The FB 1L complication shows the age and phase of the Moon.
The hand moving back and forth is driven by a rack-and-gear system
(called the “feeler-spindle” by Chronométrie Ferdinand Berthoud).
This Moon complication accumulates only one day error in 577 years
of operation.

Astronomers have found that the lunar phases gradually change over
the period of a synodic month that is estimated to be 29.53059 mean
solar days in length, i.e. 29 days 12 hours 44 minutes and 2.8-2.9 seconds.
The FB 1L approximates the synodic month to
29 days 12 hours 44 minutes and 15 seconds (29.5307291666 days).
This is accomplished thanks to gears arranged in such a way that the gear
ratio from the hour hand to the Moon indicator is:
56699/1920 = (31²×59)/(2⁷×3×5).
Note that the moonphase cam (12-pointed star) is driven by a 236-toothed
internal gear (236/12 = 59/3).

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Check out and download this 3D model on Sketchfab [ https://skfb.ly/6YIKI ]
My other 3D models can be found at [ https://sketchfab.com/cyamahat ]

Finally, for a quick factorization of the fraction given above, check out my
Fraction Simplifier on observablehq.com [ https://observablehq.com/@christophe-... ]