You miss a lot of interesting stuff though.
Have you considered the supernatural or miraculous quality of that star?
A star even as distant as the moon would fry the Earth to a crisp, yet this 'star' was close enough such that it could be recognized to be over a specific house. (maybe 300 ft or so) Check out the full moon one night and guess which specific house lies underneath it.
The Magi were priests of the Zoroastrian religion ( modern day Parsi) and traveled in large groups for protection.
Joseph and Mary were told to flee to Egypt for a time, and they left the very next day. However Mary had to fulfill the purification rites at the Temple before she could leave for Egypt.
Lev 12:1 The LORD spoke to Moses, saying,
Lev 12:2 "Speak to the people of Israel, saying, If a woman conceives and bears a male child, then she shall be unclean seven days. As at the time of her menstruation, she shall be unclean.
Lev 12:3 And on the eighth day the flesh of his foreskin shall be circumcised.
Lev 12:4 Then she shall continue for thirty-three days in the blood of her purifying. She shall not touch anything holy, nor come into the sanctuary, until the days of her purifying are completed.
and see also Luke 2:22 And when the time came for their purification according to the Law of Moses, they brought him up to Jerusalem to present him to the Lord
So then the flight to Egypt could not have occurred in under 40 days after the birth, and the Magi came the day before that flight.
But we don't have a clue as to how long after the 40 days the Magi came.