NAGT > Publications > In the Trenches > 2017 - Volume 7 > In the Trenches - July 2017 > What Really Causes Tides

What Really Causes Tides

NEIL F. COMINS (galaxy@maine.edu) is an author of text and trade books and a professor of astronomy at the University of Maine, Orono, Maine.

Solar eclipses are notable for a variety of scientific and social reasons. By blocking the intense sunlight that we normally see, they provide astronomers with information from the much dimmer outer layers of the Sun's atmosphere, the chromosphere and corona. They also enable scientists to see stars when they are almost directly behind the Sun and therefore are normally invisible to us. This was important in 1919 when Arthur Eddington photographed a total solar eclipse and imaged stars whose light paths had been affected by the Sun, thereby providing the first confirmation of Einstein's theory of general relativity.

There is one aspect of both solar and lunar (when the Moon is in the Earth's shadow) eclipses that is often overlooked, namely that during eclipses the range of ocean tides, from high to low, is extreme, especially when the Moon is particularly close to the Earth, as it will be at the time of this 2017 solar eclipse. The range from a high to the following low tide varies from day to day because the gravitational effects on the Earth of both the Moon and Sun contribute to tides. The Moon is responsible for about two-thirds of the tides, while the Sun causes the other third. When the two bodies are in a straight line with the Earth, either on the same side of Earth (new Moon) or on directly opposite sides (full Moon), their tidal effects combine directly to create especially high tides. At all other phases of the Moon, the Sun and Moon are at an angle, as measured from Earth, and hence the tides they create partially cancel each other.

So, what causes the tides? Focusing just on the Moon for now, nearly all television shows and YouTube videos purporting to explain the tides provide the explanation given by astronomer Laura Danly in 2007 on the TV show, Mysteries of the Moon: "The Moon pulls on the Earth gravitationally, and when it does so, it also pulls on the oceans, that are stretched up a little bit toward it. It pulls preferentially on the front side of the Earth, pulls the ocean toward it, and then pulls the Earth a little bit less, and then the back side, the ocean is not pulled quite as far toward the Moon. So that's why there are two bulges, that are called tidal bulges, on the Earth."

This is a good starting point for discussing tides with your students because if they have ever learned about tides, this presentation is probably consistent with what they have been told, and because this explanation is wrong. I often find that students are open to learning new things if their current beliefs are openly and effectively challenged, meaning that the correct science can show why what they think is correct is, in fact, wrong. I have seen school and college students, as well as geology and astronomy professors who taught the tides wrong for years, "light up" when they see why tides really occur. Let's explore that now.

To begin with, the Moon does not orbit the Earth. The two bodies orbit their common center of mass, often called their barycenter, which is located about 1,061 miles under the Earth's surface, in a line between the centers of the two bodies. It is the barycenter that moves in an elliptical path around the Sun, while the Earth and Moon waltz around it. For now, let's ignore the Earth's rotation; we will add in later the effects of rotation, which moves the locations of the high and low tides.

The tides generated by the Earth-Moon interaction are actually caused by two effects. First is the force of gravity from the Moon, as mentioned above. That force does indeed decrease with distance, so that the part of the Earth closest to the Moon does feel the greatest force toward the Moon and the part of the Earth farthest from it feels the least gravitational pull by the Moon. But that is not all. At the same time, the Earth's motion around the barycenter creates a force on the Earth similar to the force you feel on a merry-go-round. The merry-go-round or centrifugal force is away from the pivot point. In the case of the Earth-Moon system, that force is always directed away from the Moon.

The force on the Earth due to its orbiting with the Moon around the barycenter is not exactly a centrifugal force. The farther you are from a merry-go-round's center, the stronger the centrifugal force you feel from it. The outward force felt by the Earth is different in that every place on the Earth makes the same-sized loop and therefore every place on Earth feels the same outward force due to its motion. You can see this if you extend your arm in front of you, palm open and facing away, and make small loops, which is analogous to the Earth moving around the barycenter. Each point on your hand makes the same-sized circle; hence they all feel the same outward force. Having said that, I will use the common expression "centrifugal force" for the force on Earth away from the Moon.

Tides are caused by the competing forces of gravitational attraction from the Moon and the outward (centrifugal) force due to Earth's motion around the barycenter, which, as noted, is directed away from the Moon. In other words, to determine the total force acting at any point on or in the Earth, we take the vector sum of the two forces. At the very center of the Earth, the two forces are equal and opposite, hence they cancel. On the side of the Earth closest to the Moon, the gravitational force from the Moon is stronger than the centrifugal force, so waters on that side are pulled toward the Moon. On the side of the Earth farthest from the Moon the centrifugal force exceeds the Moon's gravitational force, so the waters there are pushed away from the Moon. This is summarized in Figure 1.

While this discussion creates the impression that the water directly under the Moon is literally pulled up by it or, conversely, pushed away on opposite side of the Earth, that is not happening. The gravitational and outward centrifugal forces can only lift the water a matter of inches. The tides are actually the result of large quantities of water from the region on Earth where the Moon is seen near the horizon flowing either toward the Moon or away from it. Referring to Figure 1, you can visualize this region by imagining a circle on Earth passing through the top and bottom on the figure and through point C.

Now let's put the Earth's rotation back in the picture. Since the Earth rotates about 27 times faster than the Moon orbits the barycenter, the Moon's location in our sky changes by the minute. As a result, the location of the high and low tides around the Earth are in continuous motion. Earth's rapid rotation, combined with the tidal force described above, causes the high tides to continually flow westward to try and keep directly under the Moon or on the exact opposite side of the Earth from it. This fails for two reasons. First, the water has inertia, meaning that it is not able to respond instantaneously as the Earth turns. Second, as the Earth rotates and water flows, the continents get in the way, disrupting the tidal activity of the oceans. As a result, the high tide on the side of the Earth facing the Moon is typically about 10º ahead of the Moon in the direction of the Earth's motion. The same argument applies to the high tide on the opposite side of the Earth from the Moon.

The gravitational pull of the high tide on the Moon's side that leads it around is actually pulling the Moon forward—in the direction of the Moon's motion. In other words, that water is giving the Moon energy, which causes it to spiral away from the Earth. The two bodies are separating today by about 1½" per year. Although the Earth is giving the Moon energy, the Moon is not speeding up as it spirals away. Rather, it is slowing down (something else that many videos get wrong). Since the total energy of the Earth-Moon system is conserved, the energy given to the Moon comes from our planet, namely from the energy stored in the Earth's rotation. This change is caused by the friction and other interactions between the oceans and the lands they encounter. As the result, the Earth's rotation rate is decreasing. Today the day is getting longer by about 0.002 seconds per century.

All the elements of the discussion above also apply to the tides created by the Sun. It is worth noting that the center of mass of the Earth-Sun system is almost exactly at the center of the Sun, rather than inside the Earth (keeping in mind that the Sun has about 333,000 times as much mass as the Earth). As a result, the Sun's motion around the center of mass of the Earth-Sun system is miniscule.

So, will the Moon continue to recede until it leaves Earth orbit? Contrary to what you often hear in the media, the answer is "No."

FOR FURTHER INFORMATION:

Comins, N.F., and Kaufmann, W., 2014, Discovering the Universe, 10th edition: New York, W. H. Freeman and Company

Comins, N.F., 1999, An in-your-face approach to student misconceptions about astronomy, in Bulletin, American Astronomical Society 195th meeting, Atlanta, January 2000, https://www.researchgate.net/publication/234403867_An_In-Your-Face_ Approach_to_Student_Misconceptions_About_ Astronomy

National Oceanic and Atmospheric Administration, 2013, Our restless tides, https://tidesandcurrents.noaa.gov/restles1.html

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