Is that a Starship Titanic reference?

@0xDBFB7 yep :-)

Bit of a difference here is that the baseball in question is having a fusion reaction with the air around it. A starship in the near-vacuum of space isn't going to have that problem. (It would of course still be catastrophic, but maybe not the giant fusion explosion described.) I suspect the damage would be somewhat more localized, as it's only where matter collides with other matter that there's a problem.

"is your entire spaceship is going to suffer a sudden and gratuitous existence failure" I can't stop laughing. As for the crew, and quoting a other What-if: they "wouldn't die of anything", they would just "stop being biology and start being physics"

idk how this makes sense, significant bloating/expansion of the shear-front cannot occur at these speeds (similar to the xkcd ref: speed of sound.) that is to say that atoms affected are very affected and everything else should not be. nvm, could of just scrolled down

Sorry, what I meant was that unlike the baseball example, where the catastrophic fusion occurs before the ball even makes it to the batter (if there is indeed any of it left to get that far), this explosion would only happen at the moment of collision, not before. Not that it makes much difference for the crew of course...

The XKCD comic suggests that the center of the mushroom cloud would be a few hundred feet behind the backstop. So a short ship (say, about 19m) might get an expanding hole, a longer ship would get an expanding hole that ends in something that looks like a thermonuclear detonation. Of course, ship bulkheads are a little stronger than air, so YMMV.

@PotatoEngineer I'm no physicist, but my guess is that when up against a rock traveling at 0.9c, ship bulkheads are not much stronger than air, relatively speaking.

@Daniel true, but bulkheads are considerably more dense than air, so I'd expect an expanding cloud of fusion to expand somewhat faster due to having collected more material. Much like the pitcher is guaranteed to be quite dead, but may survive a few nanoseconds longer simply because the superheated plasma (consisting mostly of air) turning him into physics doesn't have the density to heat him up quite as quickly, compared to a plasma created by throwing the baseball through a concrete wall.

@PotatoEngineer My understanding is that the mushroom cloud is a ways behind the backstop because that's where the ball material's inertia is finally overcome by the heat of fusion, and the ball explodes. If your ship is small enough that the rock passes fully through it before that happens, then you're about to be hit from behind by a burst of radiation (mostly high-energy x-ray), and if the explosion is energetic enough, that will be followed shortly by high-velocity debris (mostly very hot vaporised rock and ship material).

@PotatoEngineer Even if the explosion happens outside the ship, the impact will release a ludicrous amount of energy along the impact path. This will initaite fusion and turn material into plasma along that path. Dumping that much heat into the atmosphere would likely produce a sufficiently rapid and energetic change in air pressure that I'd expect it to blow seals and hull weak points, leaving you leaking what little air is left. The heat of the plasma, along with the shower of radiation (again, mostly x-ray) would start fires, as well as cooking the crew and possibly frying your electronics.

How small does the rock (particle) need to be for the ship to survive relatively unharmed? 1 g? 1 single molecule?

@PotatoEngineer: One thing I felt you've missed: Heavier elements (from iron up) use up more energy than they release in fusion. The whole XKCD scenario relies on oxygen and nitrogen being lighter, and thus exothermic in fusion. The atmosphere of the starship would contribute to an explosion, the bulkheads wouldn't (unless you build them from, say, lithium, or magnesium, which I would recommend against for various safety-related reasons). ;-)

@d-b I can't say precisely, but it would have to be pretty small. A hydrogen atom moving at 0.9c has less than one thousandth of the kinetic energy of a mosquito in flight. This is obviously quite survivable. A mosquito (~5mg) moving at 0.9c has kinetic energy on the order of hundreds of gigajoules; ten times the yield of the MOAB, the most powerful non-nuclear bomb ever used operationally. Not all of it will be effectively transferred to your spacecraft, but there's enough energy there that what does transfer is likely to be a problem. Somewhere between those two is your safety threshold.

The XKCD script underestimates the energy of the collision from what I can tell; 0.9c impact has energy sufficient to break protons/neturons into quarks. Fusion/Fission are too low energy to model what happens. Explosion "center" may be behind the batter, but that is because it is a bigger explosion than the smaller ones that occurred all along its flight path, and they'd get swallowed up (in the baseball case).

+1 for the hitchhiker's reference!