Why did Herod want to know the time of appearance of the Star of Bethlehem?

We read in Mtt 2:1-7( KJV):

Now when Jesus was born in Bethlehem of Judaea in the days of Herod the king, behold, there came wise men from the east to Jerusalem, Saying, Where is he that is born King of the Jews? for we have seen his star in the east, and are come to worship him.When Herod the king had heard these things, he was troubled, and all Jerusalem with him. ...Then Herod, when he had privily called the wise men, enquired of them diligently what time the star appeared.

Going by Herod's instructions to the Magi, his original plan was only to identify and kill the newborn king. He would however, end up killing all male babies of and below the age of two, drawing a conclusion from the information he had secretly got from the Magi( Mtt 2:16).That in deed was a hard decision m from a king in that he would lose potential candidates of his army say, twenty years in advance. His ego had been hurt by the Magi not returning to him, and the massacre was the outcome of his anger.

So, why was Herod interested at the very outset , in the time of appearance of the star ? Is it that he along with the Jews of his kingdom believed in the Messiah's birth heralded by a star; or was he simply measuring the extent of threat to his kingship by calculating the age of the newborn king ? What is the take of scholars on the topic ?

A key point is that the star the Magi spoke of to Herod was one that led them to Jerusalem. It had already been visible, and not just to them. Of course, few people would have the detailed knowledge of astronomy that the Magi had, which set them off months earlier, towards a distant land.

If this was a rare "triple conjunction" celestial event, an apparently 'backward' motion of Saturn and Jupiter, the event of 7 B.C., the first of the three alignments happened in May that year. The Magi in Persia would have noted it and calculated when the next two were due. They would realise the second one would be in September, giving them time to make the huge trip to Jerusalem. They believed the constellation of Pisces signified Israel. They believed that a special 'star' indicated a Messiah coming from heaven to establish a heavenly kingdom on earth - that was Zoroastrian belief at that time, and the Magi were likely to be Zoroastrians.

So, they were in Herod the Great's domain for the second conjunction, paid him a vital courtesy call (to save being viewed as spies) and agreed to tell him where the child was, once the third conjunction showed them. By that time, the holy family were in a house and Jesus was described as "a child" (in the Bible) which would fit in with the third conjunction happening a few weeks later. Mary and Joseph stayed near Jerusalem till after Jesus' circumcision and Mary’s purification at the temple, before fleeing to Egypt after the Magi's visit.

However, the question asks why Herod wanted to know the time of appearance of this 'Star of Bethlehem'. Please note: before he asked that (verse 7), he first asked where the Christ was to be born (verse 4). He asked this of the Jewish scholars he had called in. They explained to Herod the prophecies that said 'where' - Bethlehem of Judea. Further, the quoted prophecy said the one to be born there would rule Israel. That would be enough to make Herod apoplectic, but he had to play his cards carefully, not to give his murderous intentions away. He was 'king' and would brook no rivals!

Cunningly, he expressed an intention to show his respects to this baby Messiah, asking the Magi "what time the star appeared". Notice the tense? It was not future tense - "when will". In verse 2 the Magi had already told him that they had seen "his star" in the east, which was why they landed up at Jerusalem. But that appearing (the second movement of Saturn and Jupiter) still had not led them to where, exactly, the Messiah was. Now, everybody knew that would be insignificant little Bethlehem. The big, unresolved question remained: when would the third celestial movement be seen? The Magi had already done their calculations even before setting out on the arduous, long journey. They may have told Herod when they expected the last visible 'movement'. The Bible record does not say.

Off the Magi went, towards Bethlehem, and it was then that they saw "his star" move over to the exact location! It appeared to 'stop' right above the house where the holy family was lodging (verse 9). But, being warned of God in a dream, they did not return to Herod. Further, Joseph was told by an angel in a dream to flee to Egypt and not to return till Herod had died (which fulfilled another prophecy).

Because Herod did not know if the Magi had succeeded in locating the child, he could not be sure of the timing of this star's movements. The third and last movement was seen by the Magi likely after they had left Herod's palace. When it dawned on him that the Magi were not coming back, more time had passed. To cover all bases, Herod instructed every male baby, from birth till two year's old, to be slaughtered.

Yes, indeed, "his original plan was only to identify and kill the newborn king." But this man had a long track-record of murderous and horrific killing of all who he disliked, even those in his own family. He would have thought nothing of ordering the death of all those babies and toddlers. He cared nothing for potential Jewish army recruits when he had the Roman empire at his back.

The scholars who have proposed those points about three 'star' appearings in the year Jesus was born are:

https://religionunplugged.com/news/2020/12/14/a-rare-astronomical-event-is-happening-this-christmas-is-it-the-star-of-bethlehem

Also, David Hughes, Professor of Astronomy, University of Sheffield U.K. See an article on the triple conjunction in the British 1 September 2009 ‘Weekend’ magazine which was reviewing a BBC2 documentary on Christmas Eve that year, based on his research.

We can deduce the answer from Mt. 2:16

He ordered the massacre of all the boys in Bethlehem and its vicinity two years old and under, in accordance with the time he had ascertained from the magi.

From this we can infer that visit of the magi did not occur immediately after the Nativity. Their answer to Herod's inquiry about the timing of the star's appearance must have led him to conclude that the child could be as old as two years.

Conclusion: Herod asked about the star's timing in order to know the range of the ages of the infants of Bethlehem he would eliminate as a threat to his throne.

Herod had a very specific reason for wanting to know this information, even before the Magi failed to return.

Herod did not believe the prophecies of the Messiah, but he knew that his people did. What preoccupied the perpetually paranoid Herod was not:

But rather :

This Messiah claimant would have to meet some basic scriptural criteria about the Messiah to gain a large following (this is not hypothetical -- there were a number of people who claimed to be the Messiah).

What Herod is doing, then, in his interview with the Magi, is identifying the criteria that an alleged Messiah would need to meet if claiming to be the person heralded by this astronomical phenomenon. He's narrowing down the group of people he needs to worry about:

The murderous Herod didn't mind killing extra people who got in the way (this is the guy who killed one of his wives, two of his sons, most of his in-laws, and a lot of other people who were unfortunately in the wrong place at the wrong time).

When the Magi didn't report back, Herod cast a wide net and tried to kill everyone who met the criteria Herod had deduced. This almost certainly means Jesus was less than 2 years old at the time. The monster Herod wasn't going to risk missing his mark because his soldiers overestimated the age of a toddler in Bethlehem; he would have taken the age given by the Magi and rounded up.

Herod's paranoia & violent temperament were not unique to the end of his life, but some of his most notorious crimes were committed in his later years: see Josephus' Antiquities of the Jews Book XVII Chapters 1-7

That Herod was not in fact a faithful aherent of the Jewish faith, see (for example) Jacobs & Broyde's work here.