Detonating the world's entire nuclear arsenal at once

[FtlIsAwesome]

I've wondered as to what exactly would happen if every nuke in the world was exploded at the same time. (Obviously, we'd all die)


Consider these scenarios:

1a. All nukes gathered in the Sahara desert and detonated
1b. Detonated at south pole
1c. Detonated in southwest US

2a. All nukes evenly placed across Earth's surface, both land and ocean
2b. Nukes placed over land
2c. Nukes placed over ocean

3. Nukes detonated at some ocean floor location in Pacific

4. Nukes detonated at one point on the Moon


I'm randomly guessing that Russia and the US each have 10,000 nukes, and the other countries have around 3,000-5,000 combined, but we can't really know because it is secret information.
Would the mega-explosion be enough to alter Earth's rotation/orbit? Or in the fourth scenario, would it alter the Moon's orbit?


Just a question out of curiosity.

 

[phyzguy]

I doubt we'd all die. It's a lot of energy, but I don't think it's that much. Just a back-of-the-envelope calculation gives the following: Assume 30,000 warheads total with an average yield of 1 megaton. 1 megaton is 4x10^15 Joules, so the total energy release would be about 10^20 Joules. For comparison, The 1960 Chile earthquake, with a Richter magnitude of 9.5, was estimated to have released about 10^19 Joules. Ten times this would be a disaster, but most of the Earth would survive, especially if they were all detonated in one place. The "dinosaur killer" impact that created the Chicxulub crater is estimated at 4x10^23 Joules (These numbers are from http://en.wikipedia.org/wiki/Richter_scale).

As far as affecting the Earth's rotation, if you assume the Earth is a sphere of uniform density (it's not of course, but just for an estimate), then I calculate the rotational energy of the Earth (1/2 L Omega^2) to be about 2x10^29 Joules, so the warheads would have no significant effect. I think the same goes for altering the moon's orbit, but I haven't caclulated that.

 

[FtlIsAwesome]

Would the fallout cover a significant portion of the atmosphere?

 

[mathman]

Would the fallout cover a significant portion of the atmosphere?

That depends very much on the placement of the bombs.

 

[JaredJames]

Approximate number of nukes: http://en.wikipedia.org/wiki/List_of_states_with_nuclear_weapons#Statistics

No, in none of the cases would the Earth or the moons orbit be affected.

 

[chengqi]

If all nukes are placed averagely on the surface of the Earth and detonated at the same time,the orbit would not change,but if these nukes are placed at a special point then i think the orbit will definitely change.(according the momentume theory)

 

[chengqi]

Absolutely we would die,not becouse of radioactive substances or shock wave or the anormouse energy. If all the nukes are detonated at the same time,the sky will be filled with smoke dust isolating the sun light,then the temperature will nock down and photosynthesis will stop. And the nuclear winter is coming.we may die of extreme cold weather or suffocation.

 

[chengqi]

practice is the best way to know the answer!

 

[JaredJames]

If all nukes are placed averagely on the surface of the Earth and detonated at the same time,the orbit would not change,but if these nukes are placed at a special point then i think the orbit will definitely change.(according the momentume theory)

Absolutely we would die,not becouse of radioactive substances or shock wave or the anormouse energy. If all the nukes are detonated at the same time,the sky will be filled with smoke dust isolating the sun light,then the temperature will nock down and photosynthesis will stop. And the nuclear winter is coming.we may die of extreme cold weather or suffocation.

practice is the best way to know the answer!

I'd like to see your numbers to support all of this, particularly the change of orbit thing.

Nuclear winter I can understand but it doesn't mean everyone dies.

 

[phyzguy]

If all nukes are placed averagely on the surface of the Earth and detonated at the same time,the orbit would not change,but if these nukes are placed at a special point then i think the orbit will definitely change.(according the momentume theory)

I think you're wrong. Let's try putting in some numbers. In order to change the orbit, we would need to eject something with greater than the escape velocity. Let's suppose we impart all of the energy of the nukes to some body moving at escape velocity. This will give us an upper limit. The momentum carried by the object will be 2E/v, where v is the escape velocity, which is about 10 km/sec. So the momentum imparted to the body (and hence to the Earth) would be 2*10^20 J/10^4 m/s = 2*10^16 kg-m/s. The momentum of the Earth in its orbit is mv = 6*10^24 kg * 3*10^4 m/s = 2*10^29 kg-m/s. So the change in the Earth's momentum would be 1 part in 10^13, which is unmeasurably small. Nukes are powerful, but not compared to the momentum of the Earth.

 

[FtlIsAwesome]

Basically, the energy is not enough to have any effect on the orbit or rotation.

My guess is that the explosion would cause a nuclear winter which would radically alter the enviroment, and few life would survive.

How big of an earthquake would the explosion cause?

In the undersea detonation scenario, it would cause a tsunami that may flood coastal areas.

When detonated at Antartica, it would cause some of the ice to melt, raising the sea level.

Nukes are powerful, but not compared to the momentum of the Earth.

So how many 50 megaton Tsar Bombas are we looking at to effect Earth's rotation/orbit? A million??

 

[jimgraber]

So how many 50 megaton Tsar Bombas are we looking at to effect Earth's rotation/orbit? A million??

Just for fun, I did the calculation:
Megaton = 4 10^15 Joules
Tsar Bomba = 50 Megaton = 2 10^17 Joules

Earth Mass = 5 10^24 kg
Earth orbital velocity = 30 km/sec

Joule = kg m^2/ sec^2

E= 1/2 m v^2
Earth Orbital energy = 1/2 x 5 10^24 x (3 10^4)^2 = 2.25 10^33 Joules

So 10 ^16 Tsar Bombas equals approximately one Earth orbital energy
After that you need an efficiency factor for transfer from bombs to earth, and a criterion for “affect”
A single Bomba effects the Earth's orbit by the miniscule factor of 10^-16 times the efficiency factor.
To blow the Earth completely out of its orbit you need 10^17 to 10^18 Tsar Bombas, assuming a reasonable efficiency factor of one to ten percent.
Enjoy (or check my work)
Best.
Jim Graber

 

[chengqi]

I think you're wrong. Let's try putting in some numbers. In order to change the orbit, we would need to eject something with greater than the escape velocity. Let's suppose we impart all of the energy of the nukes to some body moving at escape velocity. This will give us an upper limit. The momentum carried by the object will be 2E/v, where v is the escape velocity, which is about 10 km/sec. So the momentum imparted to the body (and hence to the Earth) would be 2*10^20 J/10^4 m/s = 2*10^16 kg-m/s. The momentum of the Earth in its orbit is mv = 6*10^24 kg * 3*10^4 m/s = 2*10^29 kg-m/s. So the change in the Earth's momentum would be 1 part in 10^13, which is unmeasurably small. Nukes are powerful, but not compared to the momentum of the Earth.

I am really grateful to your calculation.Now,i admit my previouse estimation was wrong. Actually i did not figure out the outcome.it is a subjective idea and unscientific answer. thanks for your help.

 

[Pengwuino]

Human technology is weak.