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why are our days getting longer?

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I’ve just finished reading a book by the Welsh biologist and science communicator Steve Jones entitled Coral; a pessimist in paradise, which covers a helluva lot of ground and makes me feel inadequate as most science writers do, but one of the many things he has taught me about – something I didn’t know that I didn’t know – is that the days are getting longer, in an inexorable process of rotational slowing. This fact, and the reasons behind it, were further confirmed for me today in an episode of an elegant little podcast out of the University of Houston, called The engines of our ingenuity. I just happened to be browsing through the science and scepticism podcasts on my TV, and I sampled a few curiously titled ones…

Let me backtrack a bit. I’m very very poor (from an affluent western perspective of course) but I received a HD TV from my neighbour recently as part of a complicated deal, and now I can watch free-to-air channels I didn’t have access to before, and what’s more I’ve managed to buy a device which I’m sure many people out there know all about, called an Apple TV, which is so cheap that even I can afford it without too much suffering (what’s a few days without food? it’ll probably extend my lifespan). So now I can explore an almost endless variety of podcasts, vodcasts and classic film noir movies on youtube. That reminds me, one of the podcasts I’ve listened to, the Brain Science Podcast, was all about brain fitness – at least the episode I tuned into was – and inter alia the interviewee informed us that just about the worst thing for the brain was sitting around all day watching TV – Apple or no Apple, presumably…

Anyway I listened to this informative and also charmingly poetic three-minute episode of The engines of our ingenuity, entitled ‘How far the moon?’, narrated and presumably written by Dr John Lienhard. So I’ll share the info, if not the poetry, here.

Our earth spins at a pretty well constant rate because of the forces that set it in motion in the first place and because of Newton’s first law of motion which, put simply, states that an object will stay in the same state (resting or in motion) unless an external force acts on it. A ball spinning in the air will slow down because of air friction, but the earth is spinning in a vacuum, essentially – there’s nothing to slow it down.

Well, not quite. The earth is slowing down, and all in accordance with Newtonian physics. And it’s all due to the moon. Each day is about a twelfth of a second longer than it was when the Egyptians built the pyramids. Doesn’t sound that much, but 4000 years is a mere blip in geological and cosmological time. The moon drags at the earth gravitationally, creating high tides and low tides at a regular rate, and slowing our rate of rotation. But our earth has a much greater influence on the moon than vice versa, the moon having only an eightieth of earth’s mass. This gravitational effect slowed down the moon’s spin until it was in synch with the earth, and locked into the earth’s movement like a dancer being swung around by its partner. And so the moon faces us always. The slowing down of the earth due to the moon’s influence had the effect of loosening the embrace – the moon is slowly moving away from us. Just as a spinning dancer or skater extends her arms out to slow down or pulls her limbs in to speed up.  The moon moves away from us so that our combined rotational inertia remains constant. The distance between earth and moon, and the speed at which the moon moves away from us, is being measured thanks to an instrument, placed on the moon by Apollo astronauts, which reflects laser beams from earth. Through measuring the time taken for the beam to return, we know that the moon is moving away from us at a little under 4 cms a year. Back in the dim distant past, days lasted only 12 hours, and the moon was half of today’s distance from us. This has affected the shape of the earth, which is gradually becoming more spherical. The earth’s diameter is at its greatest at the equator and at its smallest at the poles, because of centrifugal forces operating against the force of gravity…

Okay, let me get clearer on this, with the help of this source, among others. Isaac Newton accepted the mathematics and the accuracy of Kepler’s laws of planetary motion, but the great unanswered question was why planets – and moons – traced out these orbits. Newton’s own first law stated that an object will continue in its trajectory (that is, in a straight line) or in its resting state, unless some external force acted upon it to speed it up or slow it down. This state is called a state of inertia. Clearly planets and moons were being acted upon by some force, which could only be exerted by the object being orbited. This force might be called a centripetal force, though that doesn’t explain it in this case. If you swing a stone around on the end of a string, you apply a force to the stone to keep it going, but the string, and your hand holding the string, exerts a force on the string to keep it ‘in orbit’. Its motion will be circular, providing you keep your hand still, because the length of the string is constant. But there’s nothing obvious attaching the moon to the earth. Newton pondered this for some time, until one day the apple dropped.

I’m thinking that, if the moon is moving away from us, its orbit can’t be entirely circular, it must be spiralling outwards, ever so slightly. In any case, the moon pulls the earth out of shape, and that is due to a centrifugal force that balances the centripetal force exerted by the earth on the moon. The moon is moving away due to a reduction in both these forces, and a slowing of the earth’s rotation, and hence of the moon’s orbit.

But sadly, it gets more complicated than that! This is the Newtonian explanation of how these forces operate, but it doesn’t really answer the why question. I’m not going to go deeply into that here – as if I could – but I’ll end with a quote from an astronomer’s explanation, not so much about the earth’s slowing, but about the moon’s behaviour, in terms of Newtonian and then Einsteinian physics:

First case: – Why does the Moon orbit the Earth? It just does. And you can understand how it does by analyzing the forces on the Moon caused by its orbit and finding the forces pushing in and out are equal.

Second case: – Why does the Moon orbit the Earth? Because the Earth distorts spacetime in the vicinity of the Moon, and causes it to orbit the Earth the way it does and the balance of forces to come out the way it does.

So why do massive objects distort space-time? Apparently they just do?


Written by stewart henderson

September 28, 2013 at 8:25 am

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