| Tsunamis and Tides:
As we will see, the phenomenon of tides has a natural explanation now that we understand the law of gravitation. Moreover, tides are of very general astronomical interest, not merely applicable to the oceans of the Earth. But before addressing this issue, I want to digress to describe what are usually erroneously called `tidal waves.' These have nothing, or at least very little, to do with astronomy, but the physics is fascinating. Moreover, it will help us develop a good understanding of the way in which disturbances pass through materials, an essential part of understanding what we know about the deep interior of the Earth.
As noted, the expression `tidal wave' is a complete misnomer. Such a natural phenomenon should more correctly be called a tsunami, a Japanese word meaning "harbour wave". You may know that a tsunami can be caused by (for instance) an earthquake in Chile. Many hours later, a tsunami hits Japan, having crossed the ocean at a speed of 500 miles per hour. Why does the wave not obliterate all the boats on the open ocean? How can such a big wave cross the ocean unobserved? (Often there is no warning of their arrival).
The answer is that in the open ocean the wave is effectively unobservable, not at all like a regular surface wave. Almost all the waves that you see on the ocean or a lake are generated by the wind: when it is stormy, the winds whip up choppy seas. If you were to dive down to a considerable depth, you would find the water unaffected by the purely superficial effects of the storm.
A tsunami is very different. The earthquake delivers a sudden shock which propagates outward through the ocean but which is spread out over the full depth. At the surface, the effects are modest. If you were on a ship in the open ocean, for instance, you might sense a slow rise and fall of about a meter over the space of twenty minutes or so; more likely it would pass unnoticed. But once the shock wave approaches land, and especially if it is focussed or funnelled upward by some V-shaped topographic feature underwater (as is the case in Hilo, Hawaii, for instance) the wave rises out of the sea and crashes inland, causing enormous devastation.
In the classroom, I showed a few pictures to give you some idea of the power which a tsunami delivers. As with tornadoes, the biggest danger is that you will be thrown about, perhaps against a rock, or that things will be thrown at you (remember the image of the 2x6-inch plank driven through a truck tire). You don't just body-surf your way through a tsunami!
Some of the pictures I showed were of Hilo itself, a city which has been obliterated by tsunamis twice this century. One of the photographs was taken from a ship anchored about a kilometer offshore: it felt no disturbance, but the sailors on board saw enormous waves rearing up and crashing into the city. As a frequent visitor to Hilo, I must say that I never drive down King Kamehameha Avenue without speculating about the prospects for the arrival of the next tsunami! But my fears are now a little unfounded because the harbour has been rebuilt with big breakwaters, and there are `tsunami watch' exercises in place. When a big earthquake is experienced somewhere, the potential arrival time of a tsunami can be calculated and the populace warned to evacuate. Of course, there are always some foolish people who rush down to the shore to see the arrival; in 1960, this behaviour led to several deaths.
By the way, the largest measured tsunami is recorded at an astounding 278 feet in height, as estimated by a person high on a hillside when it arrived. (The calculation involved seeing the crest at some perspective with respect to a background topographic feature. It did not simply lap up against his feet.) That was in 1771, in Ishigaki Island, Japan. The tsunami threw an 800-ton block of coral about 2 kilometers inland. There is also evidence in the geological record for thousand-foot tsunamis, and we will later see that the cometary collision thought to have killed off the dinosaurs may have caused tsunamis of even greater size.
A last point: the Guinness Book of Records tells me that the largest wave seen in the open ocean (not a tsunami) measured 112 feet in height (about the size of a ten-story building). This was seen from an American ship, the USS Ramapo, in the teeth of a 70-knot hurricane in 1933 in the North Pacific. Such waves are built up from the chance confluence of several waves moving independently, and it is unlikely that a giant wave of this sort would keep its integrity for more than a few seconds. On the other hand, there are instances of quite large 'traveling waves' which can roll on for very long distances at sea.
What Are Tides?When you hear the word `tide' you no doubt think of the way the water rises and falls at the seashore, but in astronomy tides play an important role in many contexts, so I want to describe them in a more general way. We will encounter them again in Phys 016 in the context of how whole galaxies of stars collide and interact, for instance, and they are important in the vicinity of black holes. Tides arise for a very simple reason: the gravitational force exerted by a body like the Earth depends on how far you are from it. To understand why this matters, imagine hovering at rest far above the Earth's surface (tens of thousands of kilometers above it, perhaps) and releasing two small stones in such a way that one is directly above the other, separated by a meter or so. How will they behave when you let go? The obvious, and correct, answer is that they will feel the gravitational attraction of the Earth and start to fall towards it. (The stones are so small that we can safely ignore the feeble gravitational tugs they exert on each other.) They speed up because a force is acting. Moreover, the force gets larger as they near the Earth, so the rate of acceleration itself increases. Eventually the stones will be falling quite rapidly. (Indeed, you can work out the speed with which they will reach the Earth's surface: it is exactly the speed with which you would have had to throw them upwards to just reach the height from which they began.) You now probably visualise the stones hitting the ground in quick succession, one after another. But it is not quite as simple as that. The lower stone started fractionally closer to the Earth than the higher one did, and therefore felt a somewhat stronger gravitational force. The difference may have been small, but was nonetheless real, and the lower stone will have accelerated a bit more rapidly than the upper stone, drawing ahead of it in the race to the ground. This effect has what a physicist or engineer would call `positive feedback.' As the lower stone increased its lead, the difference in the Earth's gravitational tug on the stones also grew, and the lead stone accelerated even more ahead of its lagging partner . The net result is that they drifted apart as they fell, and the lead stone have arrived much more than a metre ahead of its partner, and considerably earlier. (Air resistance is being ignored in this discussion.) Now repeat the experiment, but tie the stones together with a thin thread before you release them. Will they drift apart as they fall? Clearly, it depends on the strength of the thread. If it is the thinnest gossamer, it will presumably just tear apart; but it is strong fishing line, it will not. The use of the fishing line provides cohesion to what is now effectively a single body falling to the ground. If the two stones are securely tied together, you have in essence an irregularly-shaped body which will move in a way which is determined by the average force felt by all of its distributed atoms. All real bodies are at least somewhat extended, consisting of atoms which are distributed in various ways. When a body is near a large object like the Earth or the Sun, each atom within it will feel a gravitational force which is slightly different than that felt by any other atom. The body as a whole will be accelerated towards the massive body, but if you want to determine whether or not the atoms will `drift apart' or hang together as the body falls you will need to know how cohesive it is, and how different the gravitational forces are on the different atoms. Now consider the simple act of jumping out of an aircraft and falling feet-first towards the ground. At any given instant, your feet are somewhat closer to the Earth than your head is, and thus the gravitational pull on your feet is greater than that on your head. In other words, the Earth's gravitational field stretches your body a bit, trying to accelerate your feet more rapidly than your head. Is this an important effect? No. In the first place, any tiny tendency for your feet to race ahead of the rest of your body as you fall would be partly compensated by the air resistance which the feet encounter as they lead the way. But even if you ignore air resistance there is absolutely no problem. This is because your head is only a meter or two above your feet. Since you are about six thousand kilometers (six million meters) from the centre of the Earth, there is only a microscopic percentage difference in the gravitational force experienced by the atoms in your head and your feet. Consequently, the internal strength of your body (which relies on the chemical and electrical bonds between atoms and molecules) renders any stretching completely negligible and harmless.
When Might Tides Matter?There are two circumstances under which the effects of tidal forces are not negligible. The first of these is in a region where the gravitational field is very strong. Suppose, for instance, you were to find yourself near a neutron star (more on these later in Phys 016), an object which might be about three times the mass of the sun but which is compressed down to a ball about 10 km across (about the size of the city of Kingston). Now you find yourself within a few kilometers of an enormous amount of material, and the total gravitational field is very large. As before, your head and feet are at slightly different distances from the star, and although this may be only a small percentage difference, a tiny percentage of a large number can still amount to something significant. Indeed one can show numerically that the difference between the forces on your head and feet would be trillions of times stronger than your body could withstand, and you would be instantly torn to pieces. (Of course, there is no way that you could instantly appear beside the neutron star; you would have to travel inwards to get there, and as you go the tidal forces would get greater and greater until you were ripped apart.) ( Digression: read the famous science fiction short story `Neutron Star' by Larry Niven, and try to spot the enormous scientific goof he made in it. See me if you would like to discuss it.) A second possibility is to consider a weaker gravitational field but to imagine a very big object within it, so that the atoms in the `head' and `feet' are very widely separated; then the gravitational forces they experience can be very different. Such a case is provided by the moon near the Earth. To understand this, consider some numbers. The average distance between the center of the Earth and the center of the moon is about 240,000 miles. The edge of the Earth nearest the moon is closer by about 4000 miles, about 1.7% of the distance, and the opposite edge is 4000 miles farther away. The gravitational field of the moon is not huge, but simple calculation shows that it is about 6% stronger on the near edge than the far edge of the Earth. Is this enough to stretch the Earth appreciably? Is the Earth elongated a little in the direction of the moon? Surprisingly, the answer is `yes', the Earth does have what are called solid-body tides -- its material is elastic enough that it does get deformed in just this way. (And indeed the moon likewise experiences a solid-body deformation owing to the presence of the Earth.) Since the rocks are fairly rigid, such tides are small in size. But of course not all of the material of the Earth is as rigid as the rocks which make up most of it. In particular, much of the Earth is covered with water, which is free to slosh about and show the tidal effect in a much more pronounced way.
The Ocean Tides of the Earth.Larry Niven, the science fiction author who wrote the story Neutron Star which I mentioned in the previous section, created a fictional race of three-legged extraterrestrial characters called 'puppeteers.' They appear in several of his works, and are described as being very secretive about their planet of origin. At the end of Neutron Star, however, they inadvertently reveal a complete ignorance of the phenomenon of tides. This surprising lapse allows the narrator of the story to deduce that their planet, wherever it is, must be moonless. Of course the story is implausible, because puppeteer scientists would have encountered and considered tidal phenomena in other contexts, like neutron stars and black holes -- just as we are doing in this course. Still, let us indulge him, and imagine an extraterrestrial who has never encountered tides in any circumstances. Even so, such a creature should be able to make some sensible predictions about an ocean-covered planet with a moderately massive satellite. The reasoning is as follows: We start by imagining the Earth and the moon initially completely at rest, neither rotating on their axes nor orbiting their common center of mass, just as though some supreme intelligence had just set them down side by side. Of course this situation will not last: they will start to fall towards each other. What will happen? (We'll add the complication of the actual rotation and orbital motion in a moment.) First, consider the solid part of the Earth. As we saw early in the course, its enormous means that it would consist of an almost perfectly spherical ball of rock. The presence of the moon might result in a slight deformation elongating it in the direction of the moon (and vice versa), depending on the strengths of the rocky materials, but for present purposes, let us ignore that small deformation and assume that the rocky part of the Earth is indeed perfectly spherical. Now, what more can we say? We next remember that the spherical rock is ocean-covered (that is, it is surrounded by a layer of water), and recognize that this fluid is free to move about. We would then confidently assert that, as the Earth and moon fell towards each other, the fluid would be `stretched out' and therefore `heaped up' both on the side facing the moon and on the other side as well. (See the figure on page 142 of your text.) This is analogous to my earlier discussion of stones and human bodies falling into a strong gravitational field: unless there is plenty of cohesion to keep the body's form intact, it will be stretched out. Since the girdle of ocean water surrounding the Earth has no such cohesion, it will deform in the way shown in the figure. Indeed, as the Earth and moon draw closer towards each other, the elongation will become more and more pronounced. Let's now add a first complication. Suppose you know that the Earth is actually spinning rapidly -- once every 24 hours -- as it falls towards the moon. Then you could reason as follows: Since we are treating the Earth as a perfectly spherical lump of rock, you may want to visualise it rather like a smooth billiard ball covered with a thin layer of water within which the ball spins in a nearly frictionless way. For the reasons just described, the envelope of water will be elongated, with its long axis pointing towards the moon. Now visualise putting some sort of mark on the billiard ball. That mark will be carried around past two humps of water each day. Your confident prediction, then, would be that people on the rotating Earth should see high tides twice a day, and the times of high tide should correspond to when the moon is overhead or when it is directly beneath our feet, on the other side of the Earth. This treatment is too simplistic, of course. The Earth's surface is most definitely not as smooth as a billiard ball! Consider the other extreme. If the surface of the Earth were covered with small basins, like little lakes, the water would be trapped quite locally, and there would be no way that water from one region could slide readily over the surface to participate in the formation of a tidal bulge. In this case, the Earth people would not see tides at all. Which of these more nearly correct? In fact, the Earth is a combination of both. There are small lakes and topographic features within which water is localised, so that no tides are seen there. (An example is Lake Ontario.) But there are also enormous ocean basins, like the Atlantic and Pacific Oceans, thousands of kilometers across and within which the gravitational effect of the moon can be very different from one place to another. Tides are raised as a result. We now add the final complication. I have described the situation as though the Earth and moon are falling towards each other. This, of course, is not exactly what is happening -- they are instead in orbit around their common center of mass. It is, however, quite legitimate to say that they are 'falling around each other' as they orbit, and I can tell you without elaboration that the gist of the argument remains quite valid. The expectations of two high tides a day and their correlation with the moon's position remain essentially correct. In other words, our clever extraterrestrial got it mostly right! (In the next two sections I will present some qualifying remarks.) In particular, this model explains why there are two high tides and two low tides every day, something that surprises most people who know about the dependence upon the moon. (After all, the moon passes overhead only once a day, so the logical expectation is one high tide a day.) The exact timing of the tides, and their sizes, can be predicted and published long in advance. The tabulations are presented in the so-called `tide tables,' which are very reliable except in unpredictable episodes of very heavy weather. When a hurricane-force wind raises a `storm surge', a normal high tide can be even higher than expected and potentially quite destructive. You can understand why this can lead to confusion over the distinction between tides and tsunamis (`tidal waves').
The Influence of the Sun.The moon is not the only body which influences the tides: we must not forget the sun. It is 400 times as far away as the moon, so every atom within it has only one one-hundred-and-sixty-thousandth (1/160,000) of the gravitational effect on us that an atom in the moon has, thanks to the inverse-square law. But the sun is about 27 million times as massive as the moon, so its total gravitational effect on us is very large - about 170 times that of the moon. Why, then, does the sun not dominate the tides? It is because the sun is so remote that its gravitational effect on the near side of the Earth is almost the same as the effect it has on the far side of the Earth. The Earth is about 93,000,000 miles from the sun, so the near and far sides of the Earth differ in distance by only about 1 part in 12,000, less than one one-hundredth of one percent. Since the difference in the forces is what matters in generating tides, the sun's influence is much reduced by its remoteness. Still, the effect of the sun is not completely negligible. Indeed, you can show that its tidal influence is about half that of the moon. There are two special circumstances: 1 When the sun and moon are lined up with the Earth, the lunar and solar influences will act cooperatively and enhance the tides. Note that this is true whether they are on the same side of the Earth, as at new moon, or on opposite sides, as at full moon. (See page 143 of your text). These are the so-called spring tides. The name, by the way, has nothing to do with spring season; think instead of the water `springing up' high. 2 When the moon and the sun are at right angles, as when the moon is in the first or third quarter, their effects partially cancel. The moon's influence is still the more important, and we still have tides, but they are the much less impressive neap tides. Finally, you must also remember that neither the sun nor the moon is at a constant distance from the Earth (the orbits are not perfect circles). Thus the tides vary in size for this reason as well, to an extent that can be predicted in the tide tables.
Complications and Consequences.There are various complications. The ocean basins are not just big round pools. The ocean bottom is not smooth, and any geographic features present may restrict the ebb and flow of water. Near the shore, there are varied topographic features such as bays and inlets, mouths of rivers, and so forth. As a result, the actual times of high and low tide can depend upon your position in a rather complicated way. On a given day in a particular location, therefore, the tide will not necessarily be highest when the moon is directly overhead. But of course you will still see two high tides a day, and the tides will still be highest when the moon is full or new, but more moderate when the moon is in a quarter phase. As you know, the Earth does not spin smoothly inside a frictionless layer of water. The elongated heap of water `wants' to stay pointed at the slowly-orbiting moon, which circles the Earth once a month, while the Earth's rapid spin is trying to carry the water forward with it. The tides of the moon thus provide a net backward drag or frictional force on the ocean bottoms. Indeed, it is a reasonable analogy to say that the Earth is effectively spinning inside a `sloshy set of brake shoes.' The inevitable consequence is that the spin of the Earth is gradually slowing down. In other words, the day is longer now than it used to be. While this can be seen quite dramatically in the fossil record of the Earth, it is a trivial effect over a human lifetime. Over the last century, for instance, the day has increased in length by about one one-thousandth of a second. But wait! Do you remember the conservation laws? If the Earth's spin is slowing down, what will happen to all the angular momentum which it has now, and what happened to the angular momentum which it used to have when spinning much more rapidly? Didn't we say that angular momentum must be conserved? Yes, we did; and yes, it is. The angular momentum shows up, not in the spin of the Earth, but in the way in which the moon orbits the Earth. As a consequence, the moon is gradually spiralling outward away from the Earth, at a rate of about 4 centimeters a year. This is not mere speculation! Amazingly, this small change is measureable. At Macdonald Observatory, in Texas, astronomers regularly bounce laser beams off small retro-reflectors which were left on the moon by the Apollo astronauts. (These reflectors look something like the red rear reflectors you see on bicycles.) The slow change in distance can thus be monitored. Previous chapter:Next chapter
0: Physics 015: The Course Notes, Fall 2004 1: Opening Remarks: Setting the Scene. 2: The Science of Astronomy: 3: The Importance of Scale: A First Conservation Law. 4: The Dominance of Gravity. 5: Looking Up: 6: The Seasons: 7: The Spin of the Earth: Another Conservation Law. 8: The Earth: Shape, Size, and State of Rotation. 9: The Moon: Shape, Size, Nature. 10: The Relative Distances and Sizes of the Sun and Moon: 11: Further Considerations: Planets and Stars. 12: The Moving Earth: 13: Stellar Parallax: The Astronomical Chicken 14: Greek Cosmology: 15: Stonehenge: 16: The Pyramids: 17: Copernicus Suggests a Heliocentric Cosmology: 18: Tycho Brahe, the Master Observer: 19: Kepler the Mystic. 20: Galileo Provides the Proof: 21: Light: Introductory Remarks. 22: Light as a Wave: 23: Light as Particles. 24: Full Spectrum of Light: 25: Interpreting the Emitted Light: 26: Kirchhoff's Laws and Stellar Spectra. 27: Understanding Kirchhoff's Laws. 28: The Doppler Effect: 29: Astronomical Telescopes: 30: The Great Observatories: 31: Making the Most of Optical Astronomy: 32: Adaptive Optics: Beating the Sky. 33: Radio Astronomy: 34: Observing at Other Wavelengths: 35: Isaac Newton's Physics: 36: Newtonian Gravity Explains It All: 37: Weight: 38: The Success of Newtonian Gravity: 39: The Ultimate Failure of Newtonian Gravity: 40: Tsunamis and Tides: 41: The Organization of the Solar System: 42: Solar System Formation: 43: The Age of the Solar System: 44: Planetary Structure: The Earth. 45: Solar System Leftovers: 46: The Vulnerability of the Earth: 47: Venus: 48: Mars: 49: The Search for Martian Life: 50: Physics 015 - Parallel Readings.
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(Wednesday, 03 June, 2020.)