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  1. Supposing we had many thousands of antimatter bombs (they can be detonated in many different locations), how much total antimatter would we need in order to wipe out all humans on Earth?
  2. Supposing we had one antimatter bomb (it has to be detonated in one particular location, but it can be as big as necessary, even as big as an entire city), how much antimatter would we need in order to eradicate all animals on Earth?
  3. Supposing we had one antimatter bomb, how much antimatter would we need in order to completely blow up the Earth into millions of pieces?
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  • $\begingroup$ While I can't provide any numbers to back this up, I have a feeling the answers to Part 2 and Part 3 are going to be the same. $\endgroup$ – Frostfyre Apr 4 '15 at 3:53
  • $\begingroup$ Antimatter are difficult to create and much less to contain. Supposed you have successfully build a special tomahawk missile entirely composed of antimatter, this method of conversion of mass to energy greatly dwarfs any conventional nuclear reactions. Q3 is very hard to answer you need to completely overwhelm the gravitational pull of earth so only terraforming don't qualify for millions of pieces. You can also convert entire earth into energy but you have to look for antimatter earth to do it. $\endgroup$ – user6760 Apr 4 '15 at 5:00
  • $\begingroup$ possible duplicate of The opposite to Worldbuilding: World Destruction $\endgroup$ – Serban Tanasa Apr 4 '15 at 10:52
  • $\begingroup$ @Serban Tanasa: No, it's clearly not the same question. The question you linked is about the different ways to destroy a planet, not about the amount of antimatter needed to perform the 3 tasks in my question. Also your question only speaks about blowing up a planet completely, whereas my questions number 1 and 2 only speak about killing all humans and all animals respectively which is very different (your question very clearly states near the end "I dont just want to destroy all life on the surface, I want to reduce the entire planet to rubble so that very little remains"). $\endgroup$ – BuildingBetterWorlds Apr 4 '15 at 11:50
  • $\begingroup$ The word "antimatter" is not even mentioned anywhere in your question. Though one of the answer does say that we would need 1.3 trillion tonnes of antimatter to blow up the Earth. So if correct the answer would answer question number 3, but questions number 1 and 2 are left unanswered. $\endgroup$ – BuildingBetterWorlds Apr 4 '15 at 11:51
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Taken shamelessly from my previous answer here

If you absolutely, positively need to sterilize the surface, you must blast it from orbit. It's the only way to be sure.

The problem you'll quickly run into is that the Earth is big. You can crash 10km sized asteroids into it, and there'll still be some survivors to whine about the injustice of it all. Now, we wouldn't want that, would we? There are two surefire ways.

1. Antimatter Bombardment

No, the only way to be sure is to be thorough. You'll need a fair bit of antimatter, um, let's see...

1 Mt is $4.1\times10^{15} J$ so the Tsar Bomba (in the tested config) at $42MT = 1.72 \times10^{17} J$
2 kg of $E=mc^2 = 1.79 \times 10^{17} J$

So each 2 kg antimatter bomb (as it annihilates with 1kg ordinary matter) would have a blast similar to the Tsar Bomba, the most powerful nuclear device ever detonated in the puny humans' history. That gives you a nice $1,200 km^2$ blast incineration area. Now, if we were sloppy, we would just pepper the land area of $148,300,000 km^2$, so about 1,236 MIEVs (Multiple Independently Targetable Entry Vehicles) with 100 2kg warheads each would do.

But that would miss all the boats, planes and submarines crowding their primitive buoyancy based transportation lanes. With about 100,000 ships out there, that's a lot of survivors. $361,000,000 km^2$ to cover, you'd need another 3,009 MIEVs. You might still miss a submarine or two, but without space launch capabilities, zero industrial capacity, and an all-male crew, you're set anyway.

Pro: Clean blasts, little of that nasty radioactive slag. Also, once in atmosphere, any attempt to shoot down will only damage the containment system and detonate the antimatter.
Con: You need a lotta bombs.

2. One bomb to kill them all

We must use a bigger bomb. $<< 10^{32}J$ (gravitational binding energy of Earth)

3. Death star it

We must use an even bigger bomb. $> 10^{32}J$

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  • $\begingroup$ How does that last equation (rolled back for the time being; see revision history) work out? There's no way $10^{32} / 10^{17} = 10^{27}$, much less $10^{32} \times 10^{17} = 10^{27}$, no matter where you place any 1.72 multiplicative factor. $\endgroup$ – a CVn Apr 5 '15 at 14:39
  • $\begingroup$ I have no idea what you're talking about. $10^{32}J$ is simply the gravitational binding energy of the planet. The OP wanted it all in one bomb, so I told him his bomb must release at least that much energy. $\endgroup$ – Serban Tanasa Apr 5 '15 at 14:42
  • $\begingroup$ I rolled back the edit that added a formula at the end, which was the reason for my comment. Check the revision history; if it's appropriate, feel free to roll back my roll back! $\endgroup$ – a CVn Apr 5 '15 at 14:45
  • $\begingroup$ I believe Anonymous added that formula to calculate how many kg of antimatter that last bomb is. Not that he got it correct. $\endgroup$ – ArtOfCode Apr 5 '15 at 20:55
  • $\begingroup$ >$10^{15}kg$, it's not exactly rocket science. At least a trillion tons, probably an order of magnitude or so more when you account for noncentral location and dissipation loss. $\endgroup$ – Serban Tanasa Apr 6 '15 at 14:05
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The previous answer covered the bases fairly well for options 1 and 3. But case 2 deserves a better answer after all anti-matter is not cheap and they are always out of stock at Home Depot.

"Perhaps, just under four billion years ago, the Earth could have been hit by asteroids up to 400 kilometers across, forty times bigger than the one that is supposed to have been responsible for the K/T extinctions. Such an asteroid would boil away the oceans and transform the atmosphere into one of steam and molten rock." The resulting temperatures would be "well beyond the upper limit for life and the surface of the Earth would have been baked free of living microbes." Source: Ian Goddard and Cockell, Charles S. Impossible Extinction. Cambridge: Cambridge UP, 2003: 88.

Sorry, but I don't know where you can get the text of this book online. But, taking the statement as accurate (and the source appears to be of generally high quality to me). The asteroid belt just happens to contain a 400 km asteroid built to order, 10 Hygiea Plugging in the numbers (assuming a 17 km/sec impact) you get somewhat more than 1E28 joules, a rather significant savings compared the the gravitational potential of the earth, but still a lot of antimatter just to destroy it with a single bomb, roughly 6E10 kg of antimatter. I think this is a very conservative answer in that it is very certain to get the job done.

As we learned in real estate, location, location, location. Instead of wasting 1E28 joules in an antimatter explosion on the surface of Earth, how about a nice 1E20 J bomb set off in a carefully drilled hole inside 10 Hygiea -- wait a few months and let gravity do most of the heavy lifting (or falling in this case) when 10 Hygiea impacts the Earth. Still a single bomb, it destroys the earth and you have plenty of time for popcorn while you wait. Now you can destroy all life on earth using only about 6E4 kg of antimatter, only 60 metric tons of the good stuff.

If you really need to do this on the cheap, a 400 km asteroid is really quite a bit of overkill and a 100 km asteroid is probably enough to kill all animal life big enough to be interesting to most people although it may not completely sterilize the earth, and your only need 1 metric ton to target earth.

For a 10 km dinosaur killer asteroid, 1 kg of antimatter should be sufficient retarget the asteroid -- actually quite a bit less would actually be needed because there are quite a few near earth objects that would need only a tiny orbital deflection to serve the purpose, the largest of these earth crossers, 1866 Sysyphusone of these objects happens to fit the bill as it is probably over 8 km diameter (close enough for our imagination) and currently scheduled to pass about 17 million km from the earth on Nov 24, 2071. With careful planning, I expect less well less than 1 gram of antimatter would be needed to make this a bad day for the earth.

We could make this happen if we work at it. Given how difficult it is to make antimatter, this is probably the only way could do so using antimatter within the next 100 years. Even on larger time scales, creating enough anti-matter to destroy the earth will still be very difficult without invoking the drop a rock strategy.

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  • $\begingroup$ Dammit! ...scatch Home Depot... $\endgroup$ – Len Jan 23 '18 at 21:29
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Assuming perfect accuracy and a teleporter? Something less than 7g to kill every human. 7g divided 7 bn ways would equate to about the equivalent of 40 grams of TNT per person, something like a small hand grenade each.

A more realistic method might be to create a nuclear winter, by blowing dust up into the sky. Unfortunately that is rather slow, so a few humans will likely survive in bunkers you don't know about, for quite a long time. For that you can recreate the meteor that made the dinosaurs extinct (100 trillion tons of TNT) with about two tons of antimatter in one spot. Some humans would probably survive this, though.

This is generally ignoring the radiation effect of all the gamma rays, that might change the maths. You can maybe kill everyone with less antimatter if you settled for giving everyone cancer instead.

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  • $\begingroup$ For scenario 1, you'd probably be able to get by with even less... just tens of grains per person, targeted at the brain would be enough to cause embolisms. You could probably reduce your targets from 7 B to a few dozen by targeting, say, the leaders of a few large nations or the microprocessors in their early-warning systems, and let the ensuing nuclear strikes and counter-strikes do the rest. $\endgroup$ – 2012rcampion Apr 4 '15 at 20:46
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    $\begingroup$ Check your math. 1 kg of antimatter = 53 megaton yield, 4000 kg antimatter = 212 billion ton TNT $\endgroup$ – Gary Walker Apr 7 '15 at 0:51
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None. any large scale destruction of a city, with non antimatter device, on earth of a nuclear ready country would trigger mutually assured destruction, in what is estimated to be a thousand times over. achieving the specified result.

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1. Kill all humans with lots of small bombs

All of the other answers here are super overkill for this. If you want to kill all humans on earth, you have a couple of options:

  1. Give them a fatal dose of radiation
  2. Heat the atmosphere and cook them

According to this person 57 trillion annihilations at 30 cm gives you 1 rad of radiation. Scale that over the entire planet and you get 2.9 kg of antielectrons. Indiana Jones level kill you immediately radiation dosage is about 100000 rads, so that's about 290,000 kg of antiprotons spread out evenly.

Except the isochoric heat capacity of earth atmosphere is $C_v=.717kJ*kg^{-1}*K^{-1}$. Multiplying by the mass of the atmosphere $M_{atm}=5.1*10^{18}$ gives us how much energy it takes to heat the atmosphere by 1 degree Kelvin, $C_v*M_{atm}=3.6567*10^{18}kJ*K^{-1}$. Divide the energy put out by this annihilation and we get $\Delta K = 14000$. WAY too much.

Let's shoot to heat up the atmosphere by 200K; there's no way anyone's surviving that. $3.6567*10^{18}kJ*K^{-1} * 200K=7.313×10^{20} kJ$. Convert that into mass using $E=mc^2$ and we get $8.137×10^6 kg$ divide by 2 because half that mass is coming from regular matter and we have $4.069×10^6 kg$.

So to kill all humans you need 406,900 kg of antimatter. In all honesty you can probably get away with less because the force of the explosion will likely kill many humans. But I don't know how to calculate that.

I was planning on adding more to this response, but I think Serban covered it as well as I can for numbers #1 and #2. I definitely think #1 is overkill in his answer though.

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In John Barnes' excellent Thousand Cultures series, the ultimate nasty weapon is the teleportation of antimatter into the atmosphere as a very fine dust spread over a large volume. It basically all reacts at once release an enormous amount if IR -- enough to melt any rock within sight -- followed by a blast wave.

The very find dust gets around the problem that a chunk of antimatter in the presence of ordinary matter acts a bit like a chunk of sodium dropped into water. Instead of exploding, it sputters and fumes and splits into pieces and generally makes a mess. What's happening is that the heat produce by the initial reaction with the surface of the chunk of sodium boils the water around it and drastically slows down the reaction.

Antimatter would do the same. (On a much bigger scale to be sure -- it's not a good thing to have around the neighborhood.)

Something like this would probably be your optimal (in terms of parsimonious use of anti matter, anyway) approach for #1 and #2.

Number 3 just a really big bang deep down. I have no idea how to get that in an antimatter bomb, because of the fizzle problem noted above.

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It seems like 2, 200kg antimatter bombs, in short succession, dropped into the Yellowstone Caldera would be fairly certain to ignite a life ending volcanic eruption saving a trillion tons of antimatter, more or less.

I have no math to back this up.

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you need enough antimatter to produce a 100 megaton explosion. This will ignite the atmosphere, flash-boiling everything on the planets surface. There may be a few survivors in bunkers or submarines, but the terraformed earth will finsih them off.

To physically destroy earth? I reckon 6 100 megaton antimmatter bombs, placed deep underground, spaced evenly around the earth, will at the very least make earth unrecognisable.

Sorry I don't have the figures to support my answer.

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    $\begingroup$ The T'sar bomb was 50 megaton. The Soviets were originally going to set off a 100 megaton version (using a uranium tamper instead of a lead tamper) but changed their mind simply to allow time for the plane dropping the bomb to reach a survivable range before the bomb went off. A 100 megaton bomb would not ignite the atmosphere. There is even a discussion of this on Physics Exchange. physics.stackexchange.com/questions/66276/…. $\endgroup$ – Gary Walker Apr 10 '15 at 21:06
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    $\begingroup$ Took me a while to find it, but the debunking of the igniting the atmosphere by very large bombs is at osti.gov/scitech/servlets/purl/443240. Without getting deep into the physics, the limiting factor is simply that at atmospheric pressure, there is just not enough energy produced by N-N fusion to sustain the reaction because there are large energy losses in the form a gamma radiation and others. $\endgroup$ – Gary Walker Apr 10 '15 at 21:30

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