What would happen to a planet if its core suddenly disappeared?
I'm talking instantly and without warning, gone. I'm not concerned with how scientifically accurate this would be, because I'm absolutely sure it's impossible. I'm instead concerned with how the mantle, crust, and other parts/layers of the planet would react. Please provide some sort of scientific explanation with your claim, thanks.
The most likely result would be the instantaneous collapse of the planet, due both to gravitational forces and the force implosed by the vacuum left behind.
But, moments before that happened, everyone on the planet would vomit from the sudden drop in gravitational force. Heart attacks would occur, especially amongst the elderly.
The two people who are surviving these moments (probably because they're roller coaster buffs) would notice world-class aurora borealis as the magnetosphere experiences massive changes in its flux density.
But they wouldn't even have time to smile before the implosion happened.
What happens after is the generation of tremendous heat as a bazillion tons of mass begin to grind together, seeking equilibrium. There's no life left on the mass, but it might not completely devolve into debris (depending on its initial mass and the amount of mass left behind). However, any moons the planet once had have now spun off into space to become everything from asteroids to planetoids of their own to meteors impacting the sun.
The entire solar system would then shudder. It would take years... centuries... eons... for everything to balance itself out, but you can't significantly change planetary mass without affecting every other planet in the system. Most would simply fall into slightly modified orbits. But that really depends on the orbits and mass beforhand, which we know absolutely nothing about.
I"m going to go the opposite direction of @JBH, and say that not much is going to happen right away.
Sure, gravity will lessen instantly, but that's about it for instantaneous effects. Granted, there's a lot of things that rely on gravity to "do it's thing", but I doubt the planet would crumble in on itself.
https://en.wikipedia.org/wiki/Structure_of_the_Earth
That Wiki page shows that the inner and even outer core are relatively small parts of the inner Earth. The mantle is almost 1800 miles thick and solid rock. The page explains that at the pressure it's at, it can move, but only slowly. Even if layers of the inner mantle implode to release pressure, there's only a specific amount of room for that to happen, so the pressure should reach equilibrium over time. It may take millennia before any of that happens, or it could happen in minutes, potentially without the (average) surface dwellers even knowing about it.
There are plenty of large caves that show the Earth is self supporting.
https://www.huffingtonpost.com/2015/12/26/son-doong_n_3873341.html
Think about an archway. If it's constructed correctly, the whole arch sees pretty much the same force, as the keystone spreads the forces it sees down to the supported structure below. A sphere, even a hollow one, is very hard to compress in all directions at once. Even something as fluid as sand will stop moving and be stuck in a funnel, if there's too much compaction and not enough freedom of movement.
What will eventually and gradually happen is that the planet will move to a different orbit. The gravitational constant for the planet will have changed, due to the mass changing, so that changes the pull of the plant towards the star it's orbiting.
https://en.wikipedia.org/wiki/Orbital_mechanics#Laws_of_astrodynamics
I don't have the time or the math chops anymore, or I'd try to figure out how much difference that is. It would definitely change the temperature of the planet, but without doing the math, I don't know if it would stay in the circumstellar habitable zone for life to remain viable easily. I don't even know how long it would take if it didn't stay there, but I'd have to guess thousands or tens of thousands of years.
https://en.wikipedia.org/wiki/Circumstellar_habitable_zone
The planet would also slowly cool due to the molten core (of Earth) providing a considerable amount of heat to it's surface.
https://en.wikipedia.org/wiki/Internal_heating
You also have to take into account whether the atmosphere would remain, since it's held in by gravity.
https://en.wikipedia.org/wiki/Atmosphere#Atmospheric_escape
Any plane would probably crash. The down force counteracted by it's lift would dramatically change. They would have a tendency to have too much lift, so if the pilot wasn't skilled enough, the plane not aerobatic enough, or 1000 other problems could cause the plane to shoot up, stall, flip, or otherwise become unable to be controlled. Anything flying on autopilot would have to go to manual mode, with the autopilots having to be reprogrammed before being usable again. But that's a surface dweller problem, not a planetary concern.
If the Earth's core was removed (gradually or instantaneously), the primary effect would be loss of the global magnetic field.
The mean distance of the Earth from the Sun would change by less than 1 part in a million.
Although the first two are factual, I think the surface would not sink significantly, at least in the short term.
The Earth's global magnetic field is due to the rotation of the Earth and the (slightly out of phase) rotation of the liquid core. If the core was removed, or just vitrified, the global magnetic field would collapse. This results in two issues that would eventually destroy human civilization (at least as we know it now).
The first issue is, without a magnetic field, the Earth would have no defense against solar storms (and less protection from cosmic rays). We haven't experienced a major solar storm for over 150 years, although one just missed us in July 2012. The 2012 event was about the same magnitude as the solar storm of 1859. One study estimated that, if a storm of that strength hit Earth now, it would take between 4 and 10 years for power and other services to be fully restored. And that was if we had a magnetic field!
The second issue is the erosion of the atmosphere by the solar wind. We have an example of that with Mars. Since Mars is smaller than Earth, it has a smaller heat capacity and a greater surface to volume ratio, so its core cooled much sooner than Earth's will. According to data collected from the Mars Global Surveyor by the late Mario Acuna, Mars' core began to vitrify about 1 billion years after its formation. That explains why, long ago, Mars had a sufficiently dense atmosphere to support liquid water on the surface, and now has almost none (about 0.007% of Earth's atmosphere).
Looking at Wikipedia, or any physics text, you will see that in the equation for the mean orbital distance in a two-body problem, the sum of the masses is in the denominator. The mass of the Sun is about 333,000 times greater than that of Earth. Since the core is a small fraction of Earth's mass, the change in the sum of the two, and thus the change in Earth's mean distance from the Sun, would be less than 1 part in a million.
The Earth's construction is complex and the exact mechanical properties of many of its components are not well known, so I can only say I think nothing catastrophic would happen in the short term.
It's the loss of the magnetic field that's the big deal.
/// Note: the description of the effects of loss of the magnetic field described above is a simplification of a complex event. Although it's true that Earth's magnetic field protects us from being directly bombarded by Coronal Mass Ejections (CMEs), it's the presence of a magnetic field that causes the greatest threat to our digital world. When bombarded by CMEs, the huge movement of the magnetic fields as they collapse induces equally huge currents in anything that conducts electricity. The result is almost all electric devices are fried--permanently. ///
In the links below, I've favored Wikipedia, as it is free for everyone, which is often not the case for scientific papers.
The Solar Storm of 1859: https://en.wikipedia.org/wiki/Solar_storm_of_1859
The Solar Storm of 2012: https://en.wikipedia.org/wiki/Solar_storm_of_2012
Calculating the Mean Orbital Distance: https://en.wikipedia.org/wiki/Orbital_mechanics#Laws_of_astrodynamics
Mars Global Surveyor Magnetic Field Mission: https://mgs-mager.gsfc.nasa.gov/
How Earth's Magnetic Field is Generated: https://en.wikipedia.org/wiki/Earth%27s_magnetic_field#Earth%27s_core_and_the_geodynamo
Let's see how f**ed everything on the surface will be. Let's go with Earth. The inner core has a mass of 10^23 kg, and if we teleported that out into space, not only would it have enough mass to be its own planet, but that'll be utterly devastating. The gravitational binding energy of Earth is about 2.2510^32 J, and would go down to 2.1710^32 J. Assuming the worst-case scenario (or best-case, if you consider how long it takes for everyone and everything on the planet to die), where the inner core vanishes instantly, and as the inner core has an radius of 1221 km, the energy released by the planet collapsing in on itself would be 6.9210^31 J. That's more than a quarter of enough to destroy it completely.
The continents would crumble, the intense heat produced by friction will melt the planet, and the impact will release a shockwave that will crumble anything remaining and shed a good amount of the planet's atmosphere. Long story short, we all die. And if it disappeared over the course of a day, the magnetic field fading will kill us all, but this will be a slower and more painful death.
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