Polar orbiters and the testing of sci-fi

I'm reading Anathem because Paul told me to. And because I'm enjoying it. And because its good and thick and will sustain lots of time. Read Paul's review if you're interested in an overview; I'm not going to do that, if only because I haven't finished it (I'm about half way through, if you care). Some of the following gives away some details of the plot that Paul is careful not to give away, so don't read on if you're intending to read it.

Its mostly sci-fi tosh, of course, but there is some philosophy thrown in, and perhaps more than that its sort-of inspiring to an intellectual type person because it promotes the idea that the intellectual life is the best. Now its easy enough to say this in a book; and its easy enough to mine great ideas from the past to pad out such a work. But its rather hard to do so without making teensy little mistakes as you go along that reveal the shallowness of your understanding. In the maths-type bits, there are two I've found so far:

* in the discussion of nerve-gas farting dragons (this is one of the intellectual sections, and quite interesting, but I don't know who the concept is lifted from) the question arises as to how many different types there might be: perhaps there are... 10 different colours. So thats 10. But they might be striped: so thats another 100. But no, says a character: red-red, for example, has already been counted. So thats only an extra 90. But this if course is wrong too: red-orange is effectively the same as orange-red. So its only an extra 45.

* more interestingly, part of the plot hinges on polar orbiting satellites. In the diagrams in the book, representing a sky-view (which we can presume, though I don't think this is mentioned, be assumed to be corrected to a view from directly under the pole) the tracks of these all look like straight lines crossing at the pole. However... polar orbiters don't do this. They are inclined at an angle of about 8 degrees, typically (as [[Polar orbit]] will tell you, but only because I just added it; this was the source I found. Ha, but the gory details are at [[Sun-synchronous orbit]]). There is a good, and interesting, reason for this: they generally want to be sun-synchronous, which means their orbital plane has to shift as the earth rotates around the sun. If the orbital plane remained fixed with respect to the fixed stars, an orbit that came round at noon/midnight in summer would be at sunrise/set in winterautumn [oops - corrected - W]. But the earth is not a sphere, there is an equitorial bulge, which exerts a torque on the satellite in any orbit not equatorial or exactly polar, and which will cause the orbit to precess; it happens that 8 degrees off causes the desired degree of precession. The world of Anathem isn't earth (at least this isn't acknowledged at the start, and if it turns out to be part of some great denoument at the end, I haven't got there yet) but its a rotating planet so it has an equitorial bulge and we can assume that it will have a similar need for sun-synchronous satellites. Now as it happens the particular object that the plot is interested in *doesn't* need to be in a sun-sync orbit, probably, so unless it deliberately went into such an orbit to hide (possible) it could have been picked out quite quickly by being in an exactly-polar orbit. Either way, having all the orbits cross at the pole is wrong. Ta-ra!