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4.5 Tides and Tidal Locking

Tidal locking is a common phenomenon in our solar system. All large moons are tidally locked to their center planets—Europa is tidally locked to Jupiter, Phobos to Mars, Titan to Saturn, and the Moon to Earth. When a moon is tidally locked, it means that the moon rotates about its own axis only once every time orbits around its central planet. In other words, the moon’s rotational period (i.e., how long it takes to spin around its axis) is the same as its orbital period (i.e., how long it takes to orbit another body, in this case, the planet), yielding a 1 sping:1 orbit ratio. As a result, the same side of the moon is always facing the planet.  Moons aren’t the only celestial bodies that experience such orbital dynamics. In other planetary systems, planets are tidally locked to their central star and binary stars can be tidally locked to each other. In fact, in our solar system, Mercury is almost tidally locked to the Sun.

To fully understand the concept of tidal locking, we must first understand tidal forces—the force that quite literally creates the tides on our planet. Read and watch the resources about tidal forces below before moving on to those about tidal locking.

4.5.1 Tidal Forces

The origin of Earth’s ocean tides has been a subject of continuous investigation for over 2000 years. But the work of Newton is considered to be the beginning of the true understanding of the phenomenon. Ocean tides are the result of gravitational tidal forces. These same tidal forces are present in any astronomical body. They are responsible for the internal heat that creates the volcanic activity on Io, one of Jupiter’s moons, and the breakup of stars that get too close to black holes.

Lunar Tides

If you live on an ocean shore almost anywhere in the world, you can observe the rising and falling of the sea level about twice per day. This is caused by a combination of Earth’s rotation about its axis and the gravitational attraction of both the Moon and the Sun.

Let’s consider the effect of the Moon first. In Figure 4.13, we are looking “down” onto Earth’s North Pole. One side of Earth is closer to the Moon than the other side, by a distance equal to Earth’s diameter. Hence, the gravitational force is greater on the near side than on the far side. The magnitude at the center of Earth is between these values. This is why a tidal bulge appears on both sides of Earth.

The figure is an illustration of the earth centered within an exaggerated ellipse whose major axis is horizontal. The moon is shown to the right of the earth, moving counterclockwise. The left side of the ellipse is labeled as High tide, with a note that says “on far side, moon pulls earth more than water, creating a high tide.” The right side of the ellipse is labeled as High tide, with a note that says “on near side, moon pulls water more than earth, creating a high tide.” The top and bottom of the ellipse are labeled “Low tide.”
Figure 4.13: The tidal force stretches Earth along the line between Earth and the Moon. It is the difference between the gravitational force from the far side to the near side, along with the orbit of Earth and the Moon around each other, that creates the tidal bulge on both sides of the planet. Tidal variations of the oceans are on the order of few meters; hence, this diagram is greatly exaggerated.
The net force on Earth causes it to orbit about the Earth-Moon center of mass, located about 1600 km below Earth’s surface along the line between Earth and the Moon. The tidal force can be viewed as the difference between the force at the center of Earth and that at any other location. In Figure 4.14, this difference is shown at sea level, where we observe the ocean tides. (Note that the change in sea level caused by these tidal forces is measured from the baseline sea level. We saw earlier that Earth bulges many kilometers at the equator due to its rotation. This defines the baseline sea level and here we consider only the much smaller tidal bulge measured from that baseline sea level.)
An illustration of the earth and the tidal forces shown as arrows at the surface of the earth. Near the poles, the arrows are short and point radially inward. As we move away from the poles, the arrows get longer and point increasingly away from the center. At 45 degrees, the arrows are tangent to the surface and point toward the equator. At the equator, the arrows are longest and point directly outward.
Figure 4.14: The tidal force is the difference between the gravitational force at the center and that elsewhere. In this figure, the tidal forces are shown at the ocean surface. These forces would diminish to zero as you approach Earth’s center.
Why does the rise and fall of the tides occur twice per day? Look again at Figure 4.13. If Earth were not rotating and the Moon was fixed, then the bulges would remain in the same location on Earth. Relative to the Moon, the bulges stay fixed—along the line connecting Earth and the Moon. But Earth rotates (in the direction shown by the blue arrow) approximately every 24 hours. In 6 hours, the near and far locations of Earth move to where the low tides are occurring, and 6 hours later, those locations are back to the high-tide position. Since the Moon also orbits Earth approximately every 28 days, and in the same direction as Earth rotates, the time between high (and low) tides is actually about 12.5 hours. The actual timing of the tides is complicated by numerous factors, the most important of which is another astronomical body—the Sun.

The Effect of the Sun on Tides

In addition to the Moon’s tidal forces on Earth’s oceans, the Sun exerts a tidal force as well. The gravitational attraction of the Sun on any object on Earth is nearly 200 times that of the Moon. However, as we show later in an example, the tidal effect of the Sun is less than that of the Moon, but a significant effect nevertheless. Depending upon the positions of the Moon and Sun relative to Earth, the net tidal effect can be amplified or attenuated.

Figure 4.15 illustrates the relative positions of the Sun and the Moon that create the largest tides, called spring tides (or leap tides). During spring tides, Earth, the Moon, and the Sun are aligned and the tidal effects add. (Recall that the tidal forces cause bulges on both sides.) Figure 4.15(c) shows the relative positions for the smallest tides, called neap tides. The extremes of both high and low tides are affected. Spring tides occur during the new or full moon, and neap tides occur at half-moon.

Interactive: Watch this animation of the tides in motion.

Figure a shows the earth centered within a horizontal shaded ellipse labeled spring tide. The sun is positioned to the right of the earth and the moon is in line, in between the earth and sun, and orbits counterclockwise. Figure b shows the earth centered within a horizontal shaded ellipse labeled spring tide. The sun is positioned to the right of the earth and the moon is in line with the earth and sun but to the left of the earth, and orbits counterclockwise. Figure c shows the earth centered within a vertical shaded ellipse labeled neap tide. The sun is positioned to the right of the earth and the moon is below the earth, and orbits counterclockwise. The ellipse in part c has a noticeably smaller vertical major axis than the horizontal major axes of the ellipses in parts a and b.
Figure 4.15: (a and b) The spring tides occur when the Sun and the Moon are aligned, whereas (c) the neap tides occur when the Sun and Moon make a right triangle with Earth. (Figure is not drawn to scale.)
The Magnitude of the Tides

With accurate data for the positions of the Moon and the Sun, the time of maximum and minimum tides at most locations on our planet can be predicted accurately.

For Further Exploration

Visit this site to generate tide predictions for up to 2 years in the past or future, at more than 3000 locations around the United States.

The magnitude of the tides, however, is far more complicated. The relative angles of Earth and the Moon determine spring and neap tides, but the magnitudes of these tides are affected by the distances from Earth as well. Tidal forces are greater when the distances are smaller. Both the Moon’s orbit about Earth and Earth’s orbit about the Sun are elliptical, so a spring tide is exceptionally large if it occurs when the Moon is at perigee and Earth is at perihelion. Conversely, it is relatively small if it occurs when the Moon is at apogee and Earth is at aphelion.

The greatest causes of tide variation are the topography of the local shoreline and the bathymetry (the profile of the depth) of the ocean floor. The range of tides due to these effects is astounding. Although ocean tides are much smaller than a meter in many places around the globe, the tides at the Bay of Fundy (Figure 4.16), on the east coast of Canada, can be as much as 16.3 meters.

Two photos of the same marina at the Bay of Fundy and appear to be taken from the same location. The photo on the left was taken when the water is high, the water line is nearby and the boats are all floating in the water. The photo on the right was taken when the water is low. The water line is quite distant and the boats are resting on mud.
Figure 4.16: Boats in the Bay of Fundy at high and low tides. The twice-daily change in sea level creates a real challenge to the safe mooring of boats. (credit: modification of works by Dylan Kereluk)

Other Tidal Effects

Tidal forces exist between any two bodies. The effect stretches the bodies along the line between their centers. Although the tidal effect on Earth’s seas is observable on a daily basis, long-term consequences cannot be observed so easily. One consequence is the dissipation of rotational energy due to friction during flexure of the bodies themselves. Earth’s rotation rate is slowing down as the tidal forces transfer rotational energy into heat—a process which we call tidal heating and will be discussed in the next chapter. The other effect, related to this dissipation and conservation of angular momentum, is called “locking” or tidal synchronization which we discuss in greater detail below!

4.5.2 Tidal Locking

Read this NASA webpage and watch the embedded animations: Vogel, Tracy. “Tidal Locking.” NASA.

Watch the video below.

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