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Getting It Right The Second Time?

Dave North

“ The problem is remembering that tides are caused by force gradients, not by the force itself.”



Let's lead with two corrections.

How about that eclipse? Oops!

I didn't send in my column last month so I shirked my duty to make sure you all knew about it. Travel plans messed me all up and I didn't realize it until too late. But hopefully you got the news anyway.

My other mistake was blathering mindlessly about the neap tides taking place when the Moon is in opposition, which is completely wrong. The neap (lowest high) tides take place when the Sun and Moon are aligned at right angles to the earth, contributing nothing to each other's pull. I have no excuse for this blunder - I've known that since at least high school. I should read what I write sometimes.

This was brought to my attention by Bill Maney, who also took me to task for not mentioning the centripetal force component of the tides. While that is a factor, it's not really the main factor (and there are others, such as internal friction and the friction of water on land, etc.). I'll beg off on this one by pointing out that Cornell doesn't mention the effects of centripetal force either (though NOAA has quite a nice section on it).

Nevertheless, it's interesting. Since the Earth/Moon system is spinning around its barycenter (located inside the Earth) there's a tendency for anything 'loose' (such as water) to seem to move away from that center of rotation. Of course, there's also some distortion of the Earth and Moon as well, but it's quite small.

This is complicated by the two conflicting periods involved: the system itself spins about once every four weeks, but the Earth is spinning 'through the spin' in just under a day. The result is an effective 'push' of the water away from the Moon. However, it appears this effect is fairly weak compared to the effect of differential gravity (no, I haven't personally run the numbers, which shouldn't be all that hard. I'm just taking other folks' word for it, which isn't Best Practice. But I'm lazy- you should know that by now).

I suspect the centripetal effect is a bit more intuitive when trying to explain why, well, there's a water bulge on the side of the Earth opposite the Moon. How can gravity from the Moon (which attracts, mind you) cause water to bulge away from it? That just seems silly.

The problem is remembering that tides are caused by force gradients, not by the force itself. The water on the side of the Earth closest the Moon is about 8,000 miles closer to the Moon than the water on the opposite side. Since the Moon is roughly 240,000 miles away, that's about 1/30 of the radius. A fair percentage! So there's less gravitational attraction on the far water- even less than the water on the limbs as viewed from the Moon.

So from the Moon's point of view, that water is lighter. Weighs less, so to speak. Up it goes!

Okay, that's not the classical way of putting it. The 'textbook' description is that the Earth is being pulled away more than the water on the side furthest from the Moon. And since the Earth is (relatively) rigid and water is not, the Earth is 'lifted away' from the distal water!

Somehow I'm not sure I'm making this any easier to understand. I hope so, though.

Now for the part that was entirely new to me, even after all these years. In discussion with some friends up near Jackson one Saturday night, the question was posed "why is the Moon receding from Earth" (why is the distance increasing?)

This troubled me; I had no immediate answer. I already knew tidal stress was slowing down the rate of Earth's spin. But if something similar were happening to the Moon, one would think it would lead to a decaying orbit, where the Moon would be getting closer rather than further away.

But no!

Remember the friction of water on land? Turns out that's very important to this issue. The relatively rapid rotation of Earth 'pulls' the tidal bulge slightly ahead of the Moon in it's orbital path. It's kind of like a huge torque converter.

Those leading bulges pull on the Moon, dragging it into a faster orbit slowly but surely. Greater velocity = higher orbit. Aha!

Of course, this process will slow down and end when the Earth/Moon system is completely tidally locked. And as usual, there are other members of the club who understand these issues far better than me, and I'd love to hear about it!

Stay tuned for next month's corrections to this month's column.

Perhaps if I ever get one entirely right, I should immediately stop.


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