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I just wanna ask which option requires more destructive energy?

Option 1 : destroying a planet like earth to rubble (tiny pieces of rocks)

Or

Option 2: splitting a planet like earth in halves (2 pieces) Permanently that the gravitional binding energy of the planet won't merge the 2 pieces back together

Edit 1:for option 1 I meant rubbles the size of boulders and by destroying I mean by an explosion of destructive energy. To the point not even GBE will form the rocks back together

For option 2 I meant one clean slice in halve that overcomes GBE

P.S: I honestly can't be more descriptive than this edit and try not to overthink it. I just watch anime shit that do crazy feats and wanna know the how much difference in destructive energy is required for both options

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  • $\begingroup$ Hello, Hajhar, one point you will need to clarify to help answering your question. Option one reduced an earthlike planet to rubble. If the rubble distributed through space it have to overcome its gravitational binding energy (GBE). If the rubble stays where the planet was, then it won't have overcome its GBE. Kindly edit your question to make this clear. Thanks. $\endgroup$ – a4android Nov 1 '18 at 5:02
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    $\begingroup$ how distributed does the rubble have to be, can it coalesce back into a planet? Because moving two small planets into completely different orbits will require a lot of energy. Also keep in mind two half planets coming together from even a few inches will supply enough energy to turn the planet back into a molten ball of lava . $\endgroup$ – John Nov 1 '18 at 5:10
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    $\begingroup$ Only a very small part of Earth is solid enough to be reducible to rubble. The two options are basically equivalent. $\endgroup$ – AlexP Nov 1 '18 at 9:07
  • $\begingroup$ cutting a planet neatly in half is vastly less entropically favored than blowing the planet to bits: dG=dH−TdS−SdT $\endgroup$ – theRiley Nov 1 '18 at 11:26
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    $\begingroup$ For the "unclear" close vote, this seems pretty clear. $\endgroup$ – AndyD273 Nov 1 '18 at 12:41
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Clearly option #1:

Lets make the planet into rubble iteratively--keep chopping until it's small enough. What's the first chop? Your option #2. Thus #1 includes #2 but does more and thus requires more energy.

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    $\begingroup$ Gravitational field is conservative. Moving 10 kg against it as a whole takes the same exact energy of moving them in 10 chops, 1 kg each. $\endgroup$ – L.Dutch Nov 1 '18 at 9:20
  • $\begingroup$ @L.Dutch Yup. But moving those 1kg chops apart from each other also takes energy. $\endgroup$ – Loren Pechtel Nov 1 '18 at 11:06
  • $\begingroup$ @LorenPechtel, indeed, which is exactly what L.Dutch just said, moving an object 10 metres at a time 10 times, takes the same energy as moving it 100 metres $\endgroup$ – Blade Wraith Nov 1 '18 at 11:20
  • $\begingroup$ @ L.Dutch I'm with Loren on this one. The property you mention doesn't have anything to do with the conservative nature of the gravitational field-- all that says is that the energy required to move the individual rocks does not depend on the path they take through space. Instead, the property you mention depends on the gravitational field being constant, which it isn't if you start removing large amounts of mass from the Earth. But most importantly, it ignores the fact that when you chop the planet in half, you get to stop after moving only half of the mass, instead of all of it. $\endgroup$ – el duderino Nov 1 '18 at 12:25
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Answer... its complicated.

How big consititues as tiny pieces of rock, in a galatic sense the earth already is a tiny piece of rock, but obviously thats not what you meant. But would boulders the size of buses be enough, that's definitely tiny compared to the earth, but not compared to gravel which is indeed tiny pieces of rock... so then so is sand in a sense. the smaller you make the pieces of rock the more work it takes to do so...

So option 1 is open to interpretation... but consider its a lot easier to break apart some rocks into smaller rocks then it is to split atoms, rocks are just simple molecules of atoms arranged in a specific way.

Why is this important you ask? simple, you want to split the planet in half, now if i were to assume you meant perfectly in half which for comedic purposes i will believe you did then that perfect cut will need to be so fine that it cuts atoms apart, which takes a huge amount more energy. and i mean huge, somewhere in the region of many many 0s ber atom, and there is not just a couple of atoms between one side of the planet and the other

Then of course consider that most of the earth isn't rock... its lava and other slightly warm things, so you would only need to break about the top 20km off before what you were dealing with wasn't rock anymore, so you couldn't break it into tiny pieces of something tis not, maybe globules of lava. doesn't have the same ring to it though really.

of course that is again probably not what you meant. but consider... The only way to split the planet in two and not have them recombine due to gravitational binding energy. is to do one of two things

  1. Split them in half and move one half into a completely different orbit where they will be unlikely to ever be drawn to each other again.
  2. Split them in half and spin both halves so they orbit a central point between them while orbiting the sun.

The fact that you didn't specify that the "tiny pieces of rocks" aren't allowed to eventually bind back together means that one the planet is destroyed the debris field would form similar to the asteroid belt, that may one day bind back together to make another planet. so the tiny rocks don't need to be moved all that much.

And moving all of the rock is going to be at least the same as breaking it apart. so probably option 2 would require more energy.

Apology

i just want to apologise in advance if any of this sounded sarcastic... it wasn't meant to be, I've had one of those weeks when i went and re-read all of XKCD again... i may be thinking in his writing style right now

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So a bit of study has already gone into answering this question.
To blow up a planet into tiny rubble Death star style, it would take 2,000,000,000,000,000,000,000,000,000 joules of energy.
The entire energy output from our sun is only 380,000,000,000,000,000,000,000,000 joules, so you would need the total energy output of the sun for a week to get that much energy, just to give you a bit of perspective.

Now, you could actually get that much energy "fairly easily" if it was a positron laser, AKA an antimatter laser, because of the total mass/energy conversion that happens when matter is annihilated.

Option 2 would take a lot more energy than that, since breaking it into 2 equal parts, especially with so many liquids involved (water, molten rock, etc), and then giving those two parts enough thrust to move away from each other, is actually a lot more than just shattering them. And if you don't get the two halves far enough apart they'll just bump into each other until all that is left is a lot of smaller rocks anyway.

According to this great answer, the energy needed for that is 125,000,000,000,000,000,000,000,000,000,000 joules, which is a lot more.

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If by "reducing to rubble" you mean that every piece gets separated, then this entails much more energy than splitting into two large, gravitationally unbound pieces each of which is still gravitationally bound to itself.

In addition, you need a lot extra energy to perform the shattering, which needs to overcome chemical and mechanical bonds. This is basically the same as Loren Pechtel's observation.

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