The flaw in the nova/supernova theory is that those would have been observable to anyone in the world, which means Herod would not have needed to ask the Magi when it appeared in the sky.
It also seems clear from Scripture that the "star" was an event that likely unfolded over a long period of time -- which would explain why Herod ordered the execution of all the male children under the age of two. Jesus Christ was probably two years old when the Magi visited the Holy Family, not an infant.
Well, there are ephemerides online. They show declination, latitude.
As to Herod, he and his advisors probably left the stars to the experts at divination.
I think it’s less about the spectacle and more about the significance attached to it by the shamans of the time.
Nebuchadnezzar saw his dream, too, but needed someone to tell him what it meant.
"St. Matthew (2:1) tells us that Jesus was born "in the days of King Herod". Josephus (Ant., XVII, viii, 1) informs us that Herod died after ruling thirty four years de facto, thirty seven years de jure. Now Herod was made rightful king of Judea A.U.C. 714, while he began his actual rule after taking Jerusalem A.U.C. 717. As the Jews reckoned their years from Nisan to Nisan, and counted fractional parts as an entire year, the above data will place the death of Herod in A.U.C. 749, 750, 751. Again, Josephus tells us from that an eclipse of the moon occurred not long before Herod's death; such an eclipse occurred from 12 to 13 March, A.U.C. 750, so that Herod must have died before the Passover of that year which fell on 12 April (Josephus, "Ant"., iv, 4; viii, 4). As Herod killed the children up to two years old, in order to destroy the new born King of the Jews, we are led to believe that Jesus may have been born A.U.C. 747, 748, 749. The enrollment under Cyrinus mentioned by St. Luke in connection with the nativity of Jesus Christ, and the remarkable astronomical conjunction of Mars, Jupiter, and Saturn in Pisces, in the spring of A.U.C. 748, will not lead us to any more definite result."
A.U.C. = Ab urbe condita, which was a calendar year based since the founding of Rome.
In addition, there a few possibilities in terms of harmonizing the infancy accounts of Matthew ( the birth of Jesus, the adoration of the Magi, the flight into Egypt, the slaughter of the Holy Innocents, and the return to Nazareth) and Luke (the birth, of the adoration of the shepherds, of the circumcision, of the purification of the Virgin, and of the return to Nazareth). Insofar as the author of the encyclopedia entry goes, the third possibility quoted below is deemed the most probable:
"As Luke 2:39 appears to exclude the possibility of placing the adoration of the Magi between the presentation and return to Nazareth, there are interpreters who have located the advent of the wise men, the flight to Egypt, the slaughter of the Innocents, and the return from Egypt after the events as told in St. Luke. They agree in the opinion that the Holy Family returned to Nazareth after the purification, and then left Nazareth in order to make their home in Bethlehem. Eusebius, Epiphanius, and some other ancient writers are willing to place the adoration of the Magi about two years after Christ's birth; Papebrochi and his followers allow about a year and thirteen days between the birth and the advent of the Magi; while Patrizi agrees with those who fix the advent of the Magi at about two weeks after the purification. The text of Matthew 2:1-2 hardly permits an interval of more than a year between the purification and the coming of the wise men; Patrizi's opinion appears to satisfy all the data furnished by the gospels, while it does not contradict the particulars added by tradition."