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Water on Earth The Science of Tides

1. Causes of ocean tides

If you look into various books and web sites, you will find about three different explanations for what causes tides.  Some are equivalent to one another, some are not.  Therefore, we can say that, at least as for the general public, there is great confusion about what causes tides.

A complete scientifically correct explanation, however, does not help much either, because it is not possible to easily reduce this explanation to simple, intuitive language.  So, here I will give an explanation that is reasonably simple to understand and still, I believe, scientifically accurate (at least as far as it goes).

A simple, but reasonably correct, explanation of the tides is as follows.

First, we start with the simplest explanation.

The diagram at right represents the earth-moon system.  The shaded area around the earth represents the earth's oceans (we assume for now a uniform ocean with no continents).

Point A is at the surface of the ocean nearest the moon.  Point C is at the surface of the ocean farthest from the moon.  Point B is the center of the earth.

The arrows in the top diagram pointing toward the moon represent the force of the moon's gravity at these three points.  Since the force of gravity depends on distance, point A is attracted to the moon most strongly, point C least strongly, and point B at intermediate strength.

The lines leading downward from each point show how each point would move under the influence of the moon's gravity.  Point A moves farthest toward the moon, B, not as far, and C least of all.  The result is as if the ocean were bulging out toward and away from the moon.  Thus, as the earth rotates under this bulge, any point on earth has two high tides and two low tides each day.
Now, we will consider certain facts that will gradually make our understanding more accurate.  

First, it turns out that the direct vertical pull of the moon on the ocean (as at point A) is not anywhere near strong enough to raise the tides we observe.  The forces that actually move the oceans are the forces acting at points D and E in the diagram at right.  These act horizontally, not vertically, and moving water horizontally is a lot easier than pulling it up vertically.

Now we will take a different view of the situation, one which may seem completely at odds with the explanation already given. But in fact, this viewpoint is actually a refined version of that already given, though this may not be obvious at first.

  • Rotation of the earth-moon system around their common center of gravity

In reality, the moon does not revolve around the earth.  Both earth and moon revolve around their common center of gravity.  What is a center of gravity?  Think of it this way: If the earth and moon were connected by a stick, at what point would you have to hold your finger to balance the stick?  That's the center of gravity.  Since the earth weighs much more than the moon, the center of gravity of the earth-moon system is much closer to the earth than to the moon.  In fact, it is so much closer to the earth that the center of gravity (shown by the X in the diagram at right) is actually inside the earth - about one-third of the way in.
Now we can think about the center of the earth spinning around the common center of gravity of the earth-moon system, as in the diagram at right.

 Each circle, 1 through 4, represents one position of the earth as it circles the common center of gravity, X.

What happens to the water on the earth as the earth spins around like this?

  • Inertia

Well, think of that old trick where you attach a rope to a bucket of water and swing the bucket around over your head.  The water does not fall down when the bucket is at the top of the swing, does it?  Sometimes we think of this as "centrifugal force," but in fact there is no such force.  The reason the water does not fall down is because, as the bucket swings in a circle, the water tries to go in a straight line.
This tendency to keep going in the same direction is called inertia.
This same property of inertia makes the water on the earth swing out away from the surface both toward the moon and away from it.  This is because the earth is revolving around the center of gravity of the earth-moon system.  

Now we have a more scientifically correct explanation of tides. As I said, this explanation is more or less equivalent to the first one given, though this is not apparent.  To give a simplified version of it, just use the last three diagrams and point out that the water on the earth is whirling away from the X spot, the center of gravity of the earth-moon system.
A simple and completely correct explanation, put in terms of acceleration, can be found here.  It goes like this:  The moon exerts a force on the earth, and the Earth responds by accelerating toward the Moon [or "falling" toward the moon]; however, the waters on the side facing the Moon, being closer to the Moon, accelerate more and fall ahead of Earth. Similarly, Earth itself accelerates more than the waters on the far side and falls ahead of these waters. Thus two aqueous bulges are produced, one on the side of Earth facing the Moon, and one on the side facing away from the Moon. As Earth rotates on its axis beneath these two bulges, the rise and fall of the oceans results.

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