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My question involves the earth being blown up using theoretical dark energy. In this scenario, the crust and mantle are destroyed by precisely placed weapons so that all that remains is the core.
Would the core freeze to become a dwarf planet comprised of solid iron after it's completely exposed? Or would the sudden lack or pressure cause the matter to become gaseous? I also need to know about the moon. Would it continue to orbit the dwarf planet (if that is what remained) or would it begin its own orbit of the sun?

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    $\begingroup$ "If the world were blown to pieces", the the core would also be blown to pieces, since the core is part of the world. $\endgroup$ – RonJohn Mar 29 '18 at 16:26
  • $\begingroup$ Welcome to WorldBuilding.SE! As RonJohn pointed out, the title of your question doesn't quite match the question itself: you ask "what would remain" and then tell us that only the core would remain. It's an interesting question, though. Please take the tour and visit the help center to learn more about the site, and I hope you enjoy your stay! $\endgroup$ – F1Krazy Mar 29 '18 at 16:29
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    $\begingroup$ As the accountant said to business owner, "What do you want to happen?" $\endgroup$ – nzaman Mar 29 '18 at 16:29
  • $\begingroup$ Please edit to add how this related to worldbuilding or the question will likely be put on hold. $\endgroup$ – Unassuming Guy Mar 29 '18 at 16:42
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    $\begingroup$ If the world were blown to pieces, what would remain? "Just pieces" seems like the obvious answer. $\endgroup$ – Renan Mar 29 '18 at 16:52
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The answer depends strongly on the nature of the process which removed the rest of the planet. As it turns out, events which are capable of blowing a planet to tiny bits (in thine mercy) are pretty darn violent. They will have some effect on the core, and that effect may dramatically change the result. But for some simple cases, we'll find that you do indeed get a dwarf planet.

Let's, for a moment, assume that the outer parts of the Earth simply vanish, leaving the core. This consists of an outer core, which is liquid, and an inner core which is solid. Let's let those start to decompress. The information that the rest of the Earth vanished will propagate at the speed of sound. Now the core is quite hot, ranging from 4,000K to 10,000K, depending on where you are. This is quite a bit higher than the boiling point of iron at atmospheric pressure (much less at vacuum), which is around 3200K. Thus we should expect large amounts of the iron in the core to flash boil. This will rapidly impart a net outward velocity to all particles involved. To get a sense of just how violent this could be, I've replaced our planet with an Earth-substitute (a beaker of superheated water), and the cause of boiling replaced with the addition of sugar (which nucleates the boiling event), and made this video. (okay, maybe I lied. Professionals made that video).

Note: the core will need something to nucleate around as well. However, this is a statistical process. It's very difficult to have a lack of nucleation sites when your beaker is the size of the Earth's core

The result, in the low gravity of the remaining core, will be that the boiled iron/nickel material quickly flies outwards and starts to behave like a rarified gas (very few collisions because the particles are far apart). Now we need to talk escape velocity. Escape velocity is calculated by $V_e=\sqrt{\frac{2GM}{r}}$, where $G$ is the universal gravitational constant ($G=6.67\cdot10^{−11} \frac{m^3}{kg\cdot s^2}$), $M$ is the mass of the gravitational source, and $r$ is the radius from the center of that object that we're calculating at. The mass of the core is roughly 30% of the mass of Earth ($M=1.79\cdot10^{24}$), and its radius is roughly 3,400km ($r=3.4\cdot 10^6$). Put these together and you get $V_e=\sqrt{7.0\cdot10^{7}\frac{m^2}{s^2}}$ or $V_e=8.4\frac{km}{s}$ , which is a good portion of the escape velocity of the whole Earth before the explosion ($V_e=11.186\frac{km}{s}$).

So how fast can the nickel and iron fly? Well that's a more difficult question. It's a question of how the energy is distributed. The specific heat of iron is $450\frac{J}{kg\cdot^\circ K}$. Our iron can drop on average of roughly 4000K before solidifying, so we have about 1.8MJ/kg to work with. Now it takes a lot of energy to reach escape velocity here, 35MJ/kg, to be specific. That means even in the most extreme of circumstances we could only fling 5% of our total mass out into space, and realistically it wont be that high. This means we can assume that most of the mass does not achieve escape velocity.

So, assuming your event simply makes the crust and mantle disappear, you would have a violent flash boil, sending gas and material off into space, but then gravity would take hold once again, and all of the material would coalesce roughly back together. During this time, it is emitting radiation, cooling off into the emptiness of space. Eventually it will cool enough to not boil, and reach a liquid or solid phase. That liquid will then not have enough heating to retain its temperature without the huge insulative coat of the mantel, so it will solidify. The vast majority of the core material will remain.

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The energy needed to blow up a planet is similar to the energy needed to vaporize it. Suppose you release some energy in the center of the earth, say with an antimatter bomb. A large amount of rock is vaporized, much of it turned to plasma. The pressure produces huge splits along the earths crust, which blast out superhot rock. The earth is split into fragments that reach kilometers in height. But nothing is moving at escape velocity. The crust and mantle fragments crash back into each other. The atmosphere is replaced with a thick layer of vaporized rock. Which cools and rains down on the surface.

Suppose you released even more energy. Most of the planet is vaporized, but some fragments of the surface ride the shockwave away from the planet. Much of the planet is launched at escape velocity, mostly in the form of vapor. Some stays in orbit and some remains in a ball. The remaining mass cools into a small, metal rich planet with a ring system.

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would the sudden lack or pressure cause the matter to become gaseous?

No. It (most, at least) will turn into a gas because the core's temperature is about 10,800F, and the boiling point of iron in 5,200F. Thus, yes it'll boil off from intrinsic heat.

Once it cools off to below 5200F, then it'll still boil off since "5200F" is the boiling point at Standard Pressure.

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Ron John's answer covers what happens to the core.

As to what happens to the Moon, it depends. If the Earth is blown to pieces, but the pieces still remain bound by gravity, the Moon would still be there. It might be hit by debris, which could change its momentum and thus alter its orbit, but it would still be there.

If the non-core pieces are removed from the Earth-Moon system, though... According to this source, the core makes up for only ~32% of the mass of the Earth. Which would mean the pull between the remains of the Earth and the Moon would not be as strong. They would each orbit the sun directly, though with very close orbits. They would have encounters in intervals ranging from years to millenia depending on how they disconnect, and depending on how the encounters go, they might each be pushed to other orbits, or they might impact upon each other and form a new planet.

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