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shminux comments on To reduce astronomical waste: take your time, then go very fast - Less Wrong
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I used relativistic beaming, where nearly all of the particles come from straight ahead, multiplied by the beaming factor. Alternatively, the calculation can be done fully Newtonian in the comoving frame, with the spaceship's mass multiplied by gamma (about 10 when v=.99c).
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 :-)