The guy who put this study of the Star of Bethlehem together did do some research into what other phenomena could explain it, and came to the conclusion that it was an unusually bright conjunction of Jupiter with Venus, unusual because the conjunction was so close the two couldn't be distinguished with the naked eye, making it appear exceptionally bright; and he says the math shows that this closeness is extremely rare, which made it the best candidate for the star.
He shows this at 44 on the counter if you're interested:
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