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Present day Earth is attacked by a volley of relativistic impactors. Each is designed to hit the surface1 with a yield of 1 gigaton TNT equivalent. They're also poorly aimed. None are destined for any particular spot and about 2/3rds of them hit the ocean.

Question: Assuming most deaths result from the environmental aftermath, i.e., lingering dust decimating global crop yields and such, how many impactors are likely required to kill about 90% of the human race in the span of a decade or so?

1 Yes, I've seen the XKCD comic lol. The impactors are also emitters that burn a vacuum channel through the atmosphere at the last moment. They deposit most of their KE into whatever's in their path, land or sea.
Note: I know that's not ideal for kicking up dust. A low altitude explosion would do better. But for narrative purposes that's how the impactors behave.


Edit:

  • The weapons subverting atmosphere and impacting ground is non-negotiable. It's just part of the setup here.

  • The RKKVs, despite reaching surface level, won't penetrate deep into the planet. They pretty much annihilate themselves once they encounter material and start liberating their enormous KE. See the XKCD comic.

  • I believe most deaths will result from the aftermath, not the initial events. Effects like warming of the atmosphere or ocean from the blast energy or release of greenhouse gases will most likely be surpassed by the effects of dust blanketing the high stratosphere. Dust that high is above the machinery of weather structures that would otherwise mill it back down to the surface, so it lingers for a while and cools the planet by raising its albedo. (And as Earth cools the polar ice caps expand, further raising albedo, further cooling it.)

  • A 1 gigaton explosion sounds like a lot, but for scale the most recent example is the 1815 eruption of Mount Tambora, only 200 years ago. The total energy of Tambora is thought to be as high as 10-30 gigatons, though volcanoes usually have multiple eruptions over days or weeks and any one explosion is likely less than 1 Gt. The last time planet Earth saw a fully gigaton scale explosion was likely the Popigai impact, 35 Mya in northern Siberia.
    Though the impact physics change when you get up to relativistic speeds, the Popigai crater has a diameter of ~100 km.

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    $\begingroup$ Back in 1945 scientists believed 10-100 detonations of 50-100 Mt bombs would make the atmosphere dangerously radioactive. That's 0.5 to 10 strikes. The problem is no answer can be deterministic as humanity has never experienced e.g. a nuclear winter. However, what research has been done on nuclear winters suggests that most humans would be dead in 2-3 years just due to lack of food. So my question is this: since you can only rationalize your goal, is the declassified document sufficient? $\endgroup$
    – JBH
    Sep 4, 2023 at 1:50
  • $\begingroup$ BTW, the scientists' claim is on page 317, most of which has been redacted. Leave it to the Feds to take most of the fun out of anything. $\endgroup$
    – JBH
    Sep 4, 2023 at 1:52
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    $\begingroup$ @JBH I don't believe radioactivity will be the prime killer with highly kinetic impactors. These don't get their boom from nukes but from raw KE. There'll be some heavy metals liberated from the crust and thrown into the air, and some new elements in the fallout from sheer impact fusion, but nothing like the heavy isotopes in purely nuclear fallout. Though I think nuclear winters are a good avenue of search if radiation deaths (or lack of) can be adjusted for. $\endgroup$
    – BMF
    Sep 4, 2023 at 2:33
  • $\begingroup$ Yeah. If the impactors weren't relativistic I'd agree with you. Sure you want science-based? Radiation in the atmosphere, nuclear winter (aka dust in the atmosphere), compression wave in the atmosphere, heating of the ocean and death of almost everything in it from its own compression wave, volcanism due to impactors piercing the mantle... So I'm back to my original question. 0.5-10 impacts based on real science. Not sufficient? How many does your story need? $\endgroup$
    – JBH
    Sep 4, 2023 at 4:27
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    $\begingroup$ @JBH there seems to be a misunderstanding about how far relativistic missiles can penetrate. No doubt the crater will be deep, but it's definitely not "penetrating the mantle". The short of it is that because of effects like impact fusion at speeds >1-5% c, the impactor will disintegrate very rapidly (nanoseconds). It would be similar to a 1 gigaton detonation at ground level. And if it didn't burn a channel through the atmosphere, the impactor would detonate high up instead, near the karman line. You'll never get a relativistic bullet piercing much of anything. $\endgroup$
    – BMF
    Sep 4, 2023 at 12:01

4 Answers 4

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10

Back in 1945 scientists reported their belief that 10-100 detonations of 50-100 Mt bombs would make the atmosphere dangerously radioactive. That's 0.5 to 10 strikes.

Now, I am assuming that a relativistic strike (I'm assuming >0.5c, could be wrong, but it wasn't defined. Probably matters...) is going to cause some nuclear crapola. I think it's entirely unrealistic to use the quantity "one gigaton" and the phrase "relativistic impactors" and not believe there will be nuclear crapola. But even if we ignore it, it's not like using an air compressor to blow up sand out of a box. There will be ferocious heat and force. And although no answer can be deterministic (since humanity has never experienced the effects of such an explosion, such as e.g. a nuclear winter), what research has been done on (e.g.) nuclear winters suggests that most humans would be dead in 2-3 years just due to lack of food.

Further, drawing on information I used in an answer I wrote that referenced the Tsar Bomba as an example: 50 Mt has a 22 mile 100% destruction radius.1 One of your impacts has, using a rough linear calculation only, a 440 mile 100% destruction radius or an 880 mile 100% destruction diameter. That's 33% the width of the United States and a whomping chunk of Canada — guaranteed dead. And remember, that's not a circle we're talking about, it's an 880 mile diameter hemisphere.

On top of that are things like the dust (radioactive or otherwise) thrown into the air, the compression wave caused in the oceans, the tsunamis... and the fact that 40% of humanity live on coasts alone. The sediment churned up into the oceans would take forever to settle and it would seriously change the evaporation rate of the oceans.

Therefore, I believe the following:

  • The document I linked to above more than rationalizes a small number of impacts to kill 90% of the human race. It very much rationalizes ten.

  • I think the research into the possible destructive nature of nuclear winters (and it would only take a few of your impactors to hit land to get that winter) is more than enough to rationalize 90% dead in less than ten years.

I think other answers are vastly underestimating your impacts. Dead people. Dead fish. Crap in the atmosphere and, thanks to those ocean impacts, life-killing crap in the oceans (stirred up sediment) that will take a long time to settle. If you think I'm being too "optimistic," then double it to 20 impacts. That's a line of 100% destructive hemispheres 17,600 miles long across the 24,901 mile circumference of the Earth.

And every impact into the ocean causes a lot more damage than any impact on land. Kill the ocean, kill the humans.


1I'm going to use what information I've provided to refute any idea that there's a material difference between a 50Mt nuclear explosion and a 50Mt kinetic explosion caused by a relativistic object. The problem is time. There's too little of it with a relativistic object to ignore the heat and radiation it will cause. Can't say how much there'd be, but I'm claiming any difference is irrelevant without proof. Or at least a better set of assumptions than I'm promoting.

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  • $\begingroup$ I agree, I think I'm underestimating the scale of the impacts. And so have the other current answers. It's a hard thing to picture for sure. Thanks for your answer! $\endgroup$
    – BMF
    Sep 8, 2023 at 23:54
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Don't kick up dust — fry crops and drown cities by overheating the atmosphere.

The Earth's atmosphere weighs about 5 quadrillion metric tons, or 5 quintillion kilograms. Assuming the specific heat of the Earth's atmosphere is ~1,500 joules per kg per °Celsius (which I believe to be a high estimate) that means it takes 1,500 * 5 quintillion = 7.5E21 joules to raise the temperature of the entirety of the Earth's atmosphere by 1° Celsius. 7.5E21 joules/1 gigaton TNT energy ≈ 1,792 impactors to raise the temperature of the atmosphere by 1° Celsius.

Let's say you send ~9,000 impactors. I imagine raising the average temperature of the atmosphere by 5° Celsius in this way would have apocalyptic environmental effects, considering a degree or two less in terms of climate change is already shaping up to have unpleasant ramifications.

Obviously, the Earth would radiate this heat away over time, as there would be no ultra-strong greenhouse effect to keep the heat in, but that's small comfort for all the people who've starved to death because their crops died or were killed in sudden sea level rises.

The Chicxulub impact released approximately 3E23 joules and caused apocalyptic environmental effects; you would require over 215,000 1-gigaton impactors to kick up a similar amount of dust, considering around ⅔ of them are going to miss anything capable of being injected into the atmosphere. On the other hand, 215,000 1-gigaton impactors that inject all their energy into the atmosphere simultaneously will increase its temperature by nearly 120 degrees centigrade. Land life survived Chicxulub, but most land life — such as humans — cannot survive temperatures high enough to melt sodium, not even for minutes. Ergo, do not hit the Earth with several hundred thousand at once if you want there to be survivors.

I wouldn't specifically state how many impactors were needed if I were you, because that lets people mentally fill it in with whatever they think is reasonable, but my personal guess would be 100,000 to 300,000 at once if hitting the ground to kick up dust (i.e. comparable to Chicxulub). 10,000 to 30,000 burning up in the atmosphere daily will inject the atmosphere with several times the energy the Earth receives from the Sun on a daily basis.

So there's your answer: somewhere in the 100,000 to 300,000 range hitting the surface simultaniously for Chicxulub-esque greenhouse effects/global cooling and ~10,000 per day for the slow(er) boil.

I still recommend the "overheating the atmosphere" approach". There are several advantages of it over the "vacuum channel to the surface" approach:

  1. 100% of the impactor's energy is used, minimizing the number needed
  2. The impactors are effective regardless of where they hit, which is good, given their poor aim
  3. The impactors are not technologically complex and there is no risk of them being reverse-engineered, however unlikely that may be — and that sounds important, given that this sounds like a Dark Forest scenario
  4. If there's no need to burn a vacuum channel through the atmosphere, you can send (for instance, numbers for display only) 100,000 lumps of iron, not 1,000 or so technologically complex impactors, minimizing production costs
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  • $\begingroup$ I think you're approaching this at the wrong angle. Raising temperatures vs lowering. A meager asteroid impact or supervolcano can throw up enough material to raise Earth's albedo and drop global temps enough to kick off an ice age. That alone is likely overkill. I also think Chicxulub is a bad role model in this case. I'm only trying to starve humanity down to 10% current population, not cleanse Earth of it and 90% of all species. $\endgroup$
    – BMF
    Sep 3, 2023 at 20:12
  • $\begingroup$ It doesn't matter that 100% of the energy is used if it's used ineffectually. 300,000 gigatons is at least 300 Yellowstones. That's overkill. Also, for narrative reasons, the impactors drilling their way through is unconditional. $\endgroup$
    – BMF
    Sep 3, 2023 at 20:15
  • $\begingroup$ @BMF Point taken. Still, dumb impactors raising the temperature are probably more effective because (a) they don't need to be aimed, (b) there can be many more of them, and (c) high temperatures are more lethal than low temperatures — both kill crops, but high temperatures result in sea level rises and more violent weather and limit the ability of humans to move or work, whereas low temperatures can be insulated against with clothing. Moreover, most of the world's population lives closer to the equator, meaning heat from the equator up/down will kill more than cold from the top/bottom up. $\endgroup$
    – KEY_ABRADE
    Sep 3, 2023 at 20:16
  • $\begingroup$ @BMF Yellowstone is in the high-multi-gigaton to low-teraton range, from what I can gather. Still, if impactors drilling their way through is mandatory, it'll be in the low six digits. How many, exactly, I don't know, because the Earth has never been hit with something remotely comparable and therefore I have no basis to go off of (nuclear surface bursts and wildfires are far different from something tunneling kilometers underground), but my guess is at least 100,000 and likely more, because unlike Chicxulub, most of their energy will go into penetrating ground rather than throwing up ejecta. $\endgroup$
    – KEY_ABRADE
    Sep 3, 2023 at 20:19
  • $\begingroup$ But low temperatures are easier to achieve, is what I'm saying. It's easier to cause an ice age than global warming. In the latter case, you're dropping in every Joule. It's a bigger job by orders of magnitude. The attackers might be stupid, but they're not so wasteful. And besides, the impactors can't burn up in the atmosphere. (They don't burrow into the ground either, like your last comment seems to me to suggest. An RKKV won't make it very far into the ground.) $\endgroup$
    – BMF
    Sep 3, 2023 at 20:21
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1,600 - 4,000

Anywhere between 1,600 and 4,000 impactors will almost certainly cause a 90% depopulation.

This number might be too much, and won't necessarily leave 10% alive. I'd go for the upper end of the range if I wanted total destruction (with 90% as a minimum), and for the lower end, or even below 1,000, if I specifically wanted to preserve 10% of the population.

A lower estimate of 600 could achieve it through climatic effects, if the worst nuclear winter projections prove true, but it's unreliable. I wouldn't count on it. 90% is extreme, and industrialized countries might find a way to cope with the effects, suffering greatly reduced losses. Or they might collapse,.

On the other end of the scale, over 9,000 is definitely overkill - it would cover the whole planet in nuclear-like fireballs and extreme heat, causing lethal burns and fires. That might result in a total extinction, not just of the humanity, but of most higher lifeforms.

Below are several calculations that converge at this result.

Cold War Stockpiles

Throughout most of the Cold War, both superpowers maintained around 20,000-30,000 warheads each. In 1986, the total peaked at 70,000 warheads. Military strategists on both sides believed this was sufficient for MAD deterrence by killing up to 90% of each other's the population, at peak levels.

Some analysts considered the 90% figure exaggerated, and the lowest estimates started at 35% for the USSR and 50% for the US. Half the Soviet Union's population was spread around low-density areas, not easily susceptible to big warheads. Both superpowers maintained massive stockpiles of supplies, enough to last through a nuclear winter, should it fail to become a multi-year weather phenomenon.

Since the end of the Cold War, deterrence is maintained at a lower level, since 30% would still be insurmountable for any remotely-democratic government (possibly any). While radioactivity is an added problem, it's expected to be a relatively minor source of lethality factor in a total nuclear war, just because of how massive the rest are.

Scaling by population

The average nuclear warhead yields about 100 kT. The effect of multiple warheads scales roughly to the cube-square law: 1000x the yield is equivalent to 100x the warheads. For 1 GT impactors, this means each is roughly equivalent to 400 normal warheads. Accordingly, about 60 impactors each for the US+ and the USSR, ~300 million sized blocs, would be sufficient to depopulate each other.

Scaling this to the world by population, this arrives at ~1,500 impactors for 7.5 billion people (1 per 5 million, which might be too low for rural areas). Or 1,000 for world population as of 1986, which is probably more correct. However, since 75% of the planet is water and ice, you need 4 times that to keep the same saturation of populated areas.

Scaling by area

Scaling it by area, the US and the USSR together took up 32 million sq.km., or about 1/16 of the planet including water. This arrives at ~2,000 impactors to reproduce the effects, on the average, per unit area. More might be needed to make sure big cities are hit.

While rural areas won't have 5 million in a single impactor's radius, they are also less resistant to the effects of a nuclear (or meteor impact) winter. Still, we're working out orders of magnitude here, not precise numbers.

These two estimates give between 2,000 and 4,000 impactors to reproduce the effects of a total nuclear war between the two superpowers across the world.

Lower bound: nuclear winter

The worst-case nuclear winter projections were based on 60,000+ total warheads, equivalent to ~150 impactors. Quadruple that to make sure they hit dry land, and you need ~600. However, any 90% or higher estimates for nuclear winter lethality have been frequently criticized as an exaggeration.

Upper bound: blast and fire damage

To go on the other end of the scale, Nukemap gives about 13,000 km^2 of area for third-degree burns (11.3 cal/cm²) for a ground impact of the Tsar Bomba.

The Medical Implications of Nuclear War, considered the reference text in the field (navigation is on the right), estimates 10 cal/cm² as the radius in which superfires are likely to start.

That is likely to yield a 90% fatality rate, to anyone exposed from burns, to the rest from the fires. Treatment possibilities can be ignored at this scale, medical facilities are designed to handle at most a few percent of the population, and that's with power, water, and other amenities. Per cube-square law, a 1 GT impactor will then cover about 58,000 km^2 in similar heat.

Earth-wide that will require... Oh. Just about 9,000 impacts. The entirety of the planet, set ablaze, anything alive suffering potentially fatal burns. It will probably be overkill. Massive wildfires and deaths of basic lifeforms can simply kill the biome beyond the point of recovery, snuffing out the remaining 10% as well.

Cretaceous–Paleogene extinction event

The Chicxulub impact's energy was equivalent to about 72,000 such impactors. However, its energy was concentrated in one spot.

The cube-square law no longer applies at this scale, but it did, in absence of anything better, it would give a 1,600 gigaton impactors equivalent. That explains why the destruction from 9,000 gigatons appears, per Nukemap, to be closer to total extinction than a partial one, even worse than this event.

With that in mind, I'd add 1,600 as another possible number, since replicating the K-T extinction event clearly can be seen as sufficient for a 90% depopulation. Even this number might be too high.

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  • $\begingroup$ This is the kind of informed ballparking I was looking for, thanks! $\endgroup$
    – BMF
    Sep 4, 2023 at 15:53
  • $\begingroup$ Nukemap gives 13000 km^2 for the thermal radiation radius for third degree burns. I wouldn't call that a heavy destruction area. Buildings would be intact. Anyone inside a building, or on the other side of a hill, would survive. Even plenty of people directly exposed would survive, if given treatment for their burns. The real "heavy destruction area" is the moderate blast damage area, which nukemap gives as 1420 km^2. If we scale that up based on nukemap's formulas I get 6590 km^2 moderate blast damage area for a 1 GT explosion. That translates to 77000 impactors to cover the earth. $\endgroup$
    – causative
    Sep 4, 2023 at 19:22
  • $\begingroup$ @causative I'm considering the fire effects here. Wood is still spared, but lighter flammable materials will be set on fire. Window curtains, sofas, fabrics, anything that lacks the thermal mass to absorb 60 kJ/m2, it's all going up in flames. Not every house will ignite right away, but radiant heat spreads. It's similar to the infamous "ring of fire" mode of destruction that nuclear airbursts are designed to produce - flattening the center of the city and setting the outskirts ablaze, the fire then spreading both inwards and outwards. Covering the planet in wildfires is no small feat. $\endgroup$
    – Therac
    Sep 4, 2023 at 19:40
  • $\begingroup$ @Therac In that case you aren't talking about direct damage, and it doesn't matter what the radius is because you're relying on the fire to do the damage, and the fire can spread anywhere outside the radius. Incidentally it is ash from burning forests that is supposed to cause nuclear winter, not the nukes themselves. So this is a climate effect, not a direct effect. $\endgroup$
    – causative
    Sep 4, 2023 at 20:45
  • $\begingroup$ @causative I'd count smoke inhalation, poisoning, and suffocation as direct or nearly direct effects. Burning buildings and wildfires are very lethal. The smoke might then also cause a nuclear winter, but if the ignition area is the whole planet, it might not matter much. $\endgroup$
    – Therac
    Sep 4, 2023 at 20:52
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One

The reason is, the impactor would cause a major earthquake of magnitude 9.0 or higher, not sure if 10.0 is reachable, maybe that depends on the exact point of the impactor to land, etc. A tsunami (if landed into the ocean) would damage enough land to cause major planet-wide infrastructure disruption, including damaging power plants, but the earthquake shockwave could just trigger Yellowstone and possibly other crust instabilities causing enough volcanism to advance nuclear winter scenario. Past that, humanity would fight over the leftover resources including warmth and food, "naturally" degrading by 90%.

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    $\begingroup$ A single 1-gigaton detonation and/or a single 9.0-magnitude earthquake is not going to destroy humanity. 9.0 earthquakes have occurred before without setting off Yellowstone; I doubt even a direct surface hit from a 1-gigaton nuke would either, and the odds of one are incredibly low anyway because these impactors are not aimed. $\endgroup$
    – KEY_ABRADE
    Sep 5, 2023 at 0:35

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