This is apparantly still a great theological/archeological/astronomical mystery (at least for those who insist on the literal truth of the story). This show did not try to deny the legend - rather, it brought up several theories by modern historical astronomers as to what this "star" might actually have been -
Of the several theories, these seemed to be the main candidates:
1) - the star was a comet. Early christian era art depicts a comet form, but probably was influenced by an appearance of Haley's comet.
2) - the "star" was really an occultation of a rare Jupiter and Saturn orbital confluence by the Moon. It was barely visible to the uninitiated, but the Magi would have noticed it as they were astrologers familiar with such effects.
3) - the "star" was a supernova which has somehow escaped other historical observation. Kind of a stretch, given the accurate and carefully recorded observations of the Chinese astronomers at this time in history.
The program made some other interesting points - one being that the historical birth of christ was probably at least 5 bce and more likely about 7 bce. I was amused that they mentioned that the first creators of the A.D. western calender FORGOT THE ZERO YEAR just like the JWs did over a thousand years later.
I always check out these religious science history programs - and especially this subject, because I was always completely baffled by the JW doctrine that SATAN put up the Star of Bethlehem in a failed effort to kill the christ child through Herod. That notion probably puts up more un-answerable questions than merely trying to identify what the star might have been in legitimate astronomical terms.
Anyway, it is a good program - worth watching when they repeat it again.