The idea of the Wise Men with gifts has big problems: only Matthew mentions them, and the Syriac Church says there were 12 of them, probably representing the 12 tribes of Israel. If this were so, you would wonder why the Jews (i.e. the tribes of Israel) opposed Jesus. Perhaps it was wishful thinking... But perhaps they could have been any set of kings and 12 looked like a good number.
Unlike in nativity plays, the Wise Men did not arrive at the same time as the Shepherds, they visited Jesus at a house not a stable (Matthew 2:1–12). The fact that Herod (who in fact must have been dead at the time of Christ) allegedly ordered all children under the age of 2 to be slaughtered, indicates that they did not arrive until a good two years after the birth.
As far as any stars/planets, conjunctions are concerned,
(i) a conjunction does not last much longer than a few hours, so there would be nothing to follow.
(ii) there is a computer program, PyEphem, (http://rhodesmill.org/pyephem/
), you can download and run to show where all the major stars and planets were at any point in history - you will see that there was no "star", from which we can conclude that the author of Matthew, who was not around at the time of the alleged birth, was not inspired by God to foresee such a program. The author of Matthew has been caught out in his lies.