The Standing Invitation

Archive for October 7th, 2011

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.



Written by The S I

October 7, 2011 at 11:59 pm