The lunar phase affects when the Moon crosses the local meridian
(is due south), an event also called upper transit.
Equatorially mounted telescopes track their celestial targets by rotating around an axis that points toward the pole and is aligned with the local meridian
. Even unusual instruments, like the McMath-Pierce solar telescope on Kitt Peak in southern Arizona, take advantage of this principle.
This is simply the right ascension of stars on your local meridian
at any moment.
Here the antenna remains fixed with respect to the Earth and pointed at the local meridian
. The Earth's rotation causes the dish to scan a band of declination in the sky, making a full sweep in 24 sidereal hours.
This procedure automatically aims the instrument at the local meridian
, and you can set the mount's right-ascension circle to read the current sidereal time.