Your question is intriguing, even if the lack of information in the Bible suggests that we don’t need to know! Speculation won’t get us very far, either. However, it is possible that the conundrum hinges on the translation of the Greek word we take as “star.” Perhaps it wasn’t a scientifically identifiable heavenly body at all. That would explain why we are all scratching our heads wondering did the Magi first see “his star in the east” and then follow it west? Or did the star rising in the east simply alert them to the anticipated birth of a king in Israel as prophesied in Numbers 24:17 (1) and so the Magi packed their bags and headed west towards Israel?
The English Standard Version presents us with a slightly different take on Matthew 2:2 and 9:
“For we saw his star when it rose and have come to worship him... After listening to the king [Herod, in Jerusalem], they went on their way. And behold, the star that they had seen when it rose went before them until it came to rest over the place where the child was” (Matthew 2:2, 9).
The ESV Study Bible Notes suggest that the star was not a natural phenomenon (e.g., a comet, supernova, or conjunction of planets) but was supernatural. Given the distance to be covered from Babylon to Jerusalem (800 miles via the main trade route), and the likely size of the caravan (attendants and guards) it would have taken 40 days or so to make the journey.
The New Living Translation puts it this way:
”We saw his star as it rose and we have come to worship him... And the star they had seen in the east guided them to Bethlehem. It went ahead of them and stopped over the place where the child was” (Matthew 2:2, 9).
The NLT Study Bible Notes say “star as it rose” could also be translated as “star in the east.” Also, that the star was placed by God to guide the wise men to the Messiah and then refers to the prophecy in Numbers 24:17. (1)
Young’s Literal Translation of Matthew 2:9 says only that it was after they had got to Jerusalem and spoken with Herod that the star they had seen in the east “did go before them, till, having come, it stood over where the child was.” It directed them from Jerusalem to Bethlehem, 6 miles south.
The KJV translation that the Magi “saw his star in the east,” suggests they saw the star where they were in Babylon, which is to the east of Jerusalem. The night sky was well known to people living 2,000 years ago but it seems this star was new – that it had never before been seen and charted. Did they then follow this object for 800 miles, heading west towards Jerusalem, travelling at night? The Bible does not say.
Any astronomer living in the northern hemisphere knows that the North (or Pole) Star appears to be in a fixed position. No matter where a person lives in the northern hemisphere, if they follow a path directly towards the North Star, they will end up at the North Pole. Of course, you would have to be travelling at night to keep your eye on it. But only after they get to Jerusalem scripture says “The star went before them.” Bethlehem was only 6 miles from Jerusalem, almost directly south, so this implies very specific, localized guidance from the traveling star, which came to rest over the young Jesus’ specific location.” Since when does a star rise in the east then head west (and slightly south) for 800 miles, then move 6 miles south and stop? And where did it go to after the Magi found Jesus? Which brings us back to the Greek word ‘aster’ which is translated in Matthew’s gospel as ‘star’.
My Greek Interlinear by William D. Mounce translates the Greek word ‘anatole’ as east = the place of rising, the east, i.e., the sun. As we know, the sun appears to rise in the east and set in the west as the earth rotates. The sun, of course, is static. The Greek word ‘aster’ is translated as star – but it does not always literally mean a star. It can also mean “luminous body like a star” and refers specifically to Matthew 2:2, 7, 9, and 10. (2) It is only after they get to Jerusalem that Matthew 2:9-10 offers us a clue:
”The star they had seen in the east guided them to Bethlehem. It went ahead of them and stopped over the place where the child was. When they saw the star, they were filled with joy!”
This suggests that before they got to Jerusalem the star had disappeared, which would explain why they were so delighted to see it again. The only facts offered in the Bible are that the Magi saw a star rise in the night sky in the east where they were in Babylon and they subsequently travelled all the way to Jerusalem. Even though they knew about the prophecy of a royal birth in Israel (1), would they have known about the prophecy in Micah 5:2-4 which named Bethlehem as the place where this promised ruler would come from? After all, they had not gone directly to Bethlehem, but to Jerusalem and it was Herod the Great who told them to go to Bethlehem. Then the star they had seen in the east leads them in a southerly direction for about 6 miles and stops over the place where Jesus was.
Only one thing is certain – what they saw in the east and what they saw that lead them from Jerusalem to Bethlehem was supernatural – it was “a luminous body like a star” (2). Nothing says they followed this heavenly light from Babylon to Jerusalem, only that it seems to reappear after they got to Jerusalem and lead them to Bethlehem.
(1) ESV Study Bible Notes: Numbers 24:17 prophesied that “a star shall come out of Jacob, and a scepter shall rise out of Israel.” This was understood by Jews to point to a messianic deliverer (e.g., Dead Sea Scrolls, Damascus Document 7.18-21; Testimonia 9-13.)