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    Re: Lunar Distance Puzzle
    From: Frank Reed
    Date: 2011 Aug 20, 22:50 -0700

    Geoffrey, you asked:
    "From the ensuing dialogue about refraction, is the consensus now that the answer is "no", since any refraction model used must have some information about altitudes?"

    I would say "no" to that "no". First of all, the problem that Dave has proposed really is solvable in the sense that if you set your software, whatever that may be, to seek a minimization of some sort, it will find a lat, lon position and ALSO Greenwich Time very close to the inputs which (independently) generated the hypothetical observations. As Dave has said, "It REALLY does work!" And the lingering question has been "how the heck does it do it?" The baseline problem is, as I put it, an "either/or proposition". That is, if you throw in an error in GMT, it yields a corresponding error in position in a one-to-one fashion. So there must be some very small factor in play that separately yields positional information. Now, I am not totally convinced of this yet, simply because I haven't spent any serious time on it (I am sorry to say), but I think Herbert is probably correct in thinking that the refraction model is providing implicit altitude data. Picture one star near the zenith, another star a degree above the horizon, and the Moon halfway in between. The observed distances would give you the altitude of the Moon. This is a tough way to get altitudes, and as Herbert has already pointed out, you could do the same thing by measuring star-to-star distances. While impractical for manual observations, this does have some merit for a computerized system. Imagine measuring the angles between dozens of stars scattered all across the sky. They would show a distinctive "bunching" pattern that could be used to determine the local vertical even if there's no horizon visible, no altitudes measured. I described something like this a couple of years ago, and I even wrote a few lines of code to make something practical out of it, but it got lost in the shuffle. If you do something like this, and then throw in just one actual lunar distance, then you get latitude, longitude, and Greenwich Time all at once. The next step is to see if this actually makes sense. And after that to see if we can use our model of the process to make reliable predictions about the specific situations where this technique would never work (even in principle) and other cases where it might work well enough to be made practical, which is definitely possible with a large number of automated observations and MAY even be possible with carefully selected cases for manual sextant observations. I suspect right now that this process would fail if the three stars are sitting right on the limb of the Moon. Larger distances yield bigger differences in refraction (and also if we're using real limb-to-star observations, the limb would be refracted exactly like the star positions in the case of near occultations).

    By the way, for those of you who use my online calculator or if you have a copy of my standalone software (not the expired beta version), you can "turn off" refraction simply by setting the air pressure to a very low value like 0.01 inches Hg. If you set it to zero exactly, you'll discover that the software interprets this as missing input data and reverts to 29.80 inches Hg. But 0.01 is so low that the refraction is effectively zeroed out of the model even close to the horizon.

    -FER

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