Earth's spin is slowing down: will it stop?

Earth's rotation slowing 1 second per 1.5 yrs. So it will stop rotating after 129,066 yrs? surely not? Why not? - Question posted on Twitter by @annerooney

What's happening?
The Moon is moving away from the Earth. You can read more about that in this post, but the quick explanation is that the Earth's rotation supplies energy to the Moon, which speeds it up in its orbit. This means that the Moon's orbit around the Earth gets wider- it moves further away from us.

You could think about it like this: A couple of your mates are on a playground roundabout, and you're running around the outside of it. It's spinning fast, and you can't run fast enough to keep up, so you reach out and grab one of the handles. What happens? It drags you a little bit faster, and you feel like you're going to swing out away from the roundabout as well.

Now look at it from another point of view: imagine you're one of the people on the roundabout, and someone else grabs it from the outside. Yes, they speed up, but at the same time you can feel the roundabout's spin being slowed down.

This is similar to what's happening with the Earth's rotation: when the Earth hands over some energy to the Moon, it slows down a little bit, and our days get a little bit longer.

Why is it happening?
Various factors play a part in making this happen, but one of them is the fact that the Moon orbits the Earth slower than the Earth itself rotates. Speaking simply, the Moon has a gravitational effect on the Earth's oceans, and this introduces a friction force that works against the Earth's rotation, slowing it down.

When will it end?
Eventually, the Earth's rotation and the Moon's orbital speed will exactly match each other. When this happens, the Earth will no longer be supplying extra energy to the Moon, and the Moon won't be taking it from the Earth- the two bodies will be 'tidally locked'*.

Again, think about the roundabout analogy: if you're running around the outside at exactly the same speed as the roundabout with your mates on it is rotating, even if you grab one of the handles, you won't feel yourself either being pulled faster or slowed down.

When will this happen? Current estimates put a figure of about fifty billion years on it, but it doesn't really matter as the Sun will have either consumed the Earth or burnt it to a frazzle in about a tenth of that time.

A final thought
It might be interesting to think about why the figure of fifty billion years given above is so different from @annerooney's figure of 129,066 years.

I assume this value has been reached by thinking about how long it would take the Earth to stop rotating completely: if we know that the Earth's day is slowing by 1 second every 1.5 years, all we'd have to do us work out how many seconds there are in a day and then multiply by 1.5 to find out how many years it would take to get rid of all of them.

So why doesn't this method give an accurate answer to the question?

The simple answer is that it assumes that the slowing of the Earth's spin is happening at a constant rate. In reality, the value of 1 second per 1.5 years is just an estimate of what's happening now. In the past, the rate was faster because the difference between the speed of Earth's rotation and the Moon's orbit was more extreme (roundabout analogy: you're dawdling round the outside while the roundabout is spinning really fast - you're likely to lose an arm). In the future the rate will be slower because the rotation/ orbit speeds are closer to one another (roundabout analogy: you're legging it while the roundabout is moving more sedately, albeit still faster - you'll experience only a gentle tug).

Some interesting posts about the Moon:




* The Moon is already tidally locked to the Earth to an extent- the Moon's rotation period is the same as its orbital period, so the same face points towards us all the time.


Comments

  1. Fantastic - thank you!
    I'm writing a wacky maths book and this came up in the part about calculating when to add leap seconds to the end of June or December. It all makes sense... I'll explain that it will get into synch with the moon's rotation but that we can't do a straight linear calculation to work out when.

    You're a star!
    (@annerooney)

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  2. Thanks for asking the question in the first place, and thanks for commenting! I'd love to see the book when it's finished; please come back here and let us know about it when it's released!

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  3. Will do! It's called '50 things your your kids need to know about maths' and it should be out August 2011, published by Quercus

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  4. I'll keep an eye open for it! Glad to have had some small input into what sounds like a very worthwhile and necessary publication!

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  5. I guess by now the book should already be published, but I wanted to point out that there is an issue with this explanation. The figure that the earth is slowing at 1 second per 1.5 years is not accurate.

    The time it takes for the earth to go around the Earth is not exactly 365 days (the time for earth to make 365 rotations). For that reason we have leap years where we add an extra day. So that everything matches up. About every 1.5 years we need to add a leap second to be more precise than the extra days during leap years.

    The rate at which the earth is slowing is actually ~ 1.7 ms per century, much slower, which would result in over 5 trillion years using @annerooneys simplistic calculation. The time would be even longer taking into account the fact the decay rate is slowing with time.

    Hope there wasn't any big issues in what was said in the book.

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