The two key finds:
+ A pin and slot mechanism accounting for the moon’s elliptical orbit.
+ 26.5 x 2 = 53
The lunar cycle is closer to 29.53 days. A lot of moon phase clocks have gears with 59 teeth (as did the Antikythera mechanism) that closely approximate two lunations. The Gregorian calendar has a sidekick lunar calendar good to about one day in 8,000 years on average, which is even better than the Gregorian calendar’s approximation of the solar year (365 + 1/4 -1/100 + 1/400 = 365.2425), which is only good to about one day in 3000 years. The lunar calendar is used with the Gregorian Calendar to calculate the date of Easter.
What powered the thing? A wind-up coil spring was about 1500 years in the future................