Moon phase

A moon-phase display shows how much of the Moon's disc is lit, advancing through the cycle from new moon to new moon. The interval it must follow is the synodic month. NASA's Goddard Space Flight Center states: "The mean length of the synodic month is 29.53059 days (29d 12h 44m 03s)." The same page gives the anomalistic month as 27.55455 days and the draconic month as 27.21222 days; it is the synodic figure that governs the visible phases.

The usual watch mechanism approximates that number with one toothed disc. A patent assigned to ETA SA Manufacture Horlogère Suisse describes the conventional arrangement as a moon-phase disc fitted with "a star toothing 32, comprising 59 teeth" advanced "at a rate of one step per day", which "allows moon phase disc 18 to complete one revolution in 59 days, which equates to two lunations of 29.5 days". The same patent sets out a variant in which the disc has "135 teeth and completes one revolution in 59.0625 days, which equates to two lunations of 29.53125 days, very close to the true value".

The drift is given here as arithmetic from those two figures, not as a quoted number. A 59-tooth wheel models the lunation as 29.5 days against a true mean of 29.53059, so the display gains about 0.0306 days — a little over 44 minutes — each lunation, and a full day of error accumulates after roughly 33 lunations, about two years and eight months. The 135-tooth variant cuts that to about 0.00066 days a lunation. Neither source says how often a wearer is expected to correct the display.