The Standing Invitation

The Slippery Slope

with 4 comments

Let’s go back to school for a moment. A quick science question for you to think about: what causes the tides?

(Actually, the first answer I learned in school for that one was that God had made it that way, but the less said about that the better…)

So we all know the answer: the Moon. And we all probably have the same textbook picture in our minds of how this looks ­– something like this.

So there’s the Earth surrounded by its oceans, and the Moon’s gravitational pull attracts the water towards itself. We also know that the Sun is out there somewhere, and has its own gravitational pull. When the Moon and the Sun are in alignment, you get both forces combined and you get a very strong tide, a spring tide; and when the Sun and Moon are at right angles, you get a neap tide, which is weak.

So it’s mostly down to the Moon’s gravitational pull… right?

Well, actually…

The Moon is near, and the Sun is far away, so the Moon should have the biggest influence ­– but remember, the Sun is massive. In fact, it is two million times heavier than the Moon. How does this affect the balance? I won’t put up the equations here, but it’s actually quite simple to calculate, and it turns out that the Earth feels the Sun’s gravitational pull 177 times more than the Moon’s.

So if the Moon’s effect is so tiny, why do the tides track the Moon, and not the Sun?

What we need to understand here is the concept of a gravitational well.

This is a gravitational well. At the centre is some massive object ­– the Moon, say. We sit on the surface of the well and, if we’re not careful, we can slide down it, faster and faster, until we collide with whatever is at the centre. Key to this concept is the idea that the closer you are to the mass, the steeper the slope is.

When you’re near to the mass you are drawn towards it; if you’re a kilometre closer, you are drawn even more.

But how much that extra kilometre closer really matters depends on how far away you were to begin with. The Sun might be a huge attractor pulling you constantly, but if it’s 93 million miles away an extra step closer won’t really make much difference. The Moon is a much weaker attractor, but because you’re closer to it, distances really do matter.

So yes, we are all affected by the Sun’s gravitational pull, much more than we are by the Moon’s; but we are affected constantly, wherever on Earth we are. The Moon’s effect is much weaker, but much, much more local. It matters if the Moon is overhead or on the other side of the Earth; that extra difference represents a real change in pull, as opposed to the Sun’s stronger but uniform and therefore unnoticed pull.

That’s the gist of it, anyway.

But now we’ve got to thinking about it – look at the diagram again. What’s going on with that tidal bulge on the other side of the Earth to the Moon? We know that exists because we have two high tides every 24 hours, but why? It’s bulging away from the Moon. Surely that makes no sense?

Unfortunately that’s an even weirder story, and we’ll save it for another time.

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Written by The S I

October 2, 2011 at 11:59 pm

4 Responses

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  1. >Unfortunately that’s an even weirder story, and we’ll save it for another time.

    I’m pretty sure that the “textbook picture” is not how the water is actually distributed related to the Moon position. As far as I remember it is roughly the minor semi-axis that is directed to the Moon, not the major one. Am I right? Will you address this issue next time? I could not help asking, the picture is quite disturbing for me, moreover it is used in the current Wikipedia article.

    Yrogirg

    October 6, 2011 at 12:51 pm

  2. That’s interesting. I don’t think I’ve ever seen an illustration of the tides where it’s been the semi-minor axis that points towards the Moon; but then I can’t say I’ve really looked for one. Do you have any examples?

    When the problem of tides came up at work it brought the lab to a standstill as we tried to figure it out. This post and the one I will write in the next couple of days summarise the outcome of that long and occasionally heated discussion.

    I should immediately state that I am not a physicist, and could well be wrong about any or all of this, and welcome any corrections.

    The S I

    October 6, 2011 at 1:12 pm

    • I’ve found the book, that made me think the picture is wrong. It is a Russian textbook on general physics (not even a geophysics and the author is not a geophysicist). The reason the author believes that the common picture is wrong is the value of establishment of a port (http://en.wikipedia.org/wiki/Establishment_of_a_port). He says that establishment of a port is usually constitutes several hours — thus it is the minor semi-axis that is directed to the Moon. However I could not find any tables of the value to actually check it. Moreover the term seems to be outdated. The wikipedia article suggests a huge spread of values to suggest the mean value — no wonder, the Earth is not a smooth ball.

      To sum up I think there is not enough evidence to assume the picture presented in the post to be terribly wrong. Of course, it is rough, but despite it may be not so far from the truth. But it should be noted that none of the semi-axis can be directed precisely to the moon, since the discrepancy accounts for the increasing of the distance between the Earth and Moon. And this last observation helped me to find probably the real image — just google images for ‘tidal braking’ (for example http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit4/Images/tidalbraking.gif from the lectures http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit4/tides.html).

      >I should immediately state that I am not a physicist, and could well be wrong about any or all of this, and welcome any corrections.

      Neither do I can call myself a geophysicist or mature enough in physics in general, so don’t even think of my statements as an expert ones.

      Yrogirg

      October 6, 2011 at 2:06 pm

      • Excellent links! Thank you very much for them. I had wondered if there would be any sort of lag time caused by the Moon’s orbit around the Earth, and it’s nice to see it treated here.

        The S I

        October 6, 2011 at 2:36 pm


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