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The Van Allen belts are thickest at the poles. Apollo escaped pretty close to the equator for this reason. At the poles, they are also more energetic. At the equator, they're mainly beta particles and alpha particles.
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Thickest at the poles? Are you sure? I don't know a whole lot about it, but all of the pictures I've seen of the Van Allen belts are, well, belts. As in, around the equator. And since they're held there and energized by the Earth's magnetic field, I would think that at the poles any energetic particles would spiral down and cause aurorae, though I'm not an expert on that either.
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I think the air resistance must be huge. A cyclist going 20 mph expends 90% of his or her energy overcoming are resistance. Of course cyclists don't have to overcome gravity (I refuse to cycle uphill) but I'd still wager that air resistance will be significant.
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I think a conical rocket made out of smooth metal is a bit more aerodynamic than a cyclist. And it would also get above most of the atmosphere pretty quickly, as in before the first stage seperated. So air resistance is still a factor, but it hardly uses up 90% of the energy.