Our earth does not wobble

I remember when I saw my first iPhone (it was an iPhone 4).  What astounded me most (but seemed completely ordinary to everyone around me, even real tech geeks) was how much technology was packed inside the thing ... most astonishingly, for the cost.  The gyroscope chip inside costs about $2.60.  Adding in the cost of the accelerometer (65 cents), the spatial orientation (and changes in that orientation) is sensed and measured with extreme accuracy, for $3.25.   That's mind-boggling to someone who knew anything at all about the cost of that same technology in 1969 (the year of the first manned moon landing).

The GPS in the iPhone was itself, quite amazing, and I spent several days trying to understand (if only from a layman's standpoint) how the Global Positioning System works.  When I thought I kind of understood the basic theory of it, I still couldn't understand how a satellite, which is in a geostationary orbit around the earth, and always ... ALWAYS ... precisely above a specific point on the earth's surface could deal with the wobble of the earth.  I mean, everyone knows that the earth wobbles like a drunken sailor, right?  Isn't that why we have seasons? 

And guess what I learned? The earth does not wobble; its axis doesn't change with the seasons ... it only appears that way from a fixed point on earth. Technically, it does precess or "wobble," but that occurs in a 26,000 year cycle. Over the course of a human lifetime, the change is so small it can be disregarded; the tilt of the earth changes so slowly, GPS works well enough for most purposes (they probably correct for it mathematically).

Here's the thing:  the earth's axis points in the same direction all the time, roughly 23.5 degrees from an axis perpendicular to an imaginary plane passing through the earth and the sun.   See the diagram below, the best one I've seen to describe it.  Note, the earth is not wobbling ... the orientation of a point on the earth changes relative to the sun ... but the planet's axis of rotation remains constant relative to that imaginary plane.

And that's why geosynchronous satellites do, indeed, remain (exactly) in place above a fixed point on the earth's surface.   Because the earth's orientation relative to that satellite doesn't change.