Marcheshvan (the 8th calendar month, corresponding to our October-November). If the first week of the course of Abijah fell in the fourth week of Iyar, then its second week of ministry would fall in the third week of Marcheshvan.
 I’ll discuss this point more in depth in a later study when I actually discuss the birth of Jesus.