Tidal Tug Of War

© 2000 by Robert C. Moler

One of the hardest astronomical concepts to understand, for me at least, was the tidal force. Why, for instance, when the sun and moon are on the same side of the earth, are the ocean tides raised on the side facing the moon and sun and also on the side opposite them? It made no sense.

Before making sense of it (well I finally figured it out, I think), I'll tell you why I'm bringing it up. This month, the earth and the other bright planets, known from antiquity, will line up, with earth on one side of the sun, and the rest on the other. See the planet page for charts showing the grouping. Some so-called scientists surmise that the tidal pull of the aligned planets on the sun might intensify the current sunspot cycle and wreak havoc with the earth. This month's Sky and Telescope magazine (which, incidentally GTAS members can get at a discount) has an excellent article this month on this effect. It turns out that the tidal peak forces on the sun May 5, 2000, will be somewhat less than those on the sun back on January 6, 1990. Since we survived that, we will survive this May's peak.

In this space in January I alluded to the planetary lineup in 1982 and how it spurred the start of the GTAS. A book came out before that called the Jupiter Effect, in which planetary tidal effects were supposed to increase the sun's activity and cause, among other things, great earthquakes that would cleave the state of California in two along the San Andreas fault. Many earthquakes later, none memorable in 1982 however, California is still whole with all its 54 electoral votes intact.

The major effect we see of the tidal force of the moon and sun on the earth are the ocean tides. These are highest at new moon and full, when the moon and sun are lined up with the earth. High tides are lowest when the moon is at first and last quarters, the farthest out of line with the earth and sun. Even so high tide follows the moon, which exerts over twice the tidal force over the earth that the sun does.

I read once in an astrology book (Yeah, I know, but I was baby-sitting at the time and was bored.) that the proof that the sun, moon and planets governed our lives, was seen in the effect of the moon on the ocean tides. Since the human body was over 80% water, we were similarly affected. I about fell out of my chair at that one. The ocean tides are so great because the earth is surrounded by a world circling liquid that can easily slosh around and be affected by the moon and sun's tidal pull. Lake Michigan is too small to be bothered by such tides, though tides of sorts on an order of a foot or so can be caused by strong winds or differences in air pressure from one end of the lake to the other.

Actually the solid earth rises up a bit as the moon passes over, or under a location.

So what is the tidal force? Basically it is the difference of the gravitational force of one body from the near edge to the far edge of second body. This difference is expressed in a force that tries to pull apart the second body. A recent example of this was Comet Shoemaker-Levy 9, torn asunder by passing too close to Jupiter. The comet was literally pulled apart like taffy. Only comets aren't stretchable, so the comet ended up as a linear string of over 20 pieces strung out into and ever lengthening straight line. The mechanism that is supposed to power Jupiter's moon Io's volcanoes is the tidal pull of both Jupiter and the other satellites on Io. I wouldn't be surprised if it were proven that the moon and sun's tidal forces drive our own planet's plate tectonics.

The gravitational force between two masses is proportional to the product of the masses divided by the square of their distance. Thus the force diminishes by the inverse square of the distance. If the two masses involved are points there are no tidal forces. Other than the singularities in the centers of black holes, everything else of any mass has a size. Isaac Newton spent a lot of time in his development of his law of gravitation proving that for most interactions between two bodies that the mass of each can be thought to exist at a point in what is called the center of gravity, which is actually the center of mass.

That's OK for plotting orbits that don't get too near each body. But what of the body itself. All the mass isn't really at a point in the center.

The way I understand tidal force is seen in the diagram to the right. We will assume body 2 is orbiting body 1. I can be the other way around, but it wouldn't be as clear as this way.

Body 2 orbits Body 1 as if all its mass were centered at point B, its center. Points A and C are on opposite sides of body 2. A body at point B, in this example, orbits body 1 in a circular orbit. Point A, attached to body 2 and point B moves at the same velocity, but being closer to body 1, is actually moving to slow to keep in the circular orbit, and would want to fall closer to body 1. It can't, since its attached to body 2, but that force is still felt. Conversely point C is farther than point B, but moving with B is moving too fast to want to stay in B's circular orbit, I wants to move away from body 1. This is seen as a force away from body 1. Despite the rather legal sounding description above, it is the way I have come to understand it. And that's how the moon or other body can play tug-of-war with another body by pulling from only one side.

By the way, the moon is winning it's tug of war against the earth. The friction of the tides is slowing the earth's rotation at a rate of about a second every year and a half. Since earth's lost energy must go somewhere, it is actually pushing the moon farther away, That rate of the moon's recession is calculated to be on the order of inches per century

Questions? Comments? Send Email to me at bob@bjmoler.org

Uploaded: 04/30/00