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# Would a huge amount of asteroids hitting Earth change its rotation speed or destroy the planet?

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Earth's rotation is slowing down, and in this article Randall Munroe gives some ideas to accelerate the rotation - or at least to keep it from slowing down as quickly.

He concludes that the only "solution" would be to hit Earth with asteroids - lots of them. He gives 2 options: one with big asteroids and another with smaller ones.

To get enough spin, we have to hit the Earth with on the order of a billion liters of rock per second (several times the volumetric discharge rate of the Amazon). This adds up to about one six-mile dinosaur-killing asteroid every couple days.

If asteroid B-612 in The Little Prince is four meters across and made of rock, we’d need an average of around fifty thousand of them to enter the atmosphere each second to keep up the pressure.

I didn't check the math - although I really trust Munroe on these things - but my question is: would this ridiculous amount of asteroids continuously hitting the planet end up destroying it before accelerating its rotation? And when I say "destroy", I'm not talking only about life forms ceasing to exist, but the planet itself exploding into pieces.

Or would Earth just "lose some pieces" but continue to rotate as nothing - or almost nothing - happened?

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## 1 answer

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The Earth would be broken into pieces if the total energy delivered by the impacts was comparable to the gravitational binding energy of the planet. Earth is a sphere, so its binding energy is $$U=\frac{3GM_{\oplus}^2}{5R_{\oplus}}=2.24\times10^{32}\text{ Joules}$$ Randall says that to properly slow down the planet's rotation, we'd need to bombard it with a dinosaur-killing-sized asteroid "every couple days" for ten years. Schulte et al. 2013 place the energy of such an event at around $4\times10^{23}\text{ Joules}$; the asteroids would then deliver a total energy of $$4\times10^{23}\text{ Joules}\times\frac{10\text{ years}}{2\text{ days}}=7.3\times10^{26}\text{ Joules}$$ which is about 300,000 times too low.

It's quite possible that the asteroids would ablate away much of the surface, and I imagine that the majority of species wouldn't make it through the first couple of months, but the planet itself would survive.

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