Expert: Courtney Seligman - 10/16/2008

Question
Dear Courtney Seligman,


A friend of mine made the following analogy to prove me that mountains balance our planet while it's rotating around its axis:

"mountains, with their deep crustal roots, decrease the wobble of the Earth during its rotation around its axis and make its movement more regular and smoother, just as weights on the wheel balance the latter in order to decrease its vibration and regulate its movement."


It seems strange, indeed. But I have no enough knowledge to refute him.

Thus, could you tell me whether his theory is right or wrong, and explain to me why his analogy is biased, please?





Sincerely

Answer
Your friend's analogy is wrong, on several counts.

First, the purpose of wheel weights has nothing to do with the intrinsic rotation of the tire around its axis of rotation. If the tire were spinning in space, like the Earth does around its axis of rotation, it would keep spinning without any change in its rotation (that is, without any wobble), regardless of its shape, orientation, or direction of rotation. The angular momentum of any spinning body (such as the tire or the Earth) is constant, and the way it spins remains constant, so long as an external torque is not applied to it.

So, wheel weights or no, and mountain ranges or no, the tire would spin perfectly smoothly, and the Earth rotate perfectly smoothly, however they happen to rotate, ignoring external factors.

Of course, there are external factors, which is the reason wheel weights are needed for tires. But as you will see, mountains do not serve as wheel weights for the Earth.

For tires, the external factor is the torque delivered to the tire by the driveshaft. If the axis of the driveshaft is absolutely fixed in space, and perfectly parallel to the axis of rotation of the tire, any torque applied to the tire merely increases or decreases its rate of rotation; but in practice, absolute alignment is impossible, so the tire's axis of rotation tends to "precess" around the axis of the driveshaft. Wheel weights are used to slightly change the moment of inertia of the tire, and compensate for the inaccurate alignment.

For the Earth, the external factor is the torque delivered to the Earth by the tidal forces of the Moon and Sun, acting on the non-uniform mass distribution of the Earth. If the Earth were perfectly uniform and spherical, there would be no such torque, and the Earth would rotate uniformly; but because the rotation of the Earth causes an equatorial bulge of about 12 miles in radius (compared to the polar radius), a torque is developed about the pole of the Earth's orbit (due to the Sun's tidal force on the Earth), and simultaneously, about the pole of the Moon's orbit (due to the Moon's tidal force on the Earth).

If the axis of rotation of the Earth and the two orbital axes were in perfect alignment, there would still be no wobble or precession of the Earth's axis of rotation. But the Earth's axis of rotation is tilted 23 1/2 degrees relative to the axis of its orbit, and (depending upon the current orientation of the Moon's orbit relative to ours) between 18 1/2 and 28 1/2 degrees relative to the axis of the Moon's orbit. As a result, the average torque of the solar and lunar tidal forces, acting on the equatorial bulge, causes the Earth to precess (or "wobble") around the pole of our orbit, once every 26000 years. (The lunar axis not being aligned with the solar axis causes a slight wobbling back and forth relative to the average precession, called "nutation", once every 18 years -- the time it takes the Moon's orbit to rotate once in space, relative to ours.)

Now, if mountains could balance the Earth, they would prevent its precession; but we do precess, so nothing is counteracting this effect. In other words, the Earth doesn't seem to have any "wheel weights", mountains or otherwise.

The reason mountains don't prevent the precession is that to do so, (1) their masses would have to be comparable to the mass of the equatorial bulge, which is not possible because the bulge is much larger than any mountain range, and (2) their masses would have to be unbalanced relative to the Earth's structure in exactly the opposite way to the equatorial bulge, which is very unlikely (their actual positions being more or less random). Just as putting wheel weights at random positions would not balance a tire, putting mountains at random positions would not balance the Earth. But even if you could put them in just the right place, and they did have masses comparable to the equatorial bulge, (3) they would not represent an "extra" mass attached to the surface of the Earth, as your friend must be supposing. In fact, even continents, which are much larger and more massive than mountain ranges, do not represent extra masses attached to the outside of the Earth.

The reason for this is that in the region 30 to 80 miles below the surface of the Earth it is very hot, and the temperature of the rocks is only a few hundred degrees below their melting temperature. This makes the rocks "plastic", or deformable, when exposed to huge forces (such as the weight of the miles of rock sitting on top of them). In addition, the continents and mountain ranges are made of rocks which are only half as dense as the rocks in the region below them, and wherever the continents stick up above the average height of the Earth's surface, they have deep roots. The extra weight of the material above the surface is balanced by the deficit of weight below the surface, where denser rock is replaced by the lighter rocks in the region above, in a way similar to icebergs floating in the ocean. The continents do not float on the material below, because it is not a liquid; but since it is deformable, over long periods of time it can move in a way that "accommodates" the load above it. As a result, at a depth of about 100 miles the mass lying above you is essentially the same, whether you have an ocean basin, a continent, or a mountain range on top of a continent above you. (As an example, the Himalayas, which are the tallest mountain range, actually have several hundred feet less mass than the Indian Ocean, which lies ten miles "below" them.)

So even if mountain ranges could theoretically balance the Earth, (a) their "excess" mass doesn't amount to a hill of beans in comparison with the equatorial bulge, (b) they don't have any significant effect on the Earth's rotation or precession, and (c) your friend's analogy, while interesting, is wrong.

Courtney Seligman
Professor of Astronomy
Long Beach City College