<p>Three millions.</p>

<p>For this answer to be any fun, let's first assume that before removing the atmosphere, we have equipped all humans with oxygen supplies. In return, they are not allowed to go indoors or otherwise protect themselves.</p>

<p><a href="https://i.sstatic.net/I2fig.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/I2fig.png" alt="oxygen"></a></p>

<p>The size of meteors — as well as most other things in the Universe — has a distribution that is well described by a power-law. The larger the meteor, the rarer they are.
Small meteors can be lethal only by a direct hit, while large meteors <em>in the real world</em> can be lethal due to the effect they have on the environment; dust can cover the sky for years and prevent the Sun from keeping us warm. However, since we have removed the atmosphere, the debris will fall down immediately, and the only way to kill us is by the explosion. But, as will be shown below, the dangerous ones are the small ones because the rate at which large ones falls off so quickly.</p>

<p>The number $N$ of meteors entering Earth's atmosphere every year with a diameter $D$ (measured in meters) or larger is given by (<a href="http://adsabs.harvard.edu/abs/2002Natur.420..294B" rel="nofollow noreferrer">Brown et al. 2002</a>)
$$
\frac{N(&gt;D)}{\mathrm{year}} \simeq 37 \left( \frac{D}{\mathrm{m}} \right)^{-2.7}.
$$</p>

<strong>Minimum size needed to be lethal</strong>

<p>What makes a meteor lethal is really outside astronomy, and someone may be able to come up with a better answer, but for the sake of the argument, let's assume that the energy needed to kill a human by a direct hit is equal to the energy of a bullet fired from the world's smallest firearm, the <a href="https://en.wikipedia.org/wiki/2mm_Kolibri" rel="nofollow noreferrer">2mm Kolibri</a>, which has a muzzle energy of $E_\mathrm{lethal} \simeq 4\,\mathrm{J}$.</p>

<p>Earth orbits the Sun at 30 km/s. Depending on the direction from where the meteor arrives, it will have different speeds, but it will at least enter with the escape velocity of Earth, i.e. 11 km/s, and a typical speed is $v_\mathrm{impact} = 17\,\mathrm{km/s}$ (<a href="http://impact.ese.ic.ac.uk/ImpactEffects/effects.pdf" rel="nofollow noreferrer">Marcus et al. 2010</a>). Thus, the minimum mass to kill by a direct hit is as small as
$$
m_\mathrm{lethal} = 2 \, E_\mathrm{lethal} \, / \, v_\mathrm{impact}^2 \simeq 30 \,\mu\mathrm{g}.
$$
At an <a href="http://meteorites.wustl.edu/id/density.htm" rel="nofollow noreferrer">average density of 4 g/cm$^3$</a>, this means that a small grain of a diameter of 0.2 mm will kill you. According to the formula above, the number of such grains (or larger) that hit Earth every year is $2\times10^{11}$.
Since the surface area of Earth is 510 million $\mathrm{km}^2$, that's $n_\mathrm{hits}\sim5\times10^{-4}\,\mathrm{hits}\,\mathrm{m}^{-2}\,\mathrm{year}^{-1}$.</p>

<p>Some 7 billion people live on Earth. They each occupy roughly $1\,\mathrm{m}^2$ (and weren't allowed to protect themselves, remember), so in total they occupy an area of $A_\mathrm{folks,tot} = 7 \times 10^9\, \mathrm{m}^2$.</p>

<p>Thus, the number of people being killed by direct hit meteors every year is
$$
N_\mathrm{kill} = n_\mathrm{hits} \, \times \, A_\mathrm{folks,tot}
 = \mathbf{3\,million\,year^{-1}},
$$
or one person every 10 seconds.</p>

<strong>Death by explosion</strong>

<p>How about non-direct hits? Let's assume that the minimum size to kill you would have an energy equal to that of a hand grenade holding 100 g explosives, and that you're killed if it hits within a few meters of you, so that you "occupy" 10 m$^2$. Similar to above, you can work out that this corresponds to a meteor of ~1 cm being lethal, and that the rate at which such meteors is only $2\times10^4$ per year, so only 2-3 people would be killed in this way. Even larger explosions are even more rare. Thus, the probability of killed by a explosion is negligible compared to direct hits, so the final answer would be the above, i.e. 3 million per year.</p>

<p>Conclusion: Let's not remove the atmosphere.</p>

CC BY-SA 3.0
2017-03-26T02:32:08.147Z
That's awesome, also relevant for colonizing the moon and maybe Mars, but meteors hit those 2 bodies on average a little slower.  I think many 4J. impacts would simply leave a thin hole in a person and not be fatal, the heat, perhaps cauterizing the wound (perhaps not) but small punctures would close more quickly, less bleeding out.  Impacts wouldn't be fun but I think fewer than 3 million would be deadly.   And, I love your answer!!!  XKCD worthy.
userLTK
CC BY-SA 3.0
2017-03-26T02:36:59.880Z
Thanks @userLTK. And yes, I think you're right, I probably overestimated the death rate. It's also dubious whether the N-D relation can be extrapolated to such small sizes.
pela
CC BY-SA 3.0
2017-03-27T12:52:30.340Z
Great answer to this Fermi problem. Just a small note, you might want to specifically inlude in your units for $n_{\mathrm{hits\:per\:area}}$ a $\mathrm{year}^{-1}$.
zephyr
CC BY-SA 3.0
2017-03-27T13:29:29.707Z
I think your $1 m^2$ coverage only applies to those who are lying down (and in certain cases, that applies to a pair of people lying down heh heh).  People standing up have a cross-sectional area closer to roughly $ 0.3 m^2$  I would guess.  And if a meteor only hits our shoulder or toes, that would hurt but not kill us.
Carl Witthoft
CC BY-SA 3.0
2017-03-27T20:25:32.193Z
Thanks, @zephyr, that's included, and propagated to the result (I also had an error in the "per area" unit, which was written as m$^{-1}$).
pela
CC BY-SA 3.0
2017-03-27T20:28:17.763Z
@CarlWitthoft: But the meteors don't just come from above, but also from the front and back. They probably come _more_ from above, though, because gravity will make the paths more vertical. I'll let the 1 m$^2$ as an order-of-magnitude number, and then people can use the formulae with preferred numbers.
pela
CC BY-SA 3.0
2017-03-27T20:31:22.680Z
@CarlWitthoft: Regarding the "hits that don't kill", I assumed that since they're not allowed to go indoors, including the hospital, treating exsanguination is so difficult that we can assume that most hits result in death.
pela
CC BY-SA 3.0
2017-03-25T21:27:14.803Z
2017-03-27T20:23:25.657Z
2017-03-27T20:23:25.657Z
pela
<p>Suppose those people engage in similar activity, walking on surface etc.</p>

CC BY-SA 3.0
2017-03-25T13:47:59.440Z
What then about people killed by not having air to breath?
SE - stop firing the good guys
CC BY-SA 3.0
2017-03-27T13:26:32.280Z
@Hohmannfan your new name is "Mr. Buzzkill." :-) .  Just try to pretend for a moment that we are all  gigantic tardigrades.
Carl Witthoft
CC BY-SA 3.0
2017-03-27T13:34:27.660Z
"If you can dodge a ball you can dodge a meteor"
Carl Witthoft
<meteor><meteor-shower><meteoroid>
If Earth had no atmosphere, how many people would be killed by meteors every year?
Anixx
# If Earth had no atmosphere, how many people would be killed by meteors every year?

(Asked by: username_0 on 2017-03-25)

Suppose those people engage in similar activity, walking on surface etc.

**Tags:** meteor, meteor-shower, meteoroid

> **Comments:**
> **username_1**: What then about people killed by not having air to breath?  
> **username_2**: @Hohmannfan your new name is "Mr. Buzzkill." :-) .  Just try to pretend for a moment that we are all  gigantic tardigrades.  
> **username_2**: "If you can dodge a ball you can dodge a meteor"  

---

## 1 answers

### Answer by username_3 on 2017-03-25. Score: 10 | Accepted answer

Three millions.

For this answer to be any fun, let's first assume that before removing the atmosphere, we have equipped all humans with oxygen supplies. In return, they are not allowed to go indoors or otherwise protect themselves.

[![oxygen](https://i.sstatic.net/I2fig.png)](https://i.sstatic.net/I2fig.png)

The size of meteors — as well as most other things in the Universe — has a distribution that is well described by a power-law. The larger the meteor, the rarer they are.
Small meteors can be lethal only by a direct hit, while large meteors *in the real world* can be lethal due to the effect they have on the environment; dust can cover the sky for years and prevent the Sun from keeping us warm. However, since we have removed the atmosphere, the debris will fall down immediately, and the only way to kill us is by the explosion. But, as will be shown below, the dangerous ones are the small ones because the rate at which large ones falls off so quickly.

The number $N$ of meteors entering Earth's atmosphere every year with a diameter $D$ (measured in meters) or larger is given by ([Brown et al. 2002](http://adsabs.harvard.edu/abs/2002Natur.420..294B))
$$
\frac{N(>D)}{\mathrm{year}} \simeq 37 \left( \frac{D}{\mathrm{m}} \right)^{-2.7}.
$$

**Minimum size needed to be lethal**

What makes a meteor lethal is really outside astronomy, and someone may be able to come up with a better answer, but for the sake of the argument, let's assume that the energy needed to kill a human by a direct hit is equal to the energy of a bullet fired from the world's smallest firearm, the [2mm Kolibri](https://en.wikipedia.org/wiki/2mm_Kolibri), which has a muzzle energy of $E\_\mathrm{lethal} \simeq 4\,\mathrm{J}$.

Earth orbits the Sun at 30 km/s. Depending on the direction from where the meteor arrives, it will have different speeds, but it will at least enter with the escape velocity of Earth, i.e. 11 km/s, and a typical speed is $v\_\mathrm{impact} = 17\,\mathrm{km/s}$ ([Marcus et al. 2010](http://impact.ese.ic.ac.uk/ImpactEffects/effects.pdf)). Thus, the minimum mass to kill by a direct hit is as small as
$$
m\_\mathrm{lethal} = 2 \, E\_\mathrm{lethal} \, / \, v\_\mathrm{impact}^2 \simeq 30 \,\mu\mathrm{g}.
$$
At an [average density of 4 g/cm$^3$](http://meteorites.wustl.edu/id/density.htm), this means that a small grain of a diameter of 0.2 mm will kill you. According to the formula above, the number of such grains (or larger) that hit Earth every year is $2\times10^{11}$.
Since the surface area of Earth is 510 million $\mathrm{km}^2$, that's $n\_\mathrm{hits}\sim5\times10^{-4}\,\mathrm{hits}\,\mathrm{m}^{-2}\,\mathrm{year}^{-1}$.

Some 7 billion people live on Earth. They each occupy roughly $1\,\mathrm{m}^2$ (and weren't allowed to protect themselves, remember), so in total they occupy an area of $A\_\mathrm{folks,tot} = 7 \times 10^9\, \mathrm{m}^2$.

Thus, the number of people being killed by direct hit meteors every year is
$$
N\_\mathrm{kill} = n\_\mathrm{hits} \, \times \, A\_\mathrm{folks,tot}
= \mathbf{3\,million\,year^{-1}},
$$
or one person every 10 seconds.

**Death by explosion**

How about non-direct hits? Let's assume that the minimum size to kill you would have an energy equal to that of a hand grenade holding 100 g explosives, and that you're killed if it hits within a few meters of you, so that you "occupy" 10 m$^2$. Similar to above, you can work out that this corresponds to a meteor of ~1 cm being lethal, and that the rate at which such meteors is only $2\times10^4$ per year, so only 2-3 people would be killed in this way. Even larger explosions are even more rare. Thus, the probability of killed by a explosion is negligible compared to direct hits, so the final answer would be the above, i.e. 3 million per year.

Conclusion: Let's not remove the atmosphere.

> **Comments:**
> **username_4**: That's awesome, also relevant for colonizing the moon and maybe Mars, but meteors hit those 2 bodies on average a little slower.  I think many 4J. impacts would simply leave a thin hole in a person and not be fatal, the heat, perhaps cauterizing the wound (perhaps not) but small punctures would close more quickly, less bleeding out.  Impacts wouldn't be fun but I think fewer than 3 million would be deadly.   And, I love your answer!!!  XKCD worthy.  
> **username_3**: Thanks @username_4. And yes, I think you're right, I probably overestimated the death rate. It's also dubious whether the N-D relation can be extrapolated to such small sizes.  
> **username_5**: Great answer to this Fermi problem. Just a small note, you might want to specifically inlude in your units for $n_{\mathrm{hits\:per\:area}}$ a $\mathrm{year}^{-1}$.  
> **username_2**: I think your $1 m^2$ coverage only applies to those who are lying down (and in certain cases, that applies to a pair of people lying down heh heh).  People standing up have a cross-sectional area closer to roughly $ 0.3 m^2$  I would guess.  And if a meteor only hits our shoulder or toes, that would hurt but not kill us.  
> **username_3**: Thanks, @username_5, that's included, and propagated to the result (I also had an error in the "per area" unit, which was written as m$^{-1}$).  
> **username_3**: @username_2: But the meteors don't just come from above, but also from the front and back. They probably come _more_ from above, though, because gravity will make the paths more vertical. I'll let the 1 m$^2$ as an order-of-magnitude number, and then people can use the formulae with preferred numbers.  
> **username_3**: @username_2: Regarding the "hits that don't kill", I assumed that since they're not allowed to go indoors, including the hospital, treating exsanguination is so difficult that we can assume that most hits result in death.  

---

