Tuesday, July 08, 2003

Earth wobble mad science:

Asked by Richard, a graduate student in science, from Beardsley, MN:

How long have scientists studied the Earth's wobble? I have been told it is constant.

Whoever told you this probably meant ?the Earth is constantly wobbling,? rather than ?the Earth?s wobble is constant,? because the wobble is certainly not constant. In fact, it is chaotic, and therefore unpredictable in the long run.

We have been studying the Earth?s wobble for as long as we have been able to detect it, so it is more a question of when different observing and analytical techniques were developed, as well as technologies. As our observational and analytical capabilities increased, we discovered that there were in fact several different kinds of wobble. Like a lot of chaotic processes, the more closely we looked at it, the more detail there was!

The first level of wobble is pretty easy to understand in terms of classical physics and day-to-day experience. It is called precession--? and it is exactly the same motion as a top makes, slowly changing where its pole of rotation points because the center of mass is not directly over the top?s point of contact with the floor, and therefore gravity exerts a torque on the top. For the Earth, this motion is called precession of the equinoxes, and the torque results from the fact that the Earth is flattened at the poles and that the Earth?s axis is tilted (?inclined?) relative to the sun and so the sun is always pulling a little more on the Earth?s near-side bulge than on the far-side bulge, trying to straighten up the inclination. This is what causes the ?Pole Star? to change--?today the sky appears to rotate around a point very near the star Polaris, but precession will make other stars the ?Pole Star? in the future (and the past)! Since the cycle is about 25,800 years long, when we try to imagine the sky over ancient Stonehenge, Egypt or Sumer, precession must be taken into account, since 5,000 years ago represents almost 70 degrees around the cycle. Observationally, this change was probably detected very early on, probably by careful long-term stellar observers like the Egyptians, Babylonians and the much later Maya. Certainly we know that by the time of ancient Greece this motion was known, but not understood. If the only thing your technology was able to measure was the precession, you might think it was constant--?you would have to wait around a long time to verify the second time around!

As soon as we understood that the sun was causing torque and precession, we knew that there were other things out there torqueing the Earth around too--?the Moon certainly, but the other planets also exert tiny torques that are measurable, and these cumulatively cause the first level of detail on the cone traced out by the precession. These small deviations from the precession are called nutations, and the largest contributor is the Moon?s pull on the Earth?s bulges, causing an oscillation with a period of about 18.6 years.

As soon as we figured out dynamics and moments of inertia etc. we were able to predict other types of wobbles. When you spin an object around an axis that is not one of its principal axes, it will wobble (sometimes pretty violently; try spinning a rubber-band bound book around on various axes to see what happens). Euler applied this theory to Earth, and in 1758 predicted that an extra level of detail in the wobble should be observable with a 304 day period since the Earth was not quite spinning around its flattest point, but this wobble was not detected until 1891 by Chandler (who found it was in fact 435 days long). Euler?s calculation was for a perfectly rigid body with the shape of the Earth, but since the Earth is not quite rigid, the longer period is observed. This wobble is now called the ?Chandler Wobble? and is observed to be truly chaotic, sometimes collapsing to be almost unobservable, and sometimes growing to change the location of the pole of rotation by about 10 meters (see the USNO explanation of Earth orientation). We still do not fully understand what causes these changes, but it is definitely an internal process, probably something like damping in the fluid outer core, or mass redistribution in the mantle. We do know that since the mantle and the core have slightly different shapes they will nutate at different rates, so there is constant friction at the core-mantle boundary due to this differential nutation. Chandler was an observer and calculator of the first order, despite having only a high school degree (for more on him see his biography).

The finest level of detail observed so far are the changes in the length-of-day (LOD). Each day differs in length from others at a level of several milliseconds, and so this has only been recently observed, although it was predicted by Kant in the 1750s. The pattern of these changes is partly regular, and partly chaotic. We see regular annual variations and a variation with a period of about 200 years, and several chaotic ?patterns? with typical scales of several years to a few days. Just as that ever-spinning skater spins faster or slower depending on how she holds her arms and leg, the Earth will spin faster or slower depending on where there is more snow, water, air, rock, etc. Some of these things move around easily, some do not. Again, these individual causes can be understood easily in terms of classical physics, but there are so many possibilities that actually identifying which change causes what difference in the length of day is impossible. Since the root cause of LOD variations is the redistribution of mass in the Earth system, this must also affect the Chandler Wobble, but these changes are so slight we have not detected them yet.

To complicate all this a little more (you knew that was coming, didn?t you?), there are some other changes in how the Earth moves. The inclination of the Earth?s axis actually varies between about 21.5 degrees and 24.5 degrees with a period of about 41,000 years (present value is 23.5 degrees). This obviously affects precession and nutation. There is also a change in how elliptical the Earth?s orbit is around the sun, varying from 0.01 to 0.007, with a period of about 92,400 years--?this change affects precession rates very markedly (present value 0.016). So we have a lot of wobbles going on at the same time, some of them directly coupled to each other, some indirectly. With periods ranging from several days to almost 100,000 years, you can imagine that there is plenty of opportunity for some rather complex interference between the various phenomena. This produces the chaotic behavior that we observe, and which we believe is typical for multi-planet solar systems.

For a good discussion of these concepts at an advanced high-school level and how they affect climate, see The Motion of the Earth in Space.

I got some of the historical part of this from Historical Development of Earth Rotation Knowledge.