The ability of comets to stop and point down to a town or city is explained in my article Was the Star of Bethlehem a Comet? (Article and blog posts posted on my website http://www.merryandtrue.com).
Comets with tails have the tail streaming vertically upwards with the body of the comet pointing down to the earth just before they recede away from the earth and become invisible.
By the time the Magi reach Bethlehem, Joseph, Mary and Jesus are staying in a house, not a stable (see Matt 2:11). They have also been to the Temple in Jerusalem 40 days after the birth and the time of purification for Mary.
Jesus, as a first born son, is dedicated to the Lord in the Temple on the 40th day after birth. Mary and Joseph are offering a sacrifice of two doves when Simeon and then Anna come up and prophesy over the child (Luke 2:21-38).
The wise men reach Bethlehem when the comet is in its pointing down phase. Comets do this just before disappearing. If the comet was visible for 70 days then the wise men arrive in Bethlehem to find the child when he is already nearly two and a half months old.
Merry and True 