VACETS Regular Technical Column

The VACETS Technical Column is contributed by various members , especially those of the VACETS Technical Affairs Committe. Articles are posted regulary on [email protected] forum. Please send questions, comments and suggestions to [email protected]

November 5, 1996


The reason for earth's tides, and why high and low tides occur at regular intervals, was a subject of interest to thinkers for thousands of years, but not the good old Greeks. The Greeks live on the shores of the Mediterranean Sea. That sea happens to be relatively tideless because it is so nearly land-locked small body of water.

About 325 BC, however, a Greek explorer, Pytheas of Masslia, ventured out of the Mediterranean and into the Atlantic. There he came across good pronounced tides, with two periods of high water each day and two periods of low water in between. Each month there were two periods of particularly large range between high and low tides (spring tides) and, in between, two periods of particularly small range (neap tides). What's more, the monthly variations matched the phases of the moon. The spring tides came at first quarter and third quarter. Pytheas suggested, therefore, that the tides were caused by the moon. But, his suggestion lay fallow for two thousand years.

The main factor that spoiled the moon-tide connection for thoughtful scholars was the fact that there were two tides a day. For instance, suppose there is a high tide when the moon is high in the sky. That would make sense. The moon might well be drawing the water to itself by some mysterious force. If the water heaped up under a high moon, a point on the rotating earth, passing through the heap, would experience a high tide followed by a low tide. But a little over twelve hours later, there would be another high tide and then the moon would be nowhere in the sky. In fact, it would be on the other side of the globe. If the moon were exerting an attractional force, the water on one's side of the globe should be pulled downward in the direction of his feet. There should be a hollow in the ocean, not a heap.

Could it be that the moon exerted an attraction on the side of the earth nearest itself and a repulsion on the side opposite? Then there would be a heap on both sides and it would explain the two high tides each day.

The notion that the moon would pull in some places and push in other places must have been very hard to accept, and most scholars didn't try. So the moon's influence on the tides was put down to astrological superstition by the astronomers of early modern times.

It was only in the 17th century that a clear explanation was given -- by Newton. Newton argued that the gravitational attraction of the moon causes tides. This force has only a slight effect on the solid land mass (and it is detectable), but the great mass of water that make up the oceans is free to move. Because the gravitational force decreases with the square of the distance, the moon pulls harder on that part of the earth closest to it. The water in the oceans is puled toward the moon, resulting in a high tide on the side of the earth facing the moon. Simultaneously a high tide occurs on the opposite side of the earth. Why this second high tide? Because the pull of the noon on the far side of the earth is less (since it is farther from the moon) than the pull on the central (nearer) parts of earth, (we may visualize this as the earth being pulled away from the water on the far side, just as the water on the side of the earth near the moon is pulled away from the earth a bit) the ocean water thus tends to collect on the sides closest and farthest from the moon, and is taken from the region between, where these will be low tides. Since the moon moves relative to the earth so that it returns to the same position overhead after about 25 hours, there are 2 high and 2 low tides at any point every 25 hours (approximately 2 of each per day). Because the high tides stay more or less in line with the moon, it is as if the solid earth moved beneath the tidal bulges.

High tides do not necessarily correspond precisely to the time at which the moon is directly overhead since other forces are also acting; among the complicating factors are the rotation of the earth, friction between the solid earth and the moving water, and the gravitational pull of the sun. These factors also affect the height of the tides. For example, the highest and lowest tides occur when the sun and moon are lined up so both are pulling in the same direction (called spring tides); when the sun and moon are at right angles, the tides are smallest (neap tides).

But why spring tides and neap tides and what is the connection between tides and the phases of the moon? For that we have to bring in the sun. It too, exerts a gravitational influence on the earth. The gravitational pull of two separate heavenly bodies on the earth varies directly with the mass of the bodies in question and inversely with the square of their distance from the earth. It turns out that the sun's gravitational pull on the earth is 176 times that of the moon. However, the moon produces the major tidal effect. Why is that? The answer is that it is not the gravitational pull itself that produces the tides, but the difference in that pull upon different parts of the earth. The difference in gravitational pull over the earth's width decreases rapidly as the body under consideration is moved farther off, since, as the total distance increases, the distance represented by the width of the earth makes up a smaller and smaller part of the total. So, even though the gravitational pull of the moon is only a small fraction of that of the sun, due to the much closer distance, the tide-producing effect of the moon is about 2.2 times that of the sun.

The tides, in a way, affect time. At least, it is the tides that make our day twenty-four hours long. As the tidal bulge travels about the earth, it scrapes against shallow sea bottoms and the energy of earth's rotation is dissipated as frictional heat. This dissipational energy is enough to be slowing the earth's rotation and lengthening the day by one second every one hundred thousand years. This isn't much on the human time scale, but if the earth has been in existence for five billion years and this rate of day-lengthening has been constant throughout, the day has lengthened a total of nearly fourteen hours. When the earth was created, it must have been rotating on its axis in only ten hours (or probably less).

As the earth's rate of rotation slows down, it loses angular momentum as well, but this angular momentum cannot be dissipated as heat. It must be retained, as angular momentum, elsewhere in the moon-earth system. What the earth loses, the moon must gain and it can do this by receding from the earth. The effect of the tides, then, is to slow the earth's rotation and to increase the distance of the moon.

This slowing down of the rotation due to tidal effect would also explain why the moon faces the earth on one side. Even if there were no oceans on the earth, there would still be tidal friction, for the solid substance of the earth does yield a bit to the differential pull of the moon. This bulge of solid material traveling around the earth also contributes to internal friction and to the slowing of the earth's rotation. We can see this at work on the moon, which has no oceans. Just as the moon produces tides on the earth, so the earth produces tides on the moon. The effect of earth-on-moon is 32.5 times as much as moon-on-earth. With this much tidal effect, plus the much less original rotational energy, the moon has dissipated its rotational energy to the point where the tidal bulge is frozen into the moon, and it now faces one side only toward the earth.

There is a limit to how much the earth's rotation will be slowed. Eventually, the earth will rotate about its axis so slowly that one side will always face the moon as the moon turns in its orbit. When that happens, the tidal bulges will be frozen into place immediately under the moon and on earth's opposite side and will no longer travel about the earth. Of course, the tidal bulges of the sun will still be moving about the earth some seven times a year (a day will be about fifty times longer than today) and this will have further effects on the earth-moon system. (There is a planet-moon system that has reached that point. The planet Pluto and its moon Charon both have their faces frozen toward each other.)

We can also suspect that the tidal effect of the sun upon the planets would slow down the rotations of the planets. The closer the planet to the sun, the larger the tidal effect and the slower the planet's rotation. With a bit of wisdom of hindsight, one might suspect that the rotations of Venus and Mercury (which are very close to the sun) are very slow and these indeed were true. Mercury's rotation is one and half times in one of its year and Venus's rotation is slightly longer than its year.

The tidal effect can also be used to explain the beautiful rings of the gas giant planets but that is another story. So that's all, folks! .

Duc Ta Vo, Ph.D.
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Copyright © 1996 by VACETS and Duc Ta Vo

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