Against the background stars the Moon shifts about half a degree an hour — its own apparent diameter — which is slow enough to be invisible and fast enough to watch.

Thirteen degrees a day works out at roughly one Moon-width per hour. Line the edge up with a rooftop or a branch, look away for twenty minutes, and the gap will have opened visibly. It is also why the Moon occults stars: it does not slide past them so much as run them over.