How many impacts to kill 90% of the human race?

Question

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.

Answer 1

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.

---

_{¹ I'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.}

Answer 2

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

Answer 3

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.

Answer 4

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%.