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Luke_A_Somers comments on To reduce astronomical waste: take your time, then go very fast - Less Wrong
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So you multiplied the gas pressure by the beaming factor? But the gas pressure at rest is proportional to the temperature of the gas, and the forward-facing pressure of a relativistic ship couldn't possibly care less about the temperature of the gas.
Well to be more precise, I took the comoving stress energy tensor of photon gas, rho*diag(1,1/3,1/3,1/3) in the natural units, and Lorentz transformed it. Same for dust, only its comoving stress energy tensor is rho*diag(1,0,0,0).
Okay, so you weren't basing the braking pressure of the gas off of the atmospheric pressure of the gas, but simply off of its density?
I guess I shouldn't be too shocked that super-high vacuum is approximately frictionless.
Gas pressure at rest is also proportional to the number of molecules. (PV=nRT) Which at constant volume and known composition basically means mass, i.e. how much gas you’re hitting, which does matter.
That said, I still don’t get the exact calculation, so I’m not sure that it’s correct reasoning.
My argument is typical physicist fare - note that the answer has a spurious dependence, therefore it's wrong. That it also has one of the right dependences wouldn't matter.
I was off on what the implied steps in the derivation were, so it didn't have the problem I described.
At the interstellar temperatures (2.7K or so) the ideal gas pressure has negligible contribution to the kinetic friction at near-light speeds. The situation is somewhat different for photon gas, where pressure is always large, of the order of density * speed of light^2, not density * RT. But in the end it does not matter, since the CMB density is much much less than the dust density even in the intergalactic space.
OK, I got it, I think. I was confused both about the question and the answer :-)