The birth narratives in Matthew and Luke are amazing: woven together, with John 1:1-14 added in, they narrate 'the Christmas story'. Compared side by side, examined for possible contradictions, either of each other, or of historical facts (was Quirinius the governor of Syria when Jesus was born?), the two narratives pose a variety of opportunities to apply hermeneutical skills (see post below and comments on it).
One aspect of the narratives are the details. Was there a moving star? If so, what in astronomical terms was it? Does presuming there was some astral phenomenon assist with more accurate dating?
Anglican Curmudgeon offers the first of a series of interesting posts on the date of Jesus' birth. I won't alert you to each of the posts. If you like this first one I am sure you will return to the rest.