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Context

I am writing the section following a critical space battle where a rogue UNN Pearl of the Stars is taken down, and its CIC, reactor and, most importantly, its payload of 4 planet buster 15-gigaton interplanetary missiles, are secured.

The thermonuclear payloads are split into 5 warheads, weighing in at 3-gigatons each, for a total of 20 warheads needing to be pulled off their missiles. Think the UN missiles used against Eros in The Expanse for the kind of setting I am talking about.

The Question

Considering the kinds of nuclear weapons that have been designed and conceptualized (and declassified), what is the theoretical limiting factor for how small a gigaton-class nuclear warhead can be made.

Of course no one can put an exact number on it, but considering I don't need a scientifically accurate nuclear weapon that I expect someone somewhere to build someday, I only need to be in the right ballpark for it to be plausible to someone actually familiar with nuclear engineering. (It isn't going to fit in a briefcase.)

How small can one be made? The size of a large crate? A taker truck? 8 intermodal shipping containers? And more importantly, how much would it weigh? 500 kilos? 4 tonnes? It only matters because a few engineers need to lug it back onto their ship, and I need to know how hard of a time it will be for them.

I haven't locked this fact in, but I assume that the weapon would be designed to be as clean as reasonable considering the design constraints, possibly using antimatter as a catalyst. (but I don't understand enough about nuclear weapons to know if this is viable or will make it smaller)

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    $\begingroup$ Nuclear weapon designer Ted Taylor claimed (en.wikipedia.org/wiki/Nuclear_weapon_yield#Yield_limits) 6 megatons per metric ton bomb mass was the maximum with modern technology. Another estimate is 9.5 megatons per ton. That makes a 3-gigaton nuke either 500 or ~315.8 metric tons. If it's as dense as steel, that's ~71.5 cubic meters or ~45.1 cubic meters, respectively; if it's as dense as uranium, ~26.3 or ~16.6 cubic meters. Likely somewhere between those. Writing this as a comment because there are no actual hard science sources on this and it therefore cannot count as an answer. $\endgroup$
    – KEY_ABRADE
    Jun 23 at 5:31
  • $\begingroup$ If you have antimatter available, as mentioned in your last paragraph, then that changes everything - in practical terms it means that the size of the device is the size of the antimatter containment field generators. (And I think that "catalyst" is only a term that applies to chemical reactions, not nuclear.) $\endgroup$
    – KerrAvon2055
    Jun 23 at 7:35
  • $\begingroup$ As comments and answers indicate, these are going to be larger than any ICBM payload ever made. (Plus, since even in ridiculous, gigaton-ranged bombs, you want to get close to the surface, they'll have to be designed to survive reentry and still be in a state to detonate, which involves all sorts of additional, heavy, precautions.) I would remove the hard-science tag, though. $\endgroup$
    – jdunlop
    Jun 23 at 7:53
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    $\begingroup$ @Vesper I don't know what you mean, but if you took "taken down" literally, as atmospheric reentry, then hell no. I meant that metaphorically, as in they managed to put a gauss round through the reactor core and neutralize the ship completely, and making suicidal self-destruct impossible. $\endgroup$
    – Sam Kitsune
    Jun 23 at 19:10
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    $\begingroup$ I thought this question was going to be about pocket nukes or something, since it's phrased "How small can a nuke be?" There's nothing small about GT range weapons. $\endgroup$
    – codeMonkey
    Jun 23 at 19:42

4 Answers 4

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One gigaton is $4\times10^{18}$ joules. Deuterium fusion releases about $10^{12}$ joules/g, so you're looking at $4\times10^6$ grams (about 9000 lbs or 4.5 tons) of deuterium, minimum. In practice pure deuterium is a difficult material to work with (as a gas), so you're more likely to use lithium6 deuteride, but the numbers aren't that far off. You also need, for a conventional construction, a fission core; and to get to gigaton level you're probably going to have multiple stages of fission cladding, Tsar Bomba style, to pull everything together. Say 5 tons for a (one-) gigaton class bomb as a theoretical minimum, 50 tons as an ambitious engineering goal, and 100 - 200 tons as likely achievable if weight were the primary design goal.

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  • $\begingroup$ I think 200 tonnes is still ambitious - the fission cladding is going to be heavy, and on top of that, the conventional explosive trigger is going to be enormous. Plus, this is a warhead, not just the physics package, so you've got safeties, triggers, and whatever additional engineering is required to keep it safe while travelling through interplanetary space. Plus, given sublight travel times, an interplanetary missile would need to be horrendously overengineered. $\endgroup$
    – jdunlop
    Jun 23 at 7:46
  • $\begingroup$ The most important attribute of the weapon is its weight, as less weight means more acceleration is possible. Let's say they shrink it down to 90 tonnes per warhead, meaning 450 tonnes of payload. A full sized SpaceX Starship could carry that. $\endgroup$
    – Sam Kitsune
    Jun 23 at 19:00
  • $\begingroup$ Imagining that the entire missile would weigh in at about 20X the warhead (including the guidance, shielding, comms and fuel), or about 9 thousand tonnes, to accelerate at 20G continuously you would need around 1765MN of force or the equivalent of 33 raptor 2 engines, if they were about 30 times as powerful. $\endgroup$
    – Sam Kitsune
    Jun 23 at 19:04
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    $\begingroup$ Is that very guesstimated? Oh hell yes! Is it believable? Enough. $\endgroup$
    – Sam Kitsune
    Jun 23 at 19:06
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    $\begingroup$ @SamKitsune - bear in mind that addaon's back of the envelope calculations were for a one gigaton warhead. You specified three, so dial up all the values by a factor of 3. $\endgroup$
    – jdunlop
    Jun 23 at 21:59
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Antimatter Missiles

A Gigaton is just a massive amount of power. I think @addaon does a good job showing how enormous your "missile" would be using "conventional" hydrogen bombs -- the payload is the size of a bus, 10x as heavy, and you don't even have engines on it yet!

So use something more powerful! A 1 kg of anti-matter, 1kg regular matter reaction releases 43 megatons of energy. So a 90 kg anti-matter payload would produce a 3 gigaton explosion if you slammed it into something made of matter (assuming it all interacts before it's blown clear of the impact site...)

You'd need to add some magnetic containment to hold it, and a power source to power that, so all in all your payload size might be in the range of a few hundred pounds.

Much more workable than a city bus.

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  • $\begingroup$ This would be impractical for multiple reasons, firstly that antimatter is extremely hard to produce en masse, secondly that the containment system would weigh more than a mountain range or be split into hundreds of smaller containment vessels, both of which would quickly become far more difficult than standard nuclear weapons. $\endgroup$
    – Sam Kitsune
    Jun 23 at 20:01
  • $\begingroup$ If the anti-mater has a net charge, the containment system is just a electo-magnet system designed to keep it in the center of the vacuum vessel. You would power it off ship's power, with a battery just large enough to last the anticipated flight time. Not sure what part of that is huge. $\endgroup$
    – codeMonkey
    Jun 23 at 21:10
  • $\begingroup$ Re: it's hard to make that much anti-matter. You're asking for a warhead that is 60x the power of the Tsar Bomba, which was a 30 Ton monstrosity. It's not going to be easy. If you want 5 guys to move it, this is pretty much your only option. $\endgroup$
    – codeMonkey
    Jun 23 at 21:16
  • $\begingroup$ I do agree with @SamKitsune that such a large amount of Anti-Matter is impractical to contain. But like, why use this much ? I you use Anti-Matter Catalyzed thermonuclear fusion devices, you can get 20kt/kg of bomb. Now that is still a 150000kg device. About the mass of an Orion ship. $\endgroup$
    – ErikHall
    Jun 26 at 23:42
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3000 tons

Take a look at this article which is pretty much the exact information you want.

According to nuclear-weapons designer Ted Taylor, the practical maximum yield-to-mass ratio for fusion weapons is about 6 megatonnes of TNT per tonne (25 TJ/kg)

... for the largest Tsar Bomba, the yield was 2 megatonnes of TNT per tonne (deliberately reduced from about twice as much yield for the same weapon, so there is little doubt that this bomb as designed was capable of 4 megatonnes per tonne yield).

So let's take 5 MT/ton yield, halfway between Taylor's estimate and the Tsar Bomba, so the numbers come out round. (These are metric tons, by the way: 1000 kg each). You want 15 GT, so a simple division tells you that your bomb should weigh 3000 tons.

By the way, this is not a planet killer, or even a continent killer. 15 GT TNT is 6 * 10^19 Joules. The 1815 eruption of Mount Tambora was 1.4 * 10^20 J, twice as big, and this eruption did not destroy the planet or any continents. The Chicxulub crater that killed the dinosaurs was 3 * 10^23 J. Chicxulub wasn't a planet-killer either, but perhaps it can be argued it was a continent-killer, and four of them evenly dispersed might have been a planet killer due to the climate effects. If you want your weapons to be Chicxulub-scale, maybe multiply the yield by 1000 for 15000 GT TNT (15 TT). I only say 1000 and not 10,000 because you could increase the damage by using an airburst instead of digging a hole like Chicxulub did. Each weapon would weigh perhaps 3 million metric tons.

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  • $\begingroup$ The point of the weapon (a single missile) isn't to single-handedly end all life on earth in one go. It's meant as a deterrent, 60 gigantones of nukes per capital ship, dozens if not hundreds of capital ships all across the system, thats enough to really mess up a planet, especially one with a very tenuous ecosystem like over-burdened earth or barely-terraformed mars. $\endgroup$
    – Sam Kitsune
    Jul 20 at 4:40
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What are these 15 Gigaton missiles for?

The Tsar Bomba has been mentioned. This was 60 Megatons dropped from an aircraft. It could have been over 150 Megatons if they had not cut down on the fission cladding so it could fly. The weight of a nuke also depends on the efficiency of the explosive. We can make smaller devices with modern explosives, without the shock waves lenses of the early A-bombs. I think we might do other better than the figures suggest. But that's not the point...

In the fifties, the Tsar Bomba may have had a deployable scenario. If the USSR invaded Europe, they could have swept though the land masses, but the UK as a nuclear armed island could not be taken quickly. The Tsar Bomba would have taken out all of London for 30 miles, with all its levels of government. But the Internet was designed for that sort of thing: disperse the management, and the country has no head to cut off.

A lot of the blast for such a bomb goes up in the air. The overpressure of the shockwave levels buildings at ground level. Little shock penetrates the ground - most of it reflects back from an airburst - so if you are in a deep shelter you might survive, for all the good that will do you. If you want an underground shockwave, you are going to have to bury the thing.

So, what is a 15 Gigton weapon doing in space? It cannot sensibly be used to disperse an asteroid that threatens Earth without a separate impactor to dig a hole for it. 'Star Wars' gave us the planet-busting weapon, but it doesn't really make any sense. Gravity will re-assemble the planet. All you probably wanted to do was to kill off what was living on the immediate surface.

If you want a ship in space to threaten Earth using bombs designed to disperse small asteroids, there is another nasty treat from the fifties you could use. Clad a conventional A-bomb in cobalt. That is a 'cobalt salted' bomb and it generates large amounts of fall-out.

The Usual Note: You are writing fiction. George Lucas gave us the wildly impractical 'Death Star', and he did quite well out of that.

PS: The recent Tonga volcano explosion was estimated as bigger than the Tsar Bomba.

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    $\begingroup$ Why are nukes in space? Say hello to Master of Orion that used both warheads and bombs. Actually delivering a 10x10m nuke to a ship several hundred meters in diameter would likely eradicate it, larger ships would get dented to possibly inoperable state, and such a nuke could get launched from the other side of a planetary system. (Although solid steel could sometimes perform better, if the relative speeds are high enough) $\endgroup$
    – Vesper
    Jun 23 at 9:20
  • $\begingroup$ "'Star Wars' gave us the planet-busting weapon, but it doesn't really make any sense. Gravity will re-assemble the planet. All you probably wanted to do was to kill off what was living on the immediate surface." As was explained, the purpose of the Death Star was to serve as a threat to planets seeking to rebel against the empire following the dissolution of the Senate. Yes, Gravity will reform the planet, but the population will not. $\endgroup$
    – hszmv
    Jun 23 at 14:44
  • $\begingroup$ A one gigaton nuke detonated 100 miles above Earth could deposit 10 calories per sq cm to the land below, enough to ignite most combustible materials in a 11,000 sq mi area, about the size of Massachusetts. Radioactive fallout would be minimal. Source: "Counterforce from Space", Air force special weapons center, 1961. $\endgroup$
    – BMF
    Jun 23 at 14:45
  • $\begingroup$ @BMF Ooo! That's a new one on me. Thanks. People kinda went off exploding things in space after Starfish Prime, but that might work. Seems like an expensive way to start fires, though. $\endgroup$
    – Richard Kirk
    Jun 23 at 16:34
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    $\begingroup$ Do note that the weapons were created as MAD deterrents, never actually intended to be used in combat. If one day mars gets pissed and drops some rocks down the gravity well, every UNN capital ship in the system will personally ensure mars is a glass marble afterwords. $\endgroup$
    – Sam Kitsune
    Jun 23 at 19:14

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