The narrative suggests they had not seen the star for some time: they had seen it in the east. Now they saw it again as they went from Jerusalem to Bethlehem in confirmation of the location told them by the chief priests and scribes.
The question is asked, how can a star be positioned over a house, rather than over a city or indeed over an entire country? Given our understanding of astronomy and our observation of the apparent motion of the heavens, we would expect them all to move together, and for stars to be so distant from the earth that it would be impossible to say that a single star was above any object on earth. This star however is best thought of, not as a normal celestial object, but as something supernatural designed by God to be a sign of the most significant event since the foundation of the world: the incarnation of the Son of God. He is the one spoken of by Balaam, who, despite being a false prophet, gave that most exalted of prophecies regarding the Messiah: ‘I shall see him, but not now: I shall behold him, but not nigh: there shall come a Star out of Jacob’ (Numbers 24:17). This sign is given according to the purpose of the stars as first described during creation: ‘Let there be lights in the firmament of the heaven … and let them be for signs’ (Genesis 1:14). It is evident from the description that this star did not remain at the same angle of elevation. Perhaps we could think of it as taking a more vertical position above the earth as the wise men moved closer to the house, rather like the bubble in a spirit level which only moves to the centre as the level comes close to horizontal.
Something which people puzzle over is why the wise men came to a house. Why were Mary and Joseph and the child not in the stable anymore? Why had they moved from the stable they were in to a house? Whether there was a distant relative of theirs in Bethlehem, or somebody else who would take them in; by the time the wise men arrived they were now in a house. It was on the first night that they were turned away from accommodation and were obliged to find refuge for the night in a stable. But they would not have stayed there, and by now they were in a house. Some think it must have been more than 40 days after the birth that the scholar priests came to worship Christ. Why? Because, after 40 days, Mary went up to Jerusalem. After 40 days a Jewish mother would have her purification and she had to go and make an offering in the temple in Jerusalem. We are told in the Bible what kind of offering Joseph and Mary made: two turtle doves or two pigeons, but interestingly in the book of Leviticus that that was the offering that the poor people made, and we presumably she had not yet received the gold and the frankincense and myrrh, because if she had been in possession of them, then surely the first thing she would have done in Jerusalem would be to purchase an offering lamb. So although the Christmas cards often depict shepherds and wise men all gathered round the manger, very likely they came on different occasions, to different places.