... and I should have made that clear in the article. I had thought about that complex of questions, but decided against including it in the article, since I thought it to be already confusing enough.
It is clear that the medieval conception of the cosmos as an eternal wheelwork created by God, continuing according to the same dynamics forever, is completely false. When the huge astronomical clocks of the former centuries had the task to demonstrate the divine care in assembling the finest detail of the celestial system, modern astronomical timepieces can but show an idealised depiction of the nature.
All planets and moons within the solar system are rotating on elliptical orbits, rather than circular. Of course this affects the accuracy of all astronomical displays. Sometimes, watches add a so-called equation of time indication, which does at least take into account the Earth's elliptical orbit around the Sun. However, the Moon's deviation from the perfect circle remains unattended. As a consequence, the value for the synodic month that I used in the article is but a mean value.
To complicate things even further, the various gravitational influences from the bodies in the solar system lead to a general reduction of orbital speeds: the Earth is getting slower, making the year longer. Also its own rotation, responsible for the solar day, is becoming slower. Some 900 million years ago, a day lasted about 19 hours, instead of 24, like today. A siderical month lasted only 23 days. Currently, the Moon is increasing its distance from Earth by about 4 centimeters per year. This, too, adds over the eons and to a substantial deviation from the fixed values that are depicted by a set of wheels. Already now, the differences in the sequence of what we ccould call "time units" (hours, days, months, years) are apparent, when ancient reports on solar eclipses are contradictory to modern calculations, based on today's values of orbital intervals.
However, I think this leads into a rather philosophical discussion: What is the purpose of an astronomical timepiece? Does it make sense to depict the cosmic system in a way that it is only valid in the very moment of the model's creation, while it becomes increasingly wrong in every minute? Could be a nice discussion here ....
Regards,
Marcus