It of course depends on the focal length of the lens, but with a tele lens in the 200-400mm region (also depending on your sensor size), I would estimate that the moon crosses the image in the order of a minute. There is plenty of time to frame and focus the shot, but you have to readjust your camera every couple of shots. This motion is just the earth rotation and the same for the moon, the sun and all the stars. The rotation of the moon around the earth becomes noticeable only from day to day, as the moon roughly moves 13 degrees/day. Tracking mounts have a separate speed setting though, which does take the moons movement into account for greater precision.

Exposure time was 1/640 of a second[1]. Must say I’m surprised it was that fast, but you fight both blurriness from the motion and the quite intense light reflected by a full moon.

So first manually focus, then I aimed a bit ahead along its path and waited a few seconds. Remote trigger and tripod is necessary to avoid any camera movement.

[1] f/9, Iso 400, -3 step

Ignoring the (rather slow) orbital motion of the Moon, consider: the sky (and the Moon) appears to rotate 360°/24 h. This amounts to 360/(24*3600) = 0.004167 °/s. The apparent size of the lunar disc is about 0.5°, so it takes about 120 s for the Moon to move by its own diameter in the sky. Plenty of time.