Destroy a Planet: How to Annihilate a Planet

[NavyMan]

I was thinking about this while reading the thread about destroying a star, I thought well what would you have to do to simply annihilate a planet? Note I am not simply talking about making it devoid of life but actually destroying it utterly.

 

[DaveC426913]

- Hit it with another planet. Really hard.
- Drop it into an orbit within the Roche limit of the Sun.
- Raise it into an orbit within the Roche limit of Jupiter.

 

[Janus]

- Hit it with another planet. Really hard.
- Drop it into an orbit within the Roche limit of the Sun.
- Raise it into an orbit within the Roche limit of Jupiter.

The problem with 2 and 3 is that the Roche limit for the Sun and Jupiter as far as the Earth is concerned is very likely below the surface of these bodies. (This is because the Roche limit depends on the relative densities of the bodies involved, and the Earth is much more dense than either Jupter or the Sun.

Another problem with dropping it into a lower orbit around the Sun or lifting it out to Juptier is that, even if we assume a fluid body Roche limit (rather than a rigid body one), the amount of energy needed to drop the Earth close enough to the Sun is about 10 times greater than than the gravitational binding energy of the Earth and the amount of energy needed to lift it out to Jupiter is just about equal to the binding energy.

If you have that much energy to start with, why not just apply it directly to destroying the Earth?

 

[Janus]

The problem with #1 is that you have to find a planet that you can move into a collision course with the Earth for less energy than the binding energy of the Earth and which would still have greater than the binding energy in KE upon impact.

 

[DaveC426913]

You know, it never occurred to me, but I appear to have just assumed Earth was the target.

 

[NavyMan]

You know, it never occurred to me, but I appear to have just assumed Earth was the target.

Yeah... I was wondering about that.
What about punching a giant hole in the planet's crust? What kind of effect would it have?

 

[DaveC426913]

Yeah... I was wondering about that.
What about punching a giant hole in the planet's crust? What kind of effect would it have?

You'd have a giant crater. But you'd still have a planet.

 

[LURCH]

A couple tons of antimatter in the core might do it. But you'd need a big enough blast to blow al the pieces away from each other at sufficient volocity so that their mutuall gravitational attraction doesn't draw then back together (would that require a volocity greater than escape volocity at the core?).

It might take a smaller blast to simply plant your charge on the planet's leading edge, and deform its orbit enough to brush the corona of the host star. From their, atmosheric drag from the corona should decay the orbit until the palnet falls completely into the star.

 

[pervect]

To disassemble a planet, you'd have to supply enough energy to it to equal the gravitational binding energy of the planet.

Wikipedia has a formua for this for a spherical planet of uniform density:

http://en.wikipedia.org/wiki/Gravitational_binding_energy

E = (3/5)GM^2 / r

If you really want to integrate this formula out for yourself, you can integrate the binding energy of each spherical shell yourself, the binding energy of each spherical shell being G M_encl *dm / r, M_encl being the mass enclosed by the shell, dm being the mass of the shell, dm= 4 pi r^2 rho dr.

Anyway, using the above formula, we calculate the binding energy of the Earth as being 2*10^32 joules (the Wikipedia also gives this figure).

Dividing by c^2, we see that we have to convert 2.5*10^15 kg of matter into energy, i.e. we would need slightly over 10^15 kg of anti-matter and 10^15 kg of matter to supply an amount of energy equal to the Earth's binding energy.

There is also an interesting link that Google comes up with that comes to much the same conclusion and goes through some of the calculus.

http://www.stardestroyer.net/Empire/Tech/Beam/DeathStar.html

 

[DaveC426913]

...you'd need a big enough blast to blow al the pieces away from each other at sufficient volocity so that their mutuall gravitational attraction doesn't draw then back together...

I believe this to be unnecessary. The separate pieces eventually falling back to collect as a rock pile doesn't really consistute a 'planet' anymore - certainly not the one we started with - unless you are feeling exceptionally generous in your definitions.

I do not know whether pervect's analysis involves disassembling the planet into largish chunks or all the way down to vapour. If the latter, then I apply the same logic.

I think we can assume largish chunks is sufficient for the NavyMan's purpose, unless further qualified.

 

[scott1]

What about punching a giant hole in the planet's crust? What kind of effect would it have?

If you could put a lot of Nuclear bombs in it that could work.We do have that many Nuclear bombs we built enogh during the cold war to destory the world more then once.

 

[DaveC426913]

If you could put a lot of Nuclear bombs in it that could work.We do have that many Nuclear bombs we built enogh during the cold war to destory the world more then once.

All the man-made weapons in the world will not be enough to actually destroy the planet, though it will be enough to sterilize it of life and chew up its surface. However, the OP explicitly said 'destroy'.

 

[NavyMan]

Yes there are plenty of ways to exterminate the living things on a planet, but I was referring to the possibility of a Death Star-esque "SuperLaser" or something similar.
To Pervect:
Wow i had no idea wikipedia had that, simply amazing links.

 

[pervect]

I believe this to be unnecessary. The separate pieces eventually falling back to collect as a rock pile doesn't really consistute a 'planet' anymore - certainly not the one we started with - unless you are feeling exceptionally generous in your definitions.
I do not know whether pervect's analysis involves disassembling the planet into largish chunks or all the way down to vapour. If the latter, then I apply the same logic.
I think we can assume largish chunks is sufficient for the NavyMan's purpose, unless further qualified.

Let's take a look at the original question:

I was thinking about this while reading the thread about destroying a star, I thought well what would you have to do to simply annihilate a planet? Note I am not simply talking about making it devoid of life but actually destroying it utterly.

My interpreation of this is that he wants the planet _gone_, not just re-arranged.

In that case, the minimum energy needed is the gravitational binding energy of the planet.

Note that if you put in half the binding energy, the Earth would expand to roughly twice its radius, then re-form. I would not count this as destroyed personally.

If you also want to vaporize the planet as well as dissasemble it, you'd need to include more energy than the above calculation.

To give a very rough comparison for the magnitude of the energies of vaporization and gravitational binding, it takes about 40 kJ to vaporize 18 gm (1 mole) of water, while it takes about a million joules to boost 18 gm to escape velocity. Thus the gravitational binding energy is significantly greater than the energy it would take to just vaporize the Earth.

I'm not sure what the heat of vaporization of rock is (which would be a better model than that of water), but it seems pretty clear that the gravitational binding energy will be greater.

It's possible that the O.P. might be happy with vaporizing the Earth, and then having it cool off and re-form from the resulting gas cloud. (The gas cloud would still be gravitationally bound.) I don't have a really good number for the amount of energy it would take to vaporize the Earth - if we use the figures from water as a very rough estimate, we can see that it might be 2-3 orders of magnitude lower than the figure I quoted to disassemble the planet. This will still require much more energy than a few tons of anti-matter, though.

 

[pervect]

If you could put a lot of Nuclear bombs in it that could work.We do have that many Nuclear bombs we built enogh during the cold war to destory the world more then once.

If we very carefully spaced all our nuclear weapons in in an optimal arrangement, we might have enough to sterilize the land surface of the Earth, but we *definitely* would not have enough to destroy the planet. That's what the previous mathematical analysis was all about.

 

[NavyMan]

I think he may also have been including the fallout effects of the bombs as well. Nuclear winter etc.

 

[scott1]

All the man-made weapons in the world will not be enough to actually destroy the planet, though it will be enough to sterilize it of life and chew up its surface. However, the OP explicitly said 'destroy'.

I think you missed understood me.What I ment was dig a really deep hole put a bunch nuclear bombs in it and dentote them.

 

[NavyMan]

What if you took nuclear devices as scott1 said, but lay them within a major fault line? COuld it create massive tectonic problems?

 

[scott1]

What if you took nuclear devices as scott1 said, but lay them within a major fault line? COuld it create massive tectonic problems?

I did a google serch and found this site
http://ask.metafilter.com/mefi/28644
It says that's all of debate what would happen if you did that.

 

[NavyMan]

Interesting. I love Sgt. Sandwich's last post. Very dry humor.

 

[LURCH]

What about a collission with a large fast-mover in retrograde? That might give enough negative acceleration to de-orbit a planet.

 

[pervect]

What about a collission with a large fast-mover in retrograde? That might give enough negative acceleration to de-orbit a planet.

The orbital energy of the Earth .5 * (mass of earth) * (2 * pi * 1 au / year)^ 2
works out to be 2*10^33 joules (using google calculator).

Thus if the Earth encountered a planet of equal mass orbiting in the opposite direction, the collision would release about 10x the energy required to gravitationally disrupt both planets. The resulting cloud of debris would have zero average angular momentum, so I imagine a lot of it would wind up falling into the sun, however I haven't done any really detailed calculations.