The Standing Invitation

Posts Tagged ‘Gravity

Life in Freefall

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This is a follow-up to a post about tides, and about how this universally known phenomenon is more complicated and subtle than the standard schoolroom explanation would have us believe.

I put up a diagram of the tides copied from Wikipedia, but my attention was drawn by Yrogirg to this more realistic one that highlights the fact that the semi-major axis of the tidal bulge doesn’t point exactly at the moon; the tide reaches its peak a little bit after the moon passes directly overhead.

The question posed at the end of the earlier post is this: if the tide comes from the Moon’s gravitational pull, why does it also bulge on the other side of the Earth? Surely that is moving against the Moon’s gravity?

Perhaps there is another way of seeing it.

Imagine you have five small, identical objects, A, B, C, D and E; marbles, for example. Imagine you arrange them in your hand in a plus-shaped formation so that B is in the centre with the other four surrounding it. Then, holding them stacked on top of each other like this, you let go.

Naturally the marbles all fall together. The distances between the marbles are the same while they are in freefall, and remain constant right until they hit the floor and scatter. Of course the ABCDE assembly moves faster and faster as it falls ­– it accelerates under gravity. But as long as A, B, C, D and E experience the same acceleration, it doesn’t matter how fast they travel: they will still fall together.

But what if, as they fell, they accelerated at different rates? It can happen. Recall our earlier discussion of gravitational wells: the closer you are to something, the more it attracts you, so in some circumstances, small differences of distance have significant physical effects. What if C fell faster than B, D and E – and B, D and E fell faster than A? What would that look like? Something like this:

If the objects accelerate at different rates based on how close they are to the source of gravity, then the distances between them will increase as they fall.

The next question is: how does this look from B’s point of view?

Well, for B, things look rather odd. B knows there is a source of gravity nearby, represented by the grey ball. And it can readily understand why C appears to be moving towards the gravity source. And yet it also looks as though A is moving away from the gravity source. And if the gravity source is moving around B, then B will always see one marble moving towards it, and one marble on the other side of B appearing to move away.

But B is wrong. Nothing is moving away from the gravity source. Everything is moving towards it – including B – at different rates.

And this applies to Earth and the Moon because, although we do not feel it, we are falling towards the Moon ­– constantly, just as the Moon is falling constantly towards us. But because we are both in motion, we keep missing each other – we fall around one another, in orbit. The tides track the moving target of the Moon, trailing a little behind it as far as an observer on Earth can tell.

Put in terms of bodies in motion through space, the tidal bulge on the opposite side of the Earth makes perfect, intuitive sense. As is so often the case, what lets us down is our unconscious assumption that we are the centre of the universe.

REFERENCES

http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit4/tides.html

Written by The S I

October 7, 2011 at 11:59 pm

The Slippery Slope

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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.

Written by The S I

October 2, 2011 at 11:59 pm