Introduction to Earth Sciences I

2.4 Are the motions regular or chaotic?

Part of the answer to this question is that they are very regular. When we say that the tilt, wobble and stretch of the orbital motions have periods of 20, 40 and 100 thousand years that is usually taken to mean that these are regular periods. And in fact they are regular, but only approximately. There is a spread in period around 20 thousand (say) and it is not possible to predict exactly what the period will be. The variation is quite small so for most purposes in analyzing the past record the periods can be taken to be very nearly regular.

This is not the case for the tilt variations of Mars, however. Mars has a much greater range of tilt variations from around 11 degrees to 38 degrees. And there is no well defined period. the motion of Mars' tilt axis is an unpredictable wobbling around. It always lies between 11 degrees and 38 degrees but within that range it is very difficult to predict what the tilt will be at any time. Most of the planets have somewhat chaotic tilt variations. It is believed that the Earth may also have had a chaotic tilt variability in the past but that the presence of the Moon has acted to gravitationally stabilize the tilt by "holding it steady".

A quick look at the Chandler Wobble path leads to the conclusion suggests a somewhat unpredictable behavior. Again, like most such systems the variation has bounds -- the rotation pole and the axis of figure never get beyond a certain distance apart and the period at which one circles the other is always about 430 days, but never exactly predictable.

All of the motions then have some degree of unpredictability associated with them. Mars' tilt is highly unpredictable, Earth's precession for instance is really quite predictable. In asking the question -- are the motions chaotic -- the answer varies with the planet and the particular motion involved.

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