## Probability of dying on impact from space debris

For the discussion of math. Duh.

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Xaoc
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### Probability of dying on impact from space debris

So, I've been going through some of my old DVD's and I ran across a series from the early 2000's called Dead Like Me. In the first episode the main character is struck and killed by a toilet seat from the deorbiting MIR space station and killed instantly. That got me thinking about how improbable something like that would be so I started looking for stats related to that sort of event.

So far, I've only come across two things that seem even remotely reliable. The first is attributed to the EU Space Agency of "The annual risk of a single person to be severely injured by a re-entering piece of space debris is about 1 in 100,000,000,000" from: https://www.livescience.com/33511-falli ... -risk.html . In the same article they mention that only a single person is known to have ever been struck by space debris, and that it was so small and traveling slowly enough as to be fluttering.

Full disclosure: I have not been able to independently verify that the original quote that Live Science attributes to the EUSA is accurate. However, it is also repeated in a large number of locations ( ie: https://www.space.com/13324-dead-fallin ... risks.html ), however, most of those locations are news sites, and let's be honest... how trustworthy are they really?

The other useful source that I've found was wikipedia, specifically: https://en.wikipedia.org/wiki/Space_debris#Sources

Since only one person has ever actually been struck by a piece of space debris, I get that it is incredibly unlikely. Also, since NASA is basically refusing to attempt the calculations, stating that it is impossible, my hopes and expectations are low. However...

If we assume that the event in the first episode of the show was actually happened, what is a good ballpark for the likelihood of that happening? (Note: in the show it is stated that she was struck with such violence that finding a large enough chunk of her body to remove her soul from would have been very difficult.)

Sableagle
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### Re: Probability of dying on impact from space debris

Among the difficulties would be combining the latitudinal distribution of space debris with that of humanity and coming up with a probability that it's on course for a person.

That splatter from a toilet seat, though?

The Impact Effects Program has limiting lower bounds. I went for a 1 m iron ball at 7 km/s and 10° down-angle, 1 km away. It's unimpressive:
https://impact.ese.ic.ac.uk/ImpactEarth/cgi-bin/crater.cgi?dist=1&distanceUnits=1&diam=1&diameterUnits=1&pdens=&pdens_select=8000&vel=7&velocityUnits=1&theta=10&wdepth=&wdepthUnits=1&tdens=2500

Energy before atmospheric entry: 1.03 x 1011 Joules = 0.25 x 10-4 MegaTons TNT
The average interval between impacts of this size somewhere on Earth is less than 1 month.

The projectile lands intact, with a velocity 0.007 km/s = 0.00435 miles/s.
The energy lost in the atmosphere is 1.03 x 1011 Joules = 0.25 x 10-4 MegaTons.
Alright, so it's a big ball of iron coming at an impressive enough running speed and that's potentially messy, but it's entering the atmosphere with "Yeah, yeah, happens every month" levels of energy and even if that didn't tell you it's not going to do much the comparison of "energy before atmospheric entry" and "energy lost in the atmosphere" suggests it'll just go thud.

Transient Crater Diameter: 1.36 meters ( = 4.46 feet )
Transient Crater Depth: 48.1 cm ( = 18.9 inches )

Final Crater Diameter: 1.7 meters ( = 5.58 feet )
Final Crater Depth: 36.2 cm ( = 14.3 inches )

The air blast will arrive approximately 3.03 seconds after impact.
Peak Overpressure: 15.8 Pa = 0.000158 bars = 0.00224 psi
Max wind velocity: 0.0372 m/s = 0.0833 mph
Sound Intensity: 24 dB (Easily Heard)
Awwwwww, such a cute little impact.

That's one sodding big lump of iron compared to any normal toilet seat, too, at 4188.8 kg of iron. 888, a beast and a third.
Toilet seats on Amazon are listed as 0.8 to 2.1 kg, so Mir toilet seats were presumably around 1/3000 the mass of that iron ball.
Now, how big a chunk is big enough to extract a soul from it? Errr ... huh.
Well, slashdot reckon 3 GJ to vapourise a human, but that's going a bit further than "hard to find a big chunk."
I can say that a .50 BMG impact is nowhere near enough. That leaves many orders of magnitude. We'll need to narrow things down ...
... or will we? There's the "rule of nines" for calculating burn areas. Is dividing a body into nines enough? Front and back of torso, front and back of abdomen, arms, thighs, lower legs and head: eleven pieces. Is that enough, or do we need to divide them up further for the damage so vaguely described in the episode? Let's divide each one into four! That's at least three hits per eleventh plus the separating hits at neck, shoulder et cetera. We could call it about 40 hits, or 0.54 MJ. Alternatively, we could call it 0.95 kg of HE, because that's what's in an 81mm HE round. Assuming it's TNT, that's about 4 MJ. Well, we're within an order of magnitude. That'll do for now.
1kg projectile, 2 megajoules of kinetic energy? That makes 2000000 = 0.5 * 1 * v2 so v = 2000, three hundred times faster than that iron ball impact.
How to achieve that? Well, try having it hit the atmosphere faster.
https://impact.ese.ic.ac.uk/ImpactEarth/cgi-bin/crater.cgi?dist=1&distanceUnits=1&diam=1&diameterUnits=1&pdens=&pdens_select=8000&vel=14&velocityUnits=1&theta=10&wdepth=&wdepthUnits=1&tdens=2500

Impact Velocity: 14.00 km per second ( = 8.69 miles per second )
Energy before atmospheric entry: 4.11 x 1011 Joules = 0.98 x 10-4 MegaTons TNT
The average interval between impacts of this size somewhere on Earth is 0.1 years
The projectile lands intact, with a velocity 0.014 km/s = 0.00869 miles/s.
The energy lost in the atmosphere is 4.11 x 1011 Joules = 0.98 x 10-4 MegaTons.

Working so far, but that's doubling. We need three hundred times the velocity. Let's try tripling.
Impact Velocity: 21.00 km per second ( = 13.00 miles per second )
Energy before atmospheric entry: 9.24 x 1011 Joules = 0.22 x 10-3 MegaTons TNT
The average interval between impacts of this size somewhere on Earth is 0.2 years
The projectile lands intact, with a velocity 0.021 km/s = 0.013 miles/s.
The energy lost in the atmosphere is 9.24 x 1011 Joules = 0.22 x 10-3 MegaTons.

... and ten times that:

Impact Velocity: 210.00 km per second ( = 130.00 miles per second ) (Your chosen velocity is higher than the maximum for an object orbiting the sun)
The projectile begins to breakup at an altitude of 54300 meters = 178000 ft
The projectile bursts into a cloud of fragments at an altitude of 52200 meters = 171000 ft
The residual velocity of the projectile fragments after the burst is 198 km/s = 123 miles/s
The energy of the airburst is 1.07 x 1013 Joules = 0.25 x 10-2 MegaTons.

Well, nope. Even our 1 m iron ball isn't going to survive entry into the atmosphere at fast enough speed to hit the ground at 2 km/s. A toilet seat stands no chance. This is a bit like firing a .44 magnum at someone, seeing that the bullet slowed to a stop without getting out of his back and then trying to throw a ring-pull hard enough to get it all the way through him. Even the 1 m iron ball at 21 m/s has 929 kJ of kinetic energy, into the splattering range but shy of a quarter of the yield of 0.95 kg of TNT. The 1 kg toilet seat would have 222 Joules at that velocity, and that's .380 ACP energy range. I'm sure it's potentially lethal but it's nothing like what was described.

Now, the entire International Space Station is 417,289 kg of stuff, but it's more of an empty beer can than a bullet, and if it falls into the atmosphere on a collision course with your head ...
... it's going to come apart.

Now, a "once in 7000 years" impact, scoring a direct hit?

https://impact.ese.ic.ac.uk/ImpactEarth/cgi-bin/crater.cgi?dist=10&distanceUnits=1&diam=200&diameterUnits=1&pdens=&pdens_select=8000&vel=14&velocityUnits=1&theta=80&wdepth=&wdepthUnits=1&tdens=2500

The impact energy is 3.23 x 1018 Joules = 7.71 x 102MegaTons.
Transient Crater Diameter: 4.27 km ( = 2.65 miles )
Transient Crater Depth: 1.51 km ( = 0.938 miles )
Final Crater Diameter: 5.19 km ( = 3.22 miles )
Final Crater Depth: 486 meters ( = 1590 feet ) Richter Scale Magnitude: 6.5
Mercalli Scale Intensity at a distance of 10 km:
VII. Damage negligible in buildings of good design and construction; slight to moderate in well-built ordinary structures; considerable damage in poorly built or badly designed structures; some chimneys broken.
VIII. Damage slight in specially designed structures; considerable damage in ordinary substantial buildings with partial collapse. Damage great in poorly built structures. Fall of chimneys, factory stacks, columns, monuments, walls. Heavy furniture overturned.
The ejecta will arrive approximately 45.2 seconds after the impact.
At your position there is a fine dusting of ejecta with occasional larger fragments
Average Ejecta Thickness: 2.97 meters ( = 9.74 feet )
Mean Fragment Diameter: 14.3 meters ( = 47 feet )
Multistory wall-bearing buildings will collapse.
Wood frame buildings will almost completely collapse.
Multistory steel-framed office-type buildings will suffer extreme frame distortion, incipient collapse.
Highway truss bridges will collapse.
Highway girder bridges will collapse.
Glass windows may shatter.
Glass windows will shatter.
Cars and trucks will be largely displaced and grossly distorted and will require rebuilding before use.
Up to 90 percent of trees blown down; remainder stripped of branches and leaves.

That'd do it.
Oh, Willie McBride, it was all done in vain.