MOONPHASE
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This complication displays the phase in which the moon is located.
Astronomy
The moon’s orbital period averages 27 days, 7 hours, 43 minutes, and 6 seconds. During this time, the Earth itself has travelled approximately one-twelfth of its orbit. The moon must therefore compensate for this motion to return to the same position relative to the sun and Earth. The synodic period of a lunation thus lasts an average of 29 days, 12 hours, 44 minutes, and 2.8 seconds, or 29.530589 days.
Two Types of Mechanisms
The many decimal places in this duration make its mechanical interpretation relatively complex. Two methods are employed, offering different levels of precision.
Moon Phases with Star Wheel Drive (59 Teeth)
The simplest method rounds the lunation period to 29.5 days. By printing two moons on a star wheel with 59 teeth (2 × 29.5), this wheel only needs to advance by one tooth every 24 hours to display the moon phases. With this system, which rounds the lunation period to its first decimal place, the display will shift by one day every 2 years and 233 days.
Moon Phases with Gear Train Drive
The second mechanism rounds the lunation period to the second decimal place, or 29.53 days. Achieving this precision requires a more complex system, as it is no longer possible to drive a star wheel by one tooth daily. In this case, the star wheel cannot have a whole number of teeth.
The solution involves driving a 7-tooth star wheel (similar to a day display) every 24 hours. Attached to this star wheel is a 16-tooth pinion. When the 7-tooth wheel advances by one tooth, it rotates by 51.43°. The 16-tooth pinion also rotates by 51.43°, advancing by 2.29 teeth.
A second 16-tooth pinion, engaged with the first, reverses the rotation direction for the moon phase star wheel. This second pinion also rotates by 51.43° (2.29 teeth). Finally, this pinion drives the 135-tooth moon phase star wheel. The moon phase star wheel’s angular advancement is also 6.09549611°, corresponding to 2.29 teeth.
If we now divide the 360° circumference of the moon phase star wheel by 59.06 (two moon phases of 29.53 days), we get:
360 ÷ 59.06 = 6.09549611°.
With this mechanism, the moon phase display will shift by one day only every 122 years and 158 days. This error is due to the digits beyond the second decimal place of the lunation duration, which are not accounted for by this gear train calculation.
Display
Most of the time, two discs (representing the entirety of the moon) are positioned on the surface of the moon phase star. The moon phase is read based on the position of one or the other of these two moons within a crescent-shaped aperture on the dial. More rarely, a hand moves across a subdial located on the periphery, where the names or symbols of the moon phases are printed.