The only star that does not belong to a constellation is the Sun. The Sun travels through the 13 constellations along the ecliptic, the 12 of the Zodiac and Ophiuchus.Among the remaining stars, the nearer ones exhibit proper motion, so it is only a matter of time before some of them cross a constellation boundary and switch constellations as a consequence.mong the remaining stars, the nearer ones exhibit proper motion, so it is only a matter of time before some of them cross a constellation boundary and switch constellations as a consequence.