Mass Needed to Convert to Energy & Blow Up Earth?

[Ineedahero]

To blow up earth...

...what mass would I need to covert to pure energy (roughly)?

Like, they say a paper clip converted into pure energy is the equivalent of the atomic bomb that was dropped on Hiroshima. Is that true? If so, would a van converted into pure energy be enough to blow up Earth and kill everything on it?

E = MC squared...

Thanks

 

[wukunlin]

depends on what you need by blow up.

We had a question in my high school scholarship exam about splitting an asteroid with a bomb. The way I calculated was assuming the asteroid is spherical and we intend to split them into 2 hemispheres. with the mass of each hemisphere and the distance between their centres of mass we find the gravitational energy between them so the bomb needs at least as much energy to split them + some more to make the crack that splits the asteroid in half.

 

[Ineedahero]

By blow up, I mean shatter Earth into a whole bunch of pieces, completely knock it off its orbit and kill everything.

And what do you mean "split an asteroid in half"?

I'm saying just convert a mass of 10,000 kg into pure energy...E = MC squared...is that enough energy to destroy the earth?

 

[phinds]

To blow up earth...

Is a really bad idea

 

[wukunlin]

By blow up, I mean shatter Earth into a whole bunch of pieces, completely knock it off its orbit and kill everything.

That is 3 very different things. Energy required for each of them vary by many orders of magnitudes

And what do you mean "split an asteroid in half"?

as in shatter the asteroid into 2 pieces

I'm saying just convert a mass of 10,000 kg into pure energy...E = MC squared...is that enough energy to destroy the earth?

I can't really give you a meaningful answer (I could just answer yes/no without doing a single line of calculation) unless I know what exactly you mean by destroying the planet. If you just want to see it in pieces then it can get complicated because a huge chunk of the planet isn't even solid.
Perhaps we can hope to see someone with better geological and thermodynamics background to estimate how much energy is required to vaporize the earth.

 

[Ineedahero]

Ok, I see what you're saying - I'll try to be clearer.

The minimum amount of energy to basically guarantee all life on Earth ends.

So, if we knock it off orbit, I presume life will die because we need the sun to live.

If we shatter it into a whole bunch of tiny pieces, none of which remain in any kind orbit, obviously all life ends.

Whichever takes the least amount of energy to kill everything on earth...how much energy is that? Ballpark answer, obviously.

 

[Haborix]

Imagine the Earth as being made up of tons of small cubes (you pick the size). Then, knowing the number of atoms/molecules at the surface of every cube, find the energy you would need to put into break the bonds connecting neighboring cubes. Multiply by the number of cubes making up the Earth and then a factor of 0.5 for over-counting.

You'll have to make a few assumption about the material makeup of the Earth. There are tons of other considerations you could make to be more accurate, but I think this captures your desire to break it up into pieces (cubes, haha).

 

[Haborix]

Also, you might get a visit from the FBI if you keep asking questions like this, ha ha.

 

[Ineedahero]

I'm kind of surprised more people in the world aren't curious about this.

Seems like kind of a big deal lol

 

[wukunlin]

lol the way we deal with the planet now all life will end without any additional energy, but to answer your question:

I will take a guess and assuming nudging the planet out of the orbit is less demanding and easier to calculate.
earth's average orbital speed: 29.78 km/s
escape velocity @ Earth wrt to sun: 42.1 km/s
difference in KE (mass of Earth = 5.9736×10^24 kg) = 2.645e33 J
in E = mc^2, that is m = 2.94x10^16 kg

I'm pretty sure there are other factors (gravity of other planets) needed to shove the Earth away from the sun but that should give you an idea...

 

[Ineedahero]

2.94x10^16 kg

So...that's the mass of what?

Mass of Earth is something to the power of 24 right?

 

[wukunlin]

2.94x10^16 kg

So...that's the mass of what?

Mass of Earth is something to the power of 24 right?

yup

according to: http://en.wikipedia.org/wiki/Orders_of_magnitude_(mass)#1012_to_1017_kg

that is more than the mass of all carbon content of all organisms on Earth. And a bit less than all the carbon in the oceans.

 

[Haborix]

The volume of the Great Lakes is 2.26*10^13 m^3 (From wikipedia w/ conversions by me). Water has a density of 1000kg/m^3. So the total mass of water is ~10^16kg. You would need all the water in the Great Lakes for your sinister plan.

 

[Drakkith]

To look at it another way, you need enough energy so that the vaporized pieces of the planet cannot reform back into a sphere, meaning you need enough energy to overcome the gravitational binding energy of the planet. I don't know what that is however.

 

[256bits]

Rough guestimate - assume the Earth is all liquid water and you could calculate the amount of energy to convert the water into steam - just pick 100C and atmospheric pressure to give you a ballpark figure.

 

[A.T.]

http://qntm.org/destroy#sec3 (point 6)

 

[SW VandeCarr]

Ineedahero:"I'm saying just convert a mass of 10,000 kg into pure energy...E = MC squared...is that enough energy to destroy the earth?"

The total energy represented by 10,000 kg mass is $10^{4} kg * (3*10^{8}m/s)^2= 9*10^{20} J$

The energy of the Chicxulub asteroid impact (that killed all the dinosaurs) is given as $4.2*10^{23}J$. This impact did a lot of damage but did not split the Earth or knock it off its orbit in any significant way as far as is known.

http://en.wikipedia.org/wiki/Chicxulub_crater see impact specifics

 

[Vierstein]

Blowing up Earth and converting all of Earth's mass into pure energy are not the same thing. I guess you would need a charge at the center of the Earth large enough for the surrounding mass to reach escape velocity.