On the assumption of T-normal conditions

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Jedi Master Spock
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On the assumption of T-normal conditions

Post by Jedi Master Spock » Thu Oct 23, 2008 4:07 pm

Very often, I see the assumption of T-normal conditions made without adequate justification - and subsequent understatement of the proper error for the analysis in question.

There are several things to keep in mind. While the assumption of T-normal conditions is reasonable, it is not necessary, and in the interest of testing the strength of your propositions, you should consider how much precision your estimates have.

First, atmosphere. Humans can handle oxygen concentrations and atmospheric pressures in a wide range, all the way down to about 0.07 atmospheres of pure oxygen for extended periods, or up to about half an atmosphere partial pressure of oxygen, with short term toxicity occurring around 1.6 atmospheres. Partial pressure of nitrogen can go up to about 3 atmospheres before you start getting problems; you could also have some noble gases in the mix, possibly.

You can easily have 0.3-3.0 atmospheres of pressure provided people have a little time to adjust to it. Thus, analysis relying on atmospheric pressure when such is not in any fashion explicitly bounded will be accurate to no more than half an order of magnitude.

Second, local value for g. In order to consider measuring g from the rate things fall, and the way people move, you might ask a high school physics teacher about what sort of precision he expects from his students in trying to measure g from timing falling objects.

You will be lucky to get within 10% of g by measuring falling objects onscreen in a casual VS-debater fashion. This is further complicated by atmospheric drag, which as we've pointed out, could be substantially more or less. (See Saxton re: Endor). Even if you are a strict documentarian, the off-screen knowledge that all scenes were actually filmed within 1% of the local g value you experience at home should not be taken to be a guarantee. If you want to be safe, this would be +/- 20%, in cases where you do not know about the atmosphere, or +/- 10%, if you are certain total pressure is near T-normal. If you have nothing in the description, then it could easily be half a g - or one and a half.

Third, we now have the question of planetary mass and diameter, given an unknown density. M ~ density * r^3; g ~ M/r^2 ~ r * density. Density is most likely between 3 and 6 g/cc even just going by our own solar system (extrasolar rocky planet density is an open field of study at the moment), so we have a factor of two for variation in radius, translating to a factor of eight in volume (but only four in mass, as the planet is assumed to be half the density at that point). It's hypothetically possible for us to have anything from 2 to 20 g/cc (ten, a thousand, and a hundred, respectively), but we're generally expecting something between 0.5-1.1 times T-normal density, because that's what large rocky bodies in our solar system look like.

So in summary, if we see briefly what looks like approximately T-normal conditions and healthy happy humans moving normally with falling objects that don't seem too far off in speed, we should suspect between 0.6-4 times the Earth's mass. In most cases (especially comics, novels, and detached descriptions) we have no reason to expect much more precision than that, and in fact, should expand that to about .4-5 times Earth's mass to be safe if we don't actually see how people move and objects fall, and we should like to see an order of magnitude variation to claim absolutely certain contradiction.

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