The only natural phenomenon that fits the description of the Star of Bethlehem in Matthew is a comet.  Comets travel in elliptical paths and move fast enough that they often appear to change direction.  The Star of Bethlehem was visible for about two months.  The Wise Men followed it from East to West, from Babylon to Jerusalem, then South to Bethlehem.   The Star of Bethlehem, if a comet, would have been seen traveling towards the Sun as the Wise Men traveled from near Babylon to Jerusalem, appearing in the night sky moving West.  Then, as it traveled away from the Sun, it would have appeared to change direction, moving South in the night sky, as the Wise Men traveled South from Jerusalem to Bethlehem.  The Wisemen knew about the prophecy of a Jewish Messiah, or King of the Jews, from Jews living in Babylon since the exile in 596 BC when Jerusalem was conquered by Babylon.