Friday, July 15, 2011

Moon, turn the tides . . . gently, gently away

Previous posts have discussed the moon's orbit around the earth and the cause of the different phases that we observe from our vantage point on earth's surface. We noted that the moon's tilted orbit versus the plane of the ecliptic gives rise to the two lunar nodes (where the moon's path crosses the ecliptic), which were included along with the visible planets and the sun and moon themselves to give the nine worlds found in many ancient cosmologies, including many shamanic cultures in which the shaman's tree by which the shaman ascends to the celestial realm may have nine branches.

The moon, of course, also creates the tides, very important to surfers and to the ancient navigators who traveled the earth's oceans alike. Above is an early animated film from pioneering American animation studio Bray Productions, which contains a very good explanation of the forces which cause the tides. Today's viewers may be slightly impatient at its slow pace, but be patient and enjoy it: it's really quite worthwhile. The fact that this is a silent movie means that it was probably made prior to 1928, when Walt Disney amazed and delighted audiences by adding coordinated sound to his animated clip Steamboat Willie. Bray Productions was founded in December, 1914 and began moving heavily into educational animated productions after World War I (when their successful training videos created great demand for more), so the film above may have been produced between 1918 and 1928.

As the film illustrates, the tidal bulge on one side of the earth is fairly easy to understand (being caused by the gravitational pull of the moon), but the tidal bulge on the other side of the earth is actually caused by the fact that the moon pulls earth as well, actually pulling the earth enough to create the bulge on the other side. The tides take place as the earth itself rotates underneath this enormous "standing wave," a wave so large that its two crests are separated by half of the circumference of the earth itself.

This is easier to conceptualize if we realize that the earth and moon actually form a pair which impact one another, rather than the moon simply orbiting a stationary earth that is not affected by its orbiting partner. The video at the beginning of this previous post (which discusses the theory that the sun is actually part of a very distant binary pair) contains good animation illustrating the motion of two bodies in a binary orbit. While earth's motion in space is of course primarily impacted by its path around the sun each year, the motion of the moon around the earth each month tugs on it slightly as well (just like two dancers or ice skaters who are spinning around one another joined by their hands; we could imagine the earth as a dancer which is going around the sun but which at the same time is spinning a smaller dancer around it in a circle, their outstretched arms grasping one anothers' hands representing gravity, and this motion creates a slight pull on the earth as it goes around its larger path). This pulling on the earth creates the tidal bulge opposite the moon.

The video also illustrates the cause of spring tides and neap tides. The gravitational pull of the sun creates a slight bulge in the ocean as well. When the moon and the sun are aligned, as in a new moon or a full moon, the bulge created by the sun is added to the bulge created by the moon, causing a much higher bulge and greater tidal variances. These are known as "spring tides" (not related to the season known as spring). When the moon and the sun are not aligned, the bulges are out of phase, reducing the difference between high tide and low tide. These are known as "neap tides" (a word originating in Old English).

The action of the tides is slightly more complicated than the description above and the video would indicate, however. For one thing, we might ask why the moon is more important in the tidal action than the sun. Willard Bascom (1916 - 2000), pioneering oceanographer and scientist and author of the excellent Waves and Beaches: the dynamics of the ocean surface (1964) as well as studies on Polynesian history, explains further:
It remained for Isaac Newton to discover the law of gravity, which holds that the gravitational attraction between two objects is directly proportional to the square of the distance between them. From this relationship it can be shown that the gravitational attraction of the sun for the earth is about one hundred and fifty times that of the moon. The tremendous mass of the sun more than makes up for its much greater distance. But the moon is the primary cause of tides. Why?

The answer is that the difference in attraction for water particles at various places on the earth is far more important than total attraction. That is, because of the moon's very nearness (average only 239,000 miles) there is a big difference in the gravitational attraction from one side of the earth to the other.

The water on the side of the earth nearest the moon is some four thousand miles closer to the moon than the center of the earth; the water on the far side is four thousand miles farther away. The sun, however, is ninety-three million miles away, and a few thousand miles one way or the other make comparatively little difference. Thus, the sun's gravitational force, although far larger, does not change very much from one side of the earth to the other. So the moon is more important in producing tides. 84.
Mr. Bascom also explains that the fact that the moon is rotating around earth in the same direction that earth is turning causes the "tidal day" to be slightly longer than twenty-four hours (by about fifty minutes), because the moon's motion means that any point on earth must go slightly further than a full rotation in order to come underneath the moon again. He also explains that the friction of the earth as it rotates beneath the ocean pulls the ocean along, such that the tidal bulge is not aligned directly beneath the moon as it would be if earth's rough ocean basins were frictionless instead. Because of this friction, the tidal bulge is carried forward by the rotation of the earth and is slightly ahead of the moon; "in consequence a point on earth passes beneath the moon before high tide" (85-87). In other words, as earth rotates, the point on earth will pass the moon before it gets to the tidal bulge that the rotation of earth has carried to a point ahead of the moon that is causing it.

There are still more complications that impact the motions of the tides. Because the moon's orbit is elliptical rather than circular, the moon is closest to earth at one point (perigee) and farthest at another (apogee), which creates a change in distance that impacts the tides (a discussion of the impact of an elliptical orbit on earth's path around the sun is discussed in this previous post).

Mr. Bascom explains:
At perigee, the nearest point in its orbit, the moon is fifteen thousand miles closer; at apogee it is that much farther away. This change in distance (and therefore in the attractive force) causes tides that are, respectively, twenty percent higher and lower than average. Perigee is reached once an orbit (once a month) and only rarely does this coincide with the in-phase alignment of sun, earth, and moon. But at least twice a year both effects exist at the same time -- that is, a full moon or a new moon exists at perigee. Then the perigee tides add to the spring tides to produce the highest tides of the year. 88
Mr. Bascom also explains that, while most points on earth experience two tides a day, there are a few places which only have one high and one low a day. The reason for this is that the moon's orbit takes it to points where it is "in the tropics" -- pulling the tidal bulges to an inclination that runs across the equator, such that one bulge is more pronounced in the northern hemisphere and the other bulge (on the other side of the earth) is more pronounced in the southern hemisphere, on the other side of the equator. The diagram below will help one visualize why this would happen. This phenomenon explains why one high tide is usually much higher than the other at any point on earth, and why in some extreme locations there will only be one high tide per day.

Mr. Bascom's excellent book discusses much more than tides, and is highly recommended for everyone interested in waves, beaches and the ocean. For more about Mr. Bascom, you can check out a 1966 article in Life magazine about him on the web here (the article, "Trailbreaker of the Deeps," begins on page 108 of that online magazine; there is a table of contents on the left-hand side of the magazine which contains a link that will take you to the beginning of the article).

I myself learned about Willard Bascom from the pioneering surfboard shaper "Bob Smith," who has a blog here. His book on surfboard shaping, The Basics of Surfboard Design, is an excellent resource for surfers and shapers, and it gives due credit to the wonderful wave analysis of Willard Bascom.

Below is a video of the classic Jimi Hendrix song "Moon, turn the tides . . . gently, gently away," from his album Electric Ladyland (1968). Note that the lyrics, which do not come in until near the end of the song, include, "I can hear Atlantis, full of cheer . . ."