On the Possibility of Instantaneous Shifts of the Poles (cont.)
By Flavio Barbiero
How the poles can shift
Scientists are trying to understand what could be the overall effect on the Earth of a collision with an Apollo object. The scenarios they have come up with so far look rather dire. After all, many believe that the extinction of the dinosaurs followed an impact with an asteroid. None of these scenarios, however, has taken into consideration the possibility that such an impact could also provoke an almost instantaneous shift of the poles. This is because, compared to the Earth a one-kilometre-wide asteroid is like a tiny sphere of 2 millimetres next to a ball of 25 meters. Its mass is absolutely negligible. The displacement of the poles due directly to it, if any, can be measured in the order of centimetres.
What can not be neglected, however, is the torque provoked by the impact. Due to the very high speed of the asteroid, the impulsive torque it delivers can be of sufficient magnitude to overcome, for an instant, the reaction torque developed by the Earth. The torque , in itself, lasts for too short a period to produce any measurable effect; yet I will argue that it can trigger a process that in the end results in a change of the axis of rotation.
Let's see how.
Earth is a gyro. A gyro subject to a disturbing force reacts with a movement called "precession". Unfortunately the precession phenomenon has been studied exhaustively only for the case when the precession's rotation is much smaller than the gyro's main rotation, the only interesting case for technical applications. Scientists, therefore, are not familiar with the case in which the two rotational components have the same order of magnitude. This case is examined here in the appendix, where the behaviour of a gyro subject to a disturbing torque of increasing value is shown. It appears that when the torque reaches a critical value, equal to the maximum reaction torque that can be developed by the gyro, the latter changes its axis of rotation permanently. The new axis, which coincides with the previous precession's axis, is maintained even if the disturbing torque diminishes again, as long as its value is higher than zero. Only if and when the torque is completely null (or becomes negative), does the gyro recovers its previous rotational axis.
The behaviour of the Earth when subjected to a disturbing torque is obviously the same. In fact the Earth has a movement of precession due to the disturbing torque exercised by the Sun-Moon gravitational attraction on the equatorial bulges. This torque is one million of times smaller than the maximum reaction torque which can be developed by Earth. Simple calculations, however, allow us to establish that an object as small as a half-kilometre-wide asteroid, hitting the planet in the right spot and at the right angle, is capable of developing an impulsive torque of the same magnitude of the maximum Earth's reaction torque. In this case the Earth assumes, for a very short instant, a different axis of rotation.
If at the moment of the impact the force of the Sun-Moon gravitational attraction on the equatorial bulge has the same direction as the force developed by the impact, a shift of the poles will inevitably follow. Immediately after the impact, in fact, the torque should go down to zero, and the Earth should recover its previous rotational axis. But if the torque exerted by the sun-moon attraction has the same direction, the torque cannot be zeroed and therefore the Earth keeps "memory" of the impact and of its direction. This "memory" consists of an extremely small rotational component, with the same direction as that of the impact, in the order of 1 millionth of the normal rotation. What is particular in this rotational component is that it is fixed with respect to the Earth. If the latter was a solid gyroscope, this situation would last indefinitely unchanged. The planet, however, is not homogenous and rigid. First of all it is covered by a thin layer of water, which reacts immediately to any change of motion. Second, even the "solid" outer shell is in reality plastic and can be easily "re-shaped" by centrifugal forces.
Under the effect of this tiny rotational component, sea water begins to move towards a circle perpendicular to that rotation (the new equator). This is a very small effect, and if it was the only component, the resulting equatorial bulge would be of a few meters only. But as this happens, the value of the rotational component increases, at the expense of the main rotation, therefore increasing the centrifugal force which makes more water move towards the new equator, thus increasing the force and so on. This process starts very slowly, but accelerates progressively, until the centrifugal force developed by this rotational component grows strong enough to induce deformations of the Earth's mantle.
From here on the equatorial bulge is quickly "re-shaped" around the new axis of rotation and Earth will soon be stable again, with a different axis of rotation and different poles.
This mechanism shows that the Earth's poles, contrary to what has always been postulated, can make "jumps" in a matter of days (that is almost instantaneously) of thousands of kilometres, due to the effects of forces at first sight negligible, such as the impact of a medium-size asteroid and the Sun-Moon gravitational attraction on the equatorial bulge, combined with the effects of water mobility and the plasticity of the crust.