Aaron said:Planets do not move in the sky like stars. They can rise and set in seemingly strange places, can stop and even move backwards. They're called "wandering stars." The word planet itself comes from a root meaning "to wander."
Since you know that, you should be able to deduce when planets "align" [the closer eclipses the futher from earth's perspective] that may produce an unusual brightness, but it would be short-lasting. In fact, if this lasted much time at all, it would have to be Saturn and Jupiter, the only 'outer' planets identified, and because of their distance the brightness produced would not be that bright.
Your reference to the use of trigonmetry to determine the 'star' was directly above the Christ child is on the laughable side. Just think... all they would need to determine they are directly below a mark in the sky is a string with a small weight held above them. Gravity holds the weight and string directly 'down' and they could sight the line of reference that way. And maybe they did... they left Jerusalem and saw the phenomenon, used some similar 'instrument,' and determined they needed to travel southest and they were rapidly getting close. Still, the house in which the child was located would need to be quite isolated-- if their guide was truly a star(s) and/or planet(s). If it was a miraculous phenomenon, as 'big' as a hot air balloon, there would be no need.
Another possibility is a comet; not likely a magnificent one, but one which atronomers (which necessarily included astrologers; there was no division between the 2 for many centuries yet) would notice and study. A comet would be easier to get a fix on, it could have appeared once for days or weeks, then appeared again on its 'return' after the gravitational acceleration from the sun; and they were considered to be omens of new kings, or fallen 'old' kingdoms... like England in 1066, when an appearance of Halley's Comet encouraged William to invade and conquer. In this sense, astrology, per se, has truth in that it did influence worldly events.