This is why Star Trek's Enterprise has that forward-facing deflector dish. It wouldn't last very long without something to prevent such collisions.
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It's actually a legit concern with any (hypothetical) interstellar mission. Even hydrogen atoms will hit with significant force. Dust hits like nukes, and an asteroid is just game over.
The maxim used in a lot of sci-fi is an ablative armour plate. Often in the form of ice. Interstellar ships would likely aldo be needle like, to minimise their cross section. We could also use electric and/or magnetic fields to move smaller particles out of the way.
As for densities, I believe it's a couple of hydrogen ions per m^3 . Dust is rarer, but still present. It's only bigger rocks that are rare enough to just hope to avoid.
Didn't one of the space shuttles almost holed by a fleck of paint?
Challenger had a fleck of paint damage one of its windows on an early mission.
The ISS has been pinholed by debris a few times. Likely paint. The shuttle was damaged by foam breaking off, amongst other events.
By comparison orbital velocity is around 7km/s, while a bullet is around 0.367km/s. Any mismatch will push debris up to bullet speeds easily.
As for relativistic speeds. C is 300,000km/s assuming you get up to 1/3C (barely relativistic) you are moving at 100,000km/s or 14,000x faster than the ISS moves, or 39000x faster than a bullet. A 10g rock would hit with 10kilotons of energy. About 2/3 the energy of the first atom. bombs.
There's an xkcd about this, it would basically become a nuke near the speed of light
By my back-of-the -envelope math it is 4,500,000,000 joules. The Hiroshima bomb is listed at approximately 10,000,000,000,000 joules. I bet xkcd is far more accurate, though.
How did you calculate that? The question didn't even mention a specific speed, just "near the speed of light".
The kinetic energy for a grain of sand near the speed of light is somewhere between "quite a lot" and "literally infinity" (which is, in a sense, the reason you can't actually reach light speed without a way to supply infinite energy).
Ke=1/2 M V^2 Not relativistic. So wildly low. But certainly a low bound. My point being that nuclear bomb grade energy is certainly in the ballpark.
Did you assume the sand as having no velocity relative to the object going C?
I did. See above
Depends on the strength of your navigational deflector.
Yes. For the effects, look up pictures of the damage that space debris has on spacecrafts.
Mind to post your favourite example?
The fastest human made object moves at 1/1000 of the speed of light