[xgqfnznw] Moon phase and position

The moon's phase and right ascension in the sky defines, by the geometry of the earth, moon, sun, and background stars, a unique day of the year.

Because a given moon phase only occurs a few times a year, a particular phase and position among background stars probably won't reoccur for many years.  How often does the moon return to approximately the same given position and phase?  The moon's orbit is complicated: lunar precession.  Possibly relevant: Metonic cycle, saros.

One cannot easily take a photograph of the moon among background stars because the moon (or the sun) is too bright.  Best would be to simulate it.  Draw a diagram for a given date.  Recreate the sky on a given special date, maybe for a letterhead.

The moon travels across the background stars at about one moon diameter per hour (units program: "circle / siderealmonth * 31 arcminute", where 31 arcminute is the diameter of the moon).  How faint of stars must be included in the background of a real-time simulation to provide enough texture to notice movement?  How big should the moon be magnified?