# Destroying a planet

1. Jan 9, 2006

### 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.

2. Jan 9, 2006

### 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.

3. Jan 9, 2006

### Janus

Staff Emeritus
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 becuase 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?

4. Jan 9, 2006

### Janus

Staff Emeritus
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.

5. Jan 10, 2006

### DaveC426913

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

6. Jan 10, 2006

### NavyMan

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

7. Jan 10, 2006

### DaveC426913

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

8. Jan 10, 2006

### 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 untill the palnet falls completely into the star.

9. Jan 10, 2006

### pervect

Staff Emeritus
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

Last edited: Jan 10, 2006
10. Jan 10, 2006

### DaveC426913

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.

11. Jan 10, 2006

### scott1

If you could put alot 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.

12. Jan 10, 2006

### DaveC426913

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'.

13. Jan 10, 2006

### NavyMan

Yes there are plenty of ways to exterminate the living things on a planet, but I was refering 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.

14. Jan 10, 2006

### pervect

Staff Emeritus
Let's take a look at the original question:

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.

15. Jan 10, 2006

### pervect

Staff Emeritus
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.

16. Jan 10, 2006

### NavyMan

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

17. Jan 10, 2006

### scott1

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.

18. Jan 10, 2006

### NavyMan

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

19. Jan 10, 2006

### scott1

I did a google serch and found this site