(KGTV) - Did NASA really say that February 10th was the only day you can make a broom stand on its own?
No.
Many people posted videos of themselves balancing a broom on its end.
But you can do that any day. There was no special gravitational pull on that date and NASA never claimed there was.
A broom typically has a low center of gravity. So if you stand it on end and spread the bristles just right, you can form a tripod-like structure which will hold up the broom.