Richard beat me to punch on this. Of course we must make certain assumptions.
First, we have to assume that the calendars were correctly calculated. Some scholars think we are off by as many as 4 to 7 years, but in any event, we know Yom Kippur happens roughly around that time of year. This year, 2012, it was September 26th. It has sometimes been celebrated as late as October 14th.
Sometimes it might be earlier. The Hebrew calendar is lunar. The Hebrew year has 12 or 13 months, 360 or 390 days. The months are 29 or 30 days. Our western calendar has also changed so trying to nail down the exact date is difficult but, at most the September 25th date is going to be off by as much as 4-7 days, since we can assume that the year is not off by more that 4 to 7 years.
We can safely assume that Angel appeared to Zechariah because the text says it was his turn to be High Priest. The setting implies this was the one day each year when only the High Priest enters the Holy of Holies to offer sacrifice. Other than that day, sacrifices were offered in sanctuary, but outside the Holy of Holies.
We have to assume that Zechariah and Elizabeth conceived on that very night and that the pregnancy lasted exactly 9 month. The date of conception is probably off, because Yom Kippur is a day of fasting and abstinence. In the Hebrew tradition, it may have also included abstinence from marital love in the Pharisaic tradition, although the day does end when the sun goes down. The Hebrew day starts in the evening. In the case of John's birth, the date of birth will also vary, so we are estimating things here.
We are also assuming that Mary conceived immediately after she pronounced her fiat to the Angel Gabriel and likewise we assume it was exactly 6 months after Gabriel appeared to Zechariah. We come to that conclusion because Mary went to Elizabeth and stayed with her for 3 months until John was born. That assumes she left the day of the Annunciation and she stayed exactly 3 months. Of course we must assume that Mary's pregnancy lasted exactly 9 months.
We are certainly in the right range of days. Of course, there are folks that use what is known as the Old Calendar. That calendar is off by a couple of weeks, give or take a few weeks, so some place the birth of our Lord around January 6th. I think Eric or Richard are more qualified to speak to that issue.
Nevertheless, the theories that Christmas was invented to replace a pagan holiday and that the Lord was born during a radically different time of year are simply wrong.
According to Gospel narrative, the Lord was born between mid-December and mid-January, unless he was:
- very premature
- very late, or
- wasn't conceived on, or about the time of, the Annunciation.
I hope this helps.