A question about impacts at near c speed

• A question about impacts at near c speed by SergioZ82 on 27 Mar, 2018 07:22
• Hi,
  I was wondering what would happen to a spaceship that impacted with atoms (hydrogen and helium mainly) at the speed of light.
  I've searched on this forum and on the internet in general (i.e Quora) but I've found conflicting replies: someone says it creates radiations, others that the atoms pass through the ship without damages if not to electronic components and still others say that the ship explodes because the released kinetic energy.
  Which one is correct answer?
  
  I know that light speed is unreachable for the matter so let's hypothesize a "lower" speed: 0.8c.
  I tried to calculate the released energy at such speed (very amateurish, I'm not even sure I used the correct formula) and the result was about 7 Mev. Aren't they enough to obtain nuclear fission? The steel of the hull is not a fissionable material but what would happen to it when it's hit by a constant shower of atoms at above mentioned speed? Does the impact release enough heat to melt the hull?
  
  Please notice: I'm specifically curious about atoms, because it's impossibile to not have a constant impact during a light years long journey. Molecules, dust or bigger objects are rarer but unavoidably deadly.
  
  Thank you
• #1 by nicp on 27 Mar, 2018 07:37
• Well, this xkcd cartoon explains quite a lot... https://what-if.xkcd.com/1/
• #2 by Bynaus on 27 Mar, 2018 07:52
• It really depends on the density of the relativistic atoms. The xkcd comic with the giant thermonuclear explosion is for the case where the relativistic object (the baseball) moves within the Earth's atmosphere.
  
  You could consider cosmic rays to be the inverted situation: they move at near c speed, and collide with solar system objects, in which they trigger nuclear spallation reactions (e.g. in meteorites or in the Earth's atmosphere). So here, there is no noticeable "kinetic-thermal" effect because their number density is very low (about 1 proton per cm^2 per second or so).
  
  So depending on what density you have in mind, your effects will vary with the density of the relativistic particles and thus plot somewhere between the above extremes.
• #3 by SergioZ82 on 27 Mar, 2018 08:45
• Quote from: Bynaus on 27 Mar, 2018 07:52

  It really depends on the density of the relativistic atoms. The xkcd comic with the giant thermonuclear explosion is for the case where the relativistic object (the baseball) moves within the Earth's atmosphere.
  
  You could consider cosmic rays to be the inverted situation: they move at near c speed, and collide with solar system objects, in which they trigger nuclear spallation reactions (e.g. in meteorites or in the Earth's atmosphere). So here, there is no noticeable "kinetic-thermal" effect because their number density is very low (about 1 proton per cm^2 per second or so).
  
  So depending on what density you have in mind, your effects will vary with the density of the relativistic particles and thus plot somewhere between the above extremes.
  

  
  
  I had in mind the drifting atoms that are the most common in space, like helium and hydrogen (I hadn't thought to cosmic rays). I've read that as empty as space can be there always are a few atoms per a cubic centimeter (in the most optimistic case). Hence my speculation is this: the front section of a spaceship will inevitably be measured in square meters, so impacts are unavoidable. Then I thought how many cubic centimeters there are along a straight line 300.000 Km long, a distance that would be covered in little more than a second at 0.8c. But if we wanted to reach Proxima Centauri for example we should travel for almost 5 years to cover something like 38 thousand billions kilometers of space and along this distance the number of atoms would become considerable and virtually constant.
  
  Given the above consideration, wouldn't the baseball example be applicable?
  
  
• #4 by Bynaus on 27 Mar, 2018 09:21
• Well, you could just add up all the atoms you would likely encounter on your trip, and then compare with the atmosphere (how deep do you have to go there to encounter the same number?). I suspect that you will still get fewer particles with the spaceship even for a multi-LY voyage. Also for the baseball, the whole energy is released on a nanosecond timescale, whereas for a spaceship, it is released over many years. So all in all, you should expect the effect for the spaceship to be much closer to the cosmic ray situation than the baseball situation.
• #5 by eeergo on 27 Mar, 2018 09:21
• 
  Basic relativity: it doesn't matter if you're the spaceship accelerating relativistically through interstellar gas, or you're the scientist on Earth speeding up gas (protons, for instance) in a particle accelerator to research particle physics
  
  
  Therefore, there's little use in getting bogged down on spacecraft characteristics, or uncertainties on the particle density of the particular area you'd be travelling through to reach your preferred destination -- you can estimate the effects by just looking at relativistic particle-matter interactions and what a suitable dose of those high-energy particles would amount up to.
  
  
  The xkcd post goes through some of the details of what happens when things pass through other things at very high speeds. You can also learn about it, in a less tongue-on-cheek tone based on actual measurements, searching how any "beam stop" particle physics experiments work. In essence, you electrify (ionize) hydrogen gas to obtain protons, accelerate them through electric and magnetic fields until they are relativistic while you store them in a ring (in a path that has been evacuated to interstellar-space-level vacuum) and at some point let them fling out through centrifugal force to a target. This part is the real-life analogous to relativistic interstellar travel. Usually dose rates will be much higher than what you'd expect in a spaceship, because in these experiments you're looking to produce as many particles as you can, but you can scale by the appropriate amount since the collisions are mostly independent of each other.
  
  
  Short answer is: all the above answers you mention are correct, depending on the process you're looking at. Cross-sections are probabilistic; that is, there's some probability *any* particle of any size and energy will pass through a given target unimpeded, although this probability will be small for massive, ionizing particles such as alphas or even protons. Gammas and muons will travel farther and possibly scatter while travelling through matter, ionizing things on the way. Electrons will be somewhere in between. You won't worry too much about neutrinos unless passing next to a supernova Fission is possible when neutrons are encountered, if as you say the material is fissile, otherwise activation will likely occur - although you can have the neutron moderated down in energy, to then be absorbed (with gamma emission), or even reflected, if it encounters the right materials. In general you won't get macroscopic effects such as melting, because there won't be a well-collimated, narrow beam you're travelling through unless you're really unlucky. See the attached picture of T2K's beam target for an extreme case of what long-term proton bombardment looks like on a titanium alloy SSEM (Segmented Secondary Emission Monitor, basically a foil that lets you know how many particles you're outputting through the accelerator beam).
  
  
  PS: What we call "cosmic rays" are 99% of the times protons, electrons or alphas (helium nuclei)

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• #6 by SergioZ82 on 28 Mar, 2018 08:11
• Thank you all, in particular to eeergo for his detailed reply.
  
  So, let me recap to see if I got this right:
  
  for a spaceship that travels at 80% of the speed of light:
  
  1) the impact with atoms adrift in space is negligible. At worst the hull will be pitted with burnt spots like that in eeergo's picture but nothing really dangerous for the ship integrity
  2) what happens at atomic scale during an impact is similar to what happens in particle accelerators
  3) the impact with free electrons or neutrons could trigger a nuclear fission but since the hull material is not (likely) fissile there won't be a chain reaction, so no melting. 
  4) the impact with atoms and/or particles and cosmic rays in generals releases large amounts of gamma/x rays, so the main problem is not the hull resistance but the shielding of crew and electronic equipment.
  
  Is this correct?
  
  Another question, a bit out of context: at what speed does the mass increment begin when a particle approaches the speed of light?
• #7 by eeergo on 28 Mar, 2018 15:24
• Quote from: SergioZ82 on 28 Mar, 2018 08:11

  for a spaceship that travels at 80% of the speed of light:
  3) the impact with free electrons or neutrons could trigger a nuclear fission but since the hull material is not (likely) fissile there won't be a chain reaction, so no melting.
  

  Electrons don't trigger fission.
  
  You don't need fission to cause melting, see electron-bream welding But even with a uranium hull (unlikely ) you'd need a pretty unreasonable neutron flux to sustain a chain reaction, you'd have other things to worry about first. Bottom line is fission isn't an important showstopper when considering radiation induced damage (which is what hitting gas at relativistic speeds causes).
  
  

  Quote

  4) the impact with atoms and/or particles and cosmic rays in generals releases large amounts of gamma/x rays, so the main problem is not the hull resistance but the shielding of crew and electronic equipment.
  

  That's the idea.
  
  

  Quote

  Another question, a bit out of context: at what speed does the mass increment begin when a particle approaches the speed of light?
  

  
  There's no threshold (substitute a small velocity value on the Lorentz transform formulas to see for yourself how much even everyday life speeds get you: not much, but something), but the relativistic limit (where such effects become important) is usually set at 0.2c.
  
  More important is time dilation, since that causes particle lifetimes (and therefore penetration ranges) to increase: see cosmic muons for example.
• #8 by RonM on 28 Mar, 2018 16:02
• What's the minimum speed a strike from a stray atom produces radiation?
• #9 by eeergo on 28 Mar, 2018 17:07
• Quote from: RonM on 28 Mar, 2018 16:02

  What's the minimum speed a strike from a stray atom produces radiation?
  

  
  That's a tricky question as it involves many variables: it's as if you ask at what temperature matter starts emitting radiation.
  
  Theorist answer: no threshold.
  Experimentalist answer: it depends on the material it impacts with (physicochemical properties and shape), the particle (atom in the most rigorous sense of your question) and its energy, and most of all where you start considering an emission "radiation", in the sense of concerning for human or electronics sense.
  
  There are several primary effects (and quite a zoo of secondary/tertiary/etc ones) depending on the energy. These are most commonly described by the Bethe formula, with corrections if necessary (or complete reformulations at very low energies), through the stopping power (or mean energy loss per unit of matter traversed).
  
  http://pdg.lbl.gov/2005/reviews/passagerpp.pdf
  
  A somewhat important difference between spacecraft moving through space gas and particle accelerators that I didn't think about before but is quite obvious is: the processes by which particles are accelerated require ionization of the atoms at moderate energies. If you ram against them, they won't be ionized in the beginning. This will in principle give you several different effects, as well as more Bremmsstrahlung (stopping radiation from electrons).