Instantaneous Polar Shifts Tim Thompson, from JPL NASA, writes: Flavio Barbiero might be a mathematician, but he's not a physicist. His analysis of the gyroscope looks right, but his application of same to Earth is wholly wrong. Gyroscopes work the way they do as long as the torques applied are on a time scale that is long compared to the mechanical structure. But if you torque a gyroscope with an impulse that exceeds the shear strength of the gyroscope material, it will not produce a reaction torque, it will just break. This, for instance, is what will happen to a gyroscope if you shoot one end of it with your favorite sporting weapon. Getting shot is not a bad analogy for what happens to Earth when an asteroid hits. On the minor side of criticism, Barbiero's calculation of the torque on Earth assumes an impact velocity of 50 km/sec. But the correct average impact velocity is about 21 km/sec (+/- 6.2 km/sec l-sigma), which would make Barbiero's collider a 5-sigma event.^[1] To calculate the torque on Earth Barbiero simply does "F = ma" on the asteroid, using it's deceleration as it hits Earth for "a". This works, if and only if, one implicitly assumes that 100% of the collision energy is transferred as a force (and a torque) to Earth. But 70%-80% of the impact kinetic energy will go into vaporizing the asteroid and a bunch of Earth, and other deleterious effects on the surroundings. Only 20%-30% is available for other tasks. (These are approximations to be sure: even the experts I asked couldn't do any better.) So even if his methodology were correct, he is relying on a 5-sigma event; not impossible, but not very likely either. But these are minor quibbles. The real problem is that the whole idea is unphysical in the extreme. Earth acts approximately like a gyroscope in response to lunar and solar tides because (a) the tidal forces change very slowly when compared to the shear strength of Earth, and (b) changes in tidal force propagate through the body of Earth at the speed of gravity, which happens to be the speed of light (Earth crossing time about 0.05 seconds). This means that, in effect, the lunar and solar torques are applied to all parts of the Earth simultaneously. But an asteroid impact is (a) very fast compared to the shear strength of Earth and (b) is not applied to all points of Earth at the same time. Point (a) is really what kills Barbiero's idea at once. Instead of producing a coherent motion of Earth, like a gyroscope, the 20%-30% available energy goes into seismic waves (it's like an impulse that makes the gyroscope "ring" instead of move coherently). So Earth is in fact not "torqued" by the impact, and never can be, even in principle. It is possible to change the orientation of a planet's spin axis (its "obliquity" for the astronomers in the crowd) by impact, but not the way Barbiero does it. Forces and torques are the wrong approach; it's momentum that gets the job done. Kinetic energy is not conserved in the inelastic collision, but momentum is. A simple addition of the asteroid's momentum and Earth's spin angular momentum will show you where the new spin axis will be. But a small collision as modeled by Barbiero won't push Earth around much; that takes a really big collision. A "tip the Earth over" scale collision would also effectively sterilize the entire living surface of the planet (and probably melt it as well). It is a collision of that scale, early in the history of the Solar System, which is thought to have produced the peculiar orientation of Uranus, which rolls around the Sun on its side. A collision that big may well add some significant mass to one part of Earth, and/or redistribute Earth's own mass. That will change the location of Earth's Euler axes, which can be thought of as "axes of symmetry" for the mass distribution. A rotating body prefers that the spin axis coincide with an Euler axis. So, after Earth's spin axis is reoriented by a sufficient collision, it will then slip ("true polar wander") while the spin axis remains fixed in space, until the spin axis coincides with an Euler axis. That will take some time -- how long I don't know. But, a few years ago, a Caltech team got itself in the news for proposing a "true polar wander" event that took a few million years to reorient Earth by as much as 90 degrees with respect to its spin axis (not a collision related event). Once the Euler axis reorientation is done, Earth is stable again -- at least until something else drastic happens. Flavio Barbiero replies: I might not be a physicist, as Mr. Thompson points out, but I am confident that my Physics tutor, a first class professor colleague of Fermi, succeeded in teaching me the fundamental principles of Mechanics. Those principles included the relation between force (and torque) and energy, and the mechanics of rotating bodies, concerning both of which my critic seems to be rather confused. For instance, Thompson claims that "Gyroscopes work the way they do as long as the torques applied are on a time scale that is long compared to the mechanical structure" and adds that "If you torque a gyroscope with an impulse that exceeds the shear strength of the gyroscope material, it will just break." It is not clear if Thompson is talking about the extent (in time) or the magnitude of a torque. I fully agree that a gyro will break if subjected to a torque that exceeds the shear strength of its material. This is not, however, the case with Earth if hit by a "normal" asteroid: It will induce a torque which lasts for a very short time, without exceeding those limits. For Earth to "break" in the manner suggested by Thompson, it would have to collide with a body several orders of magnitude larger than the largest of known asteroids. From a mathematical and logical point of view, the "time scale" of a torque does not alter the behaviour of a gyroscope. In fact, gyroscopes work the way they do as long as a torque is applied to them, whether it lasts for a long or a short time. Thompson chides me for assuming an impact velocity of 50 km/sec, when the correct average impact velocity, according to him, is about 21 km/sec, "which would make Barbiero's collider a 5-sigma event." This is "not impossible," he states, "but not very likely either." This assumption is wrong. Speed is an important element in order to classify the magnitude of a collision, but not as important as the mass of the collider. In order to have a "5-sigma event," the collider would have to be an asteroid with a diameter of at least 5 km -- that is, with a mass 3 orders of magnitude larger than the body which I dealt with in my paper. As for the impact velocity of 50 km/sec assumed in my calculation, it might not be the average, but it certainly is not unlikely for a collider. The velocity of the Apollo objects with respect to Earth can vary between 15 km/sec to over 70 km/sec. Gehrels assumes an average impact velocity of about 20 km/sec, but cites comets with relative speeds up to 72 km/sec. Besides, the purpose of my calculation was not to show what transpires in an average impact, but what could happen in the worst scenario. Thompson also stated that: "To calculate the torque on Earth, Barbiero simply does 'F = ma' on the asteroid, using its deceleration as it hits Earth as 'a'. This works if, and only if, one implicitly assumes that 100% of the collision energy is transferred as a force (and a torque) to Earth..." This assumption is also wrong. The kinetic energy of an asteroid hitting Earth is given by the formula E[c ]= 1/2 mv^2, and it is entirely (100%) dissipated in the shock explosion, seismic waves, and all other effects mentioned by Thompson. Not a single bit of it is "transferred as a force to Earth," for the simple reason that forces are not produced by energy. In this instance, force is derived, instant by instant, through the product of the mass of the asteroid and its acceleration. How the kinetic energy of the body is dissipated during the impact does not matter at all in the effect of the force; the only thing that matters (besides mass) is the acceleration -- that is, how fast the body is slowed down to a halt by Earth's surface. Force will be very high if the body hits a hard surface, low if the surface is soft, very low if the body explodes in the atmosphere without reaching the surface (as in the Tunguska event), but the amount of energy dissipated will be exactly the same in all three cases. Here I have to ask Mr. Thompson to go back to his Physics text books and reacquaint himself with the concepts of force and energy. From a physical point of view, the force developed in a collision is given by the formula f = ma. There is absolutely no doubt about this. The problem crops up when one requires to discover its exact value, because there is no way to calculate the true peak of the acceleration. One simply has to make an educated guess about it. In any case, this is a minor difficulty. A greater problem results from the fact that the force (and the subsequent torque) is impulsive and there is no way to find out exactly how it acts on a massive body like Earth. (I will return to this below.) Thompson continues with: "Earth acts approximately like a gyroscope in response to lunar and solar tides, because the tidal forces change very slowly when compared to the shear strength of Earth...an asteroid impact is very fast compared to the shear strength of Earth...this is really what kills Barbiero's idea at once" In the first place, tides have nothing to do with Earth's precession. Earth acts "precisely" in accordance with gyro theory in response to lunar and solar gravitational attraction on its equatorial bulges. Because of the different distances, this attraction is stronger on the near side of the bulge than on the distant side. Therefore, due to the fact that the Moon and the Sun lie on different planes with respect to its equator, Earth becomes subject to a torque. Had Earth's equator, the ecliptic, and the lunar orbit been on the same plane, there would not be any torque and, therefore, no precession (but there still would be tides). In the second place, there is no difference, in principle, whether a force changes slowly or fast, as long as its value is below the breaking point. Of course, there are problems in evaluating the behaviour of a gyroscope when subject to an impulsive force, but not the kind raised by Thompson. The "shear strength of Earth" has no role in this behaviour. It is Earth's dimensions that play a fundamental role. In fact the duration of an impulsive force is much shorter than the time needed for it to propagate from one side of the planet to the other (about 85 minutes). This means that, in this phase, we cannot apply the formulas which are valid for a normal gyroscope (or even Earth for long-lasting forces). There is no mathematical theory developed for the transitional phase and, therefore, we cannot calculate the value of the torque, instant by instant, or its effects on each part of Earth's body, during its propagation. This does not mean that no effects would be felt on Earth. Theory and experience indicate that, during a transition phase, the same quality in behaviour applies, but with much higher instant values. Therefore, if we evaluate the effects of the impulsive force as if it was stabilized, we remain on the safe side. Thompson states that: "Changes in tidal force propagate through the body of Earth at the speed of gravity...This means that, in effect, the lunar and solar torques are applied to all parts of the Earth simultaneously...But an asteroid impact [instead]...is not applied to all points of Earth at the same time." There is, however, no difference, from a mathematical point of view, between one type of force and another. Overall, they induce the same effects. The difference, as I pointed out in my previous answer, concerns the transition phase: A force applied to a single point of the gyroscope takes a certain time to propagate to the whole body and we don't have any instruments capable of evaluating exactly what happens during this phase. This, needless to say, is a problem, but not, by any means, such as to justify Thompson's conclusion that "Earth is in fact not torqued by the impact, and never can be, even in principle." Thompson's statement, here, is the result of a long list of wrong assumptions, and is in complete disagreement with the basic principles of Mechanics. Thompson is also of the opinion that: "It is possible to change the orientation of a planet's spin axis...but not the way Barbiero does it...it's momentum that gets the job done...a small collision as modeled by Barbiero won't push Earth around much; that takes a really big collision." It's quite clear that Mr. Thompson has completely missed the point of my theory since it is obvious that he is echoing the usual "politically correct" opinion that only a major collision (with a body at least the size of Mars) can significantly change Earth's tilt. It's amazing, and inexplicable, how this opinion has been widely spread in the scientific world. In fact, this claim can only be held to be correct if one were to state that this is one way to get the job done. It is certainly wrong when one states that it's the only way. Earth's tilt is constantly changing due to precessional motion, which is provoked by almost negligible gravitational forces. Besides, there is overwhelming evidence that the poles have wandered around the globe during past geological eras. And yet this wandering was not provoked by massive planets hitting Earth. It was caused by something that leaves no perceptible scars -- the reshaping of the equatorial bulge. Thompson seems to ignore what was definitely established by Euler and Maxwell's studies since last century in that Earth's stability is provided by its equatorial bulges. It is the position of the equatorial bulge that determines the placement of Earth's rotational axis and, therefore, of its poles. If the bulge shifts, the poles will immediately follow. On the other hand, Earth's poles cannot shift if the equatorial bulge stays in place. So, in principle, all one needs in order to change the axis of rotation and its tilt, is a "reshaping" of Earth's equatorial bulge around a different axis (gyroscopic theory is absolutely clear about this, and it can be easily demonstrated and proven through experimental tests). This is what my theory deals with. According to this principle, if a torque provoked by an impact overtakes a certain "threshold" value, it "triggers" a process that, in the end, results in the "reshaping" of Earth's equatorial bulge around a different axis and, therefore, in the shifting of the poles. This is the point of the theory, and criticism should concentrate on that, instead on how to calculate the "threshold" value. Finally, Thompson offers the following: "A collision that big...will change the location of Earth's Euler axis...A rotating body prefers that the spin axis coincide with an Euler axis. So, after Earth's spin axis is reoriented by a sufficient collision, it will then slip ('true polar wander'), until...the spin axis coincides with an Euler axis. That will take some time -- how long I don't know. But [at least according to a Caltech team] a few million years." These statements have little to do with my theory, but it's worth discussing them, because they reflect a poor and imprecise understanding of the behaviour of a rotating body. A freely-rotating body always rotates around its axis of symmetry. If a mass is added abruptly to Earth, as in the case of a collision, it will form a new axis of symmetry and, therefore, Earth will immediately start rotating around it. There will, of course, be a transition phase, which will be in the order of minutes or, at most, hours -- just enough time for one side of Earth to "recognize" that a mass has been added on the other side (or, in other words, just enough time for the mechanical action of the colliding body to propagate to the entire Earth). It is simply impossible for a freely rotating body to start rotating around a different axis unless there is some disturbing torque. The repositioning of the poles immediately follows whatever shift of material transpires on Earth's surface due, for example, to erosion and/or sedimentation processes, the drift of continents, and so on. Thompson may perhaps know that the sudden displacement of mass due to a major earthquake is immediately registered by the pole's position, with a jump in the order of meters -- see, here, L. Mansinha & D. E. Smylie, Earthquake Displacement Fields and the Rotation of the Earth (N. Y., 1970), or consult the International Polar Motion Service (Ukian, Ca.). Notes ^[1] N. W. Harris & D. W. Hughes, "Asteroid Earth Collision Velocities," Planetary and Space Science (April 1994), pp. 285-289.