It does not appear that this acceleration is due to any increase in local dynamics (classical wobble) such as nutation (caused by the moon) or Chandler (still debated), as these are relatively small effects.
Our work suggests that a large percentage of what people assume to be wobble, is most likely the result of the solar system curving through space (not the earth wobbling relative to local objects), changing our perspective relative to the VLBI reference points (quasars outside the solar system). Under this explanation then it is easy to understand why there is an increase in the annual rate in modern times; it is simply the observance of Kepler’s laws at work.
According to Sri Yukteswar our sun is now moving from apoapsis (where it was at the depths of the last dark age) to periapsis (where it will be at the zenith of the next Golden Age). Kepler’s Law requires that a body is increasing in speed as it gets closer to its center of mass.
We tested Yukteswar’s three data points (and applied Kepler’s laws) against the precession equation given us by Simon Newcomb (the greatest astronomer in the US at the turn of the century - same time as Yukteswar) and found that Yukteswar’s was about 40 times more accurate in predicting the changing rate of precession than Newcomb over the last 100+ years. A link to this paper is on the BRI home page.
To boil it down to number of years it suggests the precession periodicity ranges from about 26,000 years to 22,000 years (over an entire orbit cycle) with an average close to 24,000 years (Computation at flat rate of 50”p/y is 1,296,000"/50"=25,920 years to complete one cycle, computation at 54"p/y is 1,296,000"/54"=24,000 years, etc.).
Chinese Philosopher – Lao Tzu