In recent years the long-running myth about the equinox being a day possessed of a special property which allows eggs to be balanced on their ends has grown to encompass brooms as well. And the broom-balancing myth has likewise grown to encompass days other than the equinox on which — according to NASA, supposedly — "gravitational pull" and/or a "planetary alignment" creates just the right conditions for brooms to stand on their ends unsupported:
As with the egg-balancing myth, this broom-standing phenomenon has nothing to do with equinoxes or planetary alignments. With some practice and patience, anyone can make a broom (or an egg) stand on its end any day of the year.
As explained in this video, a broom typically has a low center of gravity positioned just above the bristles. So if you stand a broom on end and spread the bristles just right, you can form a tripod-like structure which will hold up the broom: