The idea of the Earth's orbit or rotation being disturbed is a common catastrophe theme, exploited in movies such as The Day the Earth Caught Fire, not to mention the theories of Velikovsky. In The Day the Earth Caught Fire, nuclear explosions send Earth spiraling toward the Sun, and only a last-ditch counter-explosion saves the world. The movie features one of the best scripts of any science-fiction film, but the story line is impossible. Unless mass were expelled from the Earth, or some force were applied from outside the Earth, it would be impossible to change the Earth's orbit or rotation. To see this, sit in a swivel chair equipped with casters. Now, without touching the floor or anything outside the chair, try to get the chair rotating. Try to move it across the floor. Its just about impossible (that you can do it at all is due to a small amount of friction between the chair and the floor.) The principle here is called conservation of momentum. While in the chair, you are an isolated system. You had zero rotational momentum to begin with, and zero linear momentum, and regardless of what you do, zero they stay. What little motion you impart to the chair results from there being some friction in the casters and swivel, so that you do interact very slightly with the floor. An astronaut floating free in space without a safety line or propulsion would be utterly helpless to reach safety even a few feet away. He would have no way to acquire momentum. Nothing acting solely from on or within the Earth could change its orbit or seriously alter its rotation.
The operative word there is "seriously." Internal processes can and do affect the earth's rotation slightly.
One way to move an object is to throw mass in the opposite direction, the way jets or rockets do. The mass and the object move in opposite directions, but the center of mass of the whole system at each instant tends to stay fixed. If our astronaut had a wrench he could throw it and move himself. He might also vent off some excess oxygen to propel himself. But expelling enough mass to affect the gigantic bulk of the Earth is a stupendous task. No nuclear blast from any bomb now in existence would blast material free of the earth at all. The largest spacecraft have far less effect on the Earth than a flea jumping off an elephant.
If we think really big and imagine blasting a chunk out of the Earth as big as North America and 100 miles thick so that its final speed, after escape, with respect to the Earth is 25,000 miles an hour, we will have expelled only 1/500 of the total mass of the Earth. The Earth would move in the opposite direction 1/500 as fast or 50 miles an hour. The speed of the Earth in its orbit is about 67,000 miles an hour. We will not change the orbit of the Earth very much--if we apply the impulse to speed up the earth in its orbit we would put the Earth into a new orbit with its most distant point about 70,000 miles further from the Sun than now--and the Earth's distance from the Sun varies now by three million miles over the course of a year! Exactly the same arguments apply to changing the orbit of the Earth through the impact of a large asteroid. The largest asteroid, Ceres, about 600 miles in diameter, is only about as massive as our hypothetical chunk of Earth above. Changing the orbit of a planet is a tall order. An impact big enough to have even a tiny effect on the Earth's orbit or rotation would almost certainly destroy all life on Earth as well.
Yet another common catastrophist theme has to do with causing the Earth's axis to shift somehow. When I mention continental drift to non-scientists, I often am asked if having the continents all together as they were 200 million years ago might have unbalanced the Earth. Surprisingly, the Earth's continents are closely bunched now. If you look down on Paris on a globe, you will see a hemisphere containing most of the Earth's land. If you look down on the opposite point on the globe (southeast of New Zealand), you will see a hemisphere almost entirely covered by ocean. The Earth is very asymmetrical - in fact there is very little land on earth diametrically opposite other land - but a second surprising point is that the distribution of continents and oceans has almost no effect on the balance of the Earth. First of all, the crust is only 1/300 of the Earth's mass, and second, recall that the crust 'floats' on the plastic mantle. Continental crust is thick and high, but it's light. Oceanic crust is thin and low, but it's dense. This buoyant effect, called isostasy, in effect makes the Earth self-balancing. The plasticity of the Earth's interior has another important side effect. The centrifugal force resulting from the Earth's rotation causes the Earth to bulge at the Equator by about 14 miles. Changing the rotation of a sphere is hard, changing the rotation of an ellipsoid like the Earth is harder yet. The Earth has a lot of extra mass where it counts most. Finally, recall your attempt to get your swivel chair rotating; the Earth cannot cause its own rotation to change significantly.
Some people think of the Earth's axis "flipping over," like a top falling on its side or perhaps like one of the novelty tops that spontaneously flips over. But tops change their motion because they are balanced on a firm surface and because gravity is pulling them downward. Under zero gravity conditions, like in a spacecraft, both types of tops would spin until they slowed due to air resistance. In space, with no air, they would spin forever, and not flip or fall over. The Earth is spinning like a top, but like one spinning in space.
The amount of energy contained in the earth's rotation is pretty large: 2.1 x 1029 joules. You'd have to supply an appreciable fraction of that to change the earth's rotation in any major way. To put this number in perspective, a megaton is 4 x 1015 joules. You'd have to supply about 5 x 1014 megatons, or about 100 million times the total nuclear arsenal of the Earth. So we can see that the science fiction theme of a nuclear blast affecting the earth's rotation is just plain impossible. The kinetic energy of the earth in its orbit is about 2.7 x 1033 joules or about 10,000 times its rotational energy, so the entire earth's nuclear arsenal could hardly affect the earth in its orbit even if we could somehow deliver the energy effectively.
Another way to look at this is that it takes 400,000 joules to melt a kilogram of rock, so to change the earth's rotation, you'd liberate enough energy to melt 5 x 1023 kilograms of rock or almost 10 per cent of the earth.
Catastrophes of this sort crop up in the strangest places. David Graham's novel Down to a Sunless Sea starts out as a fairly engrossing story of transoceanic airliners trying to reach safety in the midst of a nuclear war. To escape fallout, which is worst in the Northern Hemisphere, two airliners head for Antarctica. So far so good, from a literary standpoint, that is. But after the planes reach McMurdo Station, Graham introduces a preposterous deus ex machina ending; one of the scientist passengers discovers that the nuclear bombardment has tilted the Earth's axis and Antarctica will eventually end up astride the equator!
Now hold it a minute. Apart from the inability of nuclear weapons to affect the Earth's rotation, there's a fatal flaw in the story. The reason for going to Antarctica is to escape fallout, which is being spread by the wind, but the Earth's wind belts are governed by the Earth's rotation. If the Earth's rotation changes, any guarantees Antarctica may have enjoyed against fallout become null and void. Graham's characters don't even get the inclination of the Earth's axis right. "About nineteen degrees?" asks one. "Nineteen and a half" corrects the "expert." The actual value is 23 1/2 degrees. All in all, it's about as amateurish a way to end a story as concluding with "then I fell out of bed and woke up."
Charles Berlitz, best known for his books on the Bermuda Triangle, also branched out into catastrophes with a 1981 book entitled Doomsday 1999 A.D., a tour de force that combined many favorite catastrophist themes. One of his arguments is that the concentration of ice near the South Pole could cause the Earth to wobble. He advocates getting rid of the ice by melting it (perhaps anticipating the global warming debate?). All the arguments against changing the Earth's rotation that apply to the continents apply in spades here. The Antarctic ice cap is only 1/100,000 of the Earth's mass, and isostasy has balanced the load of the ice by causing the crust to sink--slowly. The plastic mantle had ample time to flow out of the way. Finally, if you want to balance or unbalance a wheel, where do you put the weight--on the axle or on the rim? The Earth's rotation axis passes through the poles, and a massive ice cap near the poles can hardly affect the Earth's rotation. And because of its equatorial bulge, the Earth does have a lot of extra mass where it does count for stability. (Oh, by the way, did you catch Doomsday in 1999? I missed it.)
One scientific term that has added to public confusion on this point is "wandering poles." When rocks cool from the molten state, magnetic minerals in them become magnetized by the Earth's magnetic field. If the rocks have not been too badly disturbed we can figure out where the magnetic pole was when the rocks formed. The north magnetic pole is now in northern Canada, the southern in Antarctica, both about a thousand miles from the geographic poles. If we plot the apparent location of the magnetic poles through geologic time as seen from any given continent, the poles appear to have wandered widely across the Earth. In the days before continental drift became accepted, some scientists thought that the magnetic poles actually had moved, but we now believe, on both theoretical and observational grounds, that the magnetic poles are always close to the geographic poles. Most planets that are known to have magnetic fields have their magnetic axes close to their rotation axes. Geologists are now convinced that the continents, rather than the poles, have wandered, and the accepted term now for the apparent motion of the magnetic poles is "apparent polar wander."
In addition to apparent polar wander, however, there is a real polar wander. The crust of the earth can slide over its plastic interior in response to mass imbalances. The rotation axis of the Earth stays fixed, but the crust as a whole can move relative to the poles. The term is still a misnomer - it's the crust that moves, not the poles.
Simulations of the evolution of the early solar system don't end up with nine large regularly-spaced planets. Instead, they end up with hundreds of small planets that merge by collision, and collisions between similar-sized planets could certainly radically change their rotations. Some planetary geologists have suggested the slow rotation of Venus and the extreme axial tilt of Uranus may have resulted from early collisions.
Rotating objects have momentum, called angular momentum. For the Earth, that amounts to about 5.9 x 1033 kg-m2/sec. Now imagine an asteroid hitting the earth a grazing blow right on the equator. That would be the most effective way an asteroid could change the earth's rotation, either speeding it up or slowing it down. The asteroid has angular momentum relative to the center of the earth, equal to its mass times its velocity times the distance to the center of the earth. Typical impacts in the inner solar system involve velocities of about 30 kilometers per second, and for a grazing impact the distance from the center of the earth will be 6400 kilometers. In meters, those figures are 30,000 and 6,400,000, respectively. So to have angular momentum comparable to earth's we have mass x 30,000 x 6,400,000 = 5.9 x 1033, or mass = 3 x 1022 kilograms. Since the earth itself has a mass of 6 x 1024 kilograms, we're talking about something with 5 per cent of the mass of the earth, or about 4.5 times the mass of the moon. This is way bigger than any known asteroid.
How would this affect the earth? The asteroid has kinetic energy = 1/2(mass)(velocity)2. = 1.3 x 1031 joules. Let's assume the asteroid stops the earth's rotation cold. That means that 2.1 x 1029 joules of its energy goes into stopping the earth's rotation, leaving about 98 per cent expressed in other forms, like heat. It takes 400,000 joules to melt a kilogram of rock, so there's enough energy left over to melt 3 x 1025 kilograms of rock. That's about five times the mass of the earth. Even allowing for a lot of energy radiating to space or being blasted off as ejecta, this puppy will melt most if not all of the earth. So don't sweat the long-term environmental effects. If the earth is ever hit hard enough to affect its rotation significantly, nobody will be around to tell about it.
Let's assume the earth is hit a glancing blow by something big enough to change it's rotation by one second a day, or 1/86400 of its present value. The earth's angular momentum is about 5.9 x 1033 kg-m2/sec. Our hypothetical asteroid has to have 5.9 x 1033/86400 kg-m2/sec = 6.8 x 1028 kg-m2/sec angular momentum. If it hits at 30 km/sec or 30,000 m/sec, and the radius of the earth is 6,400,000 meters, its mass would be 3.6 x 1017 kg. If its density is 3000 kg per cubic meter, it would have a volume of 1.2 x 1014 cubic meters, or roughly a cube about 49 kilometers on a side. This is way bigger than anything to have hit since the last stages of planetary accretion and would certainly vaporize enough rock and rain down enough hot debris to sterilize the surface.
On the other hand, an asteroid 10 kilometers in diameter, comparable to the one that caused the extinction of the dinosaurs, would have a mass of 1.5 x 1015 kilograms. If it hit the earth a grazing blow on the equator, its angular momentum would be 1.5 x 1015 x 30,000 x 6,400,000 = 3 x 1026 kg-m2/sec. That's about 1/20,000,000 of the earth's angular momentum, meaning it could change the earth's rotation by about 1/20,000,000, or change the length of the day by about .004 seconds. This is pretty tiny, but still several thousand times the effect of the great 2004 Indonesian earthquake. Even an impact big enough to cause a global catastrophe would still have only a tiny effect on the earth's rotation.
Nothing could seem simpler than a spinning top or a revolving wheel, but the rotation of real objects is a remarkably complex business. If objects are not perfectly symmetrical around their rotation axis, they naturally wobble around their rotation axis. The Earth, which is not perfectly spherical, wobbles observably. Even movements of weather systems modify the wobbles.
Forces from outside can affect the rotation of planets. We have already discussed impact, which could not have a serious effect on the Earth's rotation barring something big enough to extinguish all life on Earth. Another process is precession - a rotating object's axis oscillates if a sideways force is applied to it. The Earth's axis precesses over a period of 26,000 years because of the attraction of the Sun and Moon and, to a lesser extent, the planets. Superimposed on the Earth's normal precession is a slow oscillation of the Earth's axial tilt over a period of 41,000 years. Right now the tilt is decreasing. The tropics are moving toward the equator at about 15 meters a year. Actually, it's not the axis that changes in tilt but the plane of the earth's orbit.
The Moon actually acts to keep the earth's axis tilt within moderate limits. Planets like Mars that lack large moons can precess greatly due to the gravitational pull of other planets (Mars' two tiny moons are not large enough to have any significant effect). Some planetary geologists believe precession has played a role in changing the climate of Mars, but precession is slow.
Another process that can change the rotation of a planet is tidal braking. Tides create friction, and this friction can slow the rotation of a planet. Lest anyone think this is a possible way to accomplish some of Velikovsky's catastrophes, it is not. A close brush with Venus or Mars would not last long enough nor generate enough friction to stop the Earth and re-start it as Velikovsky claims happened. Nevertheless, the same side of the Moon always faces the Earth, and Mercury's rotation is locked to its revolution around the Sun because of tidal braking. Perhaps most spectacular, tidal stresses in Jupiter's innermost moon, Io, probably generate enough heat through friction to keep Io's interior hot and cause it to be volcanically active. Tidal braking of the Earth by the Moon has slowed the Earth's rotation from 400 revolutions per year to the present 365 over the last half-billion years. Neither tidal braking nor precession, however, can be used to explain the sorts of catastrophes that pseudoscientists insist happened.
It's only a matter of time before catastrophists point to chaos theory to show that orbits can wander all over the place. In it's simplest terms, a system is chaotic if a tiny difference in conditions at one time amplifies to huge differences later on. Almost any complex system is chaotic. What chaos means is that you can't predict the behavior of systems accurately in the very long term. We will probably never be able to predict weather in detail a year in advance. Chaos does not mean systems have no limits or are unstable. Weather is chaotic because tiny variations in local conditions eventually cause predictions to become unreliable, but that does not mean we are likely to see temperatures of +200 or -200 degrees or that it will snow in July in Florida.
A good example of chaos in action is a water fountain. Some fountains shoot a vertical jet that falls back on itself, changing in very complex ways. This is a chaotic system because tiny fluctuations in water pressure, breezes, surface tension, and so on lead to variations that are impossible to predict. Nevertheless, we know the fountain isn't going to stop suddenly of its own accord, or blast a jet through the roof, or spray horizontally. There are limits even if the actual behavior cannot be predicted far in advance.
The Solar System is chaotic. Tiny inaccuracies in measurements of the planets now would add up to very large differences in a million years. We cannot say with any accuracy where the planets were in the sky 100 million years ago. And in the very long term planets can modify each others' orbits. The discovery of extra-solar planets has led to a lot of fresh discoveries about orbital evolution. Solar Systems with lots of giant planets like Jupiter or bigger either fling planets out of the solar system, merge them in collisions, or, if they're lucky, settle down into stable orbits. In our solar system, Jupiter is a stabilizing influence. It keeps the other planets nearly in the same orbital plane and keeps orbits from getting too eccentric. Many planetary scientists argue that life on Earth requires a planet like Jupiter to maintain stability and sweep up potential impacting objects.
Created 8 July 1998, Last Update 02 June 2010
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