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It doesn't seem that a relativistic ship travelling in deep space would need much shielding due to particles at rest in the space frame, appearing relativisitc now in the ship's frame. Here's the calculation I did:

Let's imagine a ship the size of a space shuttle travelling with γ of 7 (β = 0.99 ). I assume that when a society can build such a ship, it will be a decent size, comparable to our space shutttle, and use such values therein. I'll approximate the cockpit as a flat circle(normal vector parrallel to direction of travel) with a diameter of 8.7m, for an area of 59 m^2. Now, let's allow 1 proton per m^3 (over estimate) in deep space and sort them in an area of 59 m^2 so that, at a particular time, 30 protons or so will impact the cockpit of our ship. I know that 1 proton per m^3 is a volume density, so making such a number an area density is, again, an overestimate.

In the ship's frame, the ship will be at rest, and 30 protons will impact the cockpit. THe rest mass of a proton is 900 MeV, we have 30, and they each have γ=7, so the ship will encounter an energy of 1.89(10^11) eV worth of energy.

Compare this to the energy of a dental X-ray. E=hf, f = 10^17, so the energy of a photon here is 65eV. In a typical dental X-ray, there would be 10^26 particles or so, so we have about 10^27 eV in a dental X-ray, and ~10^11 eV from outerspace protons.

Thus, a ship travelling with a γ = 7 will encounter much less energy from protons in deep space than it would by bombarding it with a dental X-ray. It is true that the deep space protons themselves are far more energetic than a dental X-ray photon, but there are so few, would it even be worth much worry? I would guess there are more relativistic protons from our own atmosphere via solar wind that pass through a human body per second than a ship travelling at light speed would have to worry about in deep space.

Does this calculation make sense? Why is shielding from outer-space protons appearing relatvistic in the ship's frame so much of a problem for near light speed travel? Or maybe its not so big a deal for β=0.99 but is more of a concern for higher β's.

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# Would a relativistic ship really need much shielding?

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