How long is one cycle of the earths wobble?

The Chandler wobble has a period of about 1.2 years, or 433 days. This wobble is a movement in the Earth's axis of rotation over time. The location North Pole moves about 6 meters over the course of this period.

The Earth's precession is also sometimes referred to as a wobble. This is a change in the axis of the Earth's rotation relative to its orbit around the sun and takes quite a bit longer: about 23,000 years.

Thank you, methos, for teaching me something I never even heard of. I originally thought that edgeview was asking about precession.

I found this link to a nice article on Chandler wobble.

I'm starting to realize that HowStuffWorks, despite its folksy-sounding name, presents rather well-written and well-organized tutorials on science, plus you can keep drilling down for more detail. Highly recommended.

You're welcome, Professor. And thank you for posting the HowStuffWorks link. I've found that site very useful as well because it usually manages the delicate balance between detail and clarity quite well.