How much force needed to blow open a planet?

I recently asked this question about what would happen if a fusion bomb went off in the core of a planet, and the answer was relatively uninteresting. As was aptly said in my previous answer, the effect of a nuclear bomb in the core would be very small.

So I have a new question (suggested by Tim B.), which is hopefully a little more interesting. How much force would be required in the inner core to blow open a planet? And by blow "open" I mean create a deep chasm down to the magma, but not necessarily blowing the planet apart. In other words, how can I fracture a planet with energy coming from the core? I am aware that such a chasm would probably become a volcano.

And one of my usual bonus questions: Could this happen without blowing the planet apart?

• It is extremely difficult to blow apart a planet, a chasm would immediately fill with magma effectively to the brim due to the extreme pressure. The earth is a 5,973,600,000,000,000,000,000 tonne ball of iron with some crusty impurities on top. very little will hurt it in the way you describe. – John Meacham Oct 23 '14 at 8:10
• A useful and humorous site on the various methods to destroy the earth. qntm.org/destroy – John Meacham Oct 23 '14 at 8:15
• Another What-If XKCD candidate if I ever saw one. – user4239 Oct 23 '14 at 19:22
• About 8 turbolasers' worth. – Mason Wheeler Jul 11 '16 at 17:49
• @user4239 what-if.xkcd.com/15 What if you exploded a nuclear bomb (say, the Tsar Bomba) at the bottom of the Marianas Trench? Answer: "Surprisingly little—especially compared to what would happen if you put it just under the surface." – RonJohn Sep 21 '18 at 11:49

I'm a physicist (kind of :D) and I love this question. I'll try to estimate the amount of force necessary.

Firstly, I'm assuming that the earth is split in two hemispheres and we are trying to separate those. I'm only considering gravitational force, otherwise the problem would be too complicated. By integration I found that the center of mass of each hemisphere is $\frac{3R}{8}$ away from the center, so the distance between the two centers of mass is $\frac{6R}{8}$.

Most equals ($=$) mean approximately equal to ($\approx$), but because the method to calculate this force is already a huge approximation, it won't really matter.

\begin{align} G &= 6.67\times 10^{-11}~\text{m}^3\cdot\text{kg}^{-1}\cdot\text{s}^{-2} \\ M &= 5.97\times 10^{24}~\text{kg} \\ m &= \frac{M}{2} = 2.99\times 10^{24}~\text{kg} \\ R &= 6.37\times 10^{6}~\text{m} \\ \frac{6R}{8} &= 4.78\times 10^{6}~\text{m} \end{align}

Newton's Law of Gravitation:

$$F = \frac{G m^2}{r^2} = 2.61\times 10^{25}~\text{N}$$

which is: 2.610.000.000.000.000.000.000.000 Newtons which is 2 septilions and 610 sextillion or something hahaha

That's the force each of those hemispheres exerts on the other, so to separate them, you would need a force larger than this value.

NEW: I'll add to these calculations the amount of energy necessary to separate these two hemispheres in a way that they wouldn't pull each other and be together again.

$U = \frac{G m^2}{r} = 1.25\times 10^{32}~\text{joule}$ which is HUGE.

Just for you to have an idea, the sun releases $3.85\times 10^{26}~\text{J}$ per second of energy in the form of light. You would need all the energy that the sun releases over a period of $3.76~\text{days}$ (assuming you weren't losing any, which is almost impossible).

Really cool :D

New 2: According to Wikipedia, the Earth receives $174~\text{petawatts}$ at the upper atmosphere, which is $1.74\times 10^{17}~\text{W}$.

To gather enough energy to blow the planet apart, one would need to save all the energy that hits the Earth for $7.18\times 10^{14}~\text{s}$, which is $23\,100\,000$ years. Don't forget that people need energy to live and that it's almost impossible to manage to gather all of it.

So... maybe someday :D

• Hey, great answer, I just don't see the final value in Joules. Is it 1.25 * 10^32? And you might want to look up the MathJax notation, it might make things clearer. – DonyorM Oct 23 '14 at 13:32
• Thanks! Yes it is. Oh, is that so? I'll check it out! – SlySherZ Oct 23 '14 at 14:05
• This is the energy to split the world completely apart, a level far above what he's after. He just wants to crack it open a bit--cataclysmic, not world destroying. – Loren Pechtel Oct 23 '14 at 22:46
• I like the more destructive force :D Now being serious, how is it possible to calculate that if even he doesn't know clearly what he wants – SlySherZ Oct 23 '14 at 23:14
• Capturing all the energy from the sun and concentrate it on a small distant planet is hard. How many years worth of energy you need if you can use only energy of the sun captured on a planet, or planet-size spaceship? – Peter M. Oct 25 '14 at 0:05

Please clarify your question. You're asking about force "in the core", but then also talk about making "chasms in magma... to the core"; as in, from the outside-in?

To answer the "could this be done without blowing the planet apart", I think that plainly, yes it could, given that an asteroidal impact could remove a significant amount of material from a planet and yet leave the majority of the body whole (if in a state of severe disarray); our own moon, in fact, is believed to have formed this way.

Regarding the 'core' scenario, the core of a planet is subject to ludicrously high pressure due to the gravitational attraction of its constituent matter. To significantly shift any amount of material near or at the core of a planet would require a force at least equal to that pressure x the area over which it would be applied.

A very grand simplification would be to express that area as a proportion of the area of a virtual sphere, the radius of which is the distance out from the true center of the planet where the force is acting. You could then apply the same proportion to the planet's mass to arrive at a rough idea of the order of magnitude of the force you would need to overcome gravitational pressure alone to push that material outward away from the core at a constant rate of speed.

Of course, that doesn't begin to address the structural constraints of the problem, displacing solids within solids, or the sticky issue of how to apply that force at that point in the first place.

• Hey, thanks for the answer. I guessed that the chasms might not extend all the way to the core, even if the source of the explosive was at the core, because the core is higher pressure so would resist change. Basically the question is, how could a fracture a planet with an explosion coming from the core? – DonyorM Oct 23 '14 at 7:48
• I was going to suggest an impact event. The Earth's crust is a thin shell floating on liquid magma with a hard metal core. If you want to crack the skin, the easiest way would be to hit the hard, brittle skin, not the iron ball in the middle or the goopy syrup above it. – superluminary Oct 23 '14 at 14:44
• I do think an impact scenario would be the primary 'natural' method to achieve what is described; however with above clarification the asker is clearly talking about a force at the core. In which case you're want to do some version of the approximation I mention above; or use some other better model of rupturing a solid of known density from the inside. – NathanDetr0it Oct 24 '14 at 21:21

protected by L.Dutch♦Sep 21 '18 at 12:07

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