How Often Does The Moon Return To The Same Point In The Sky From A Fixed Location On Earth?

I point a telescope at a full moon one night so that the moon is centered in the eyepiece, and I leave the telescope locked in this position. If I understand correctly, the moon will shift a few degrees each night either north or south of the east-west line, so on the second day the moon will not be centered in the eyepiece. After how many days will the moon (any phase) be centered in the telescope again? How long before the next full moon is centered in this telescope?