As long as you are carrying your magic number to nine significant figures, don't forget to allow for the perturbations right here on Planet Earth that could perturb its motions. A few examples:

Butterflies, including the migratory monarch butterflies.

Recurring boom-bust cycles of lemmings in Arctic regions.

The sudden redistribution of water when millions of toilets were flushed going into halftime at the Super Bowl.

Not to mention big shakes such as sporadic major earthquakes and volcanic eruptions.

For all we know, the cumulative effect of these actions could alter our planet's spin and precession rates slightly, mucking up your calculations.