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    Re: Lunar Distance Puzzle
    From: Frank Reed
    Date: 2011 Aug 16, 22:43 -0700

    Herbert, you wrote:
    "Frank is right when he says that in a universe without refraction, the third distance does not add any information that isn't already contained in the first two."

    I'm not convinced that I was right on this score yet, by the way. It was just a first guess based on the sensitivity to the refraction details that you and a couple of other folks mentioned. I'm still trying to puzzle out what's going on, though I have to say I've only had a few minutes here and there to sit down and think about it. I do wonder whether Dave's case may be unusually tough because Altair and Vega were nearly in the same direction (position angle) from the Moon at the time of the "observations" and also relatively perpendicular to the Moon's motion.

    Here's a hypothetical case I've been thinking through just in the past fifteen minutes. Let's go to some spot on the Earth with the Moon reasonably high in the sky and find some stars around the Moon at some time T that are all five minutes of arc from the Moon's limb to the nearest second of arc and spread around the Moon approximately every 45 degrees in position angle (they're there if we go faint enough). So one star is five minutes of arc above the Moon's north pole as we see it in the sky, one five minutes of arc from the south pole, one five minutes of arc away from the leading limb of the Moon, one five minutes from the trailing limb, and four more at points halfway in between those. Looking at each of those in pairs, what happens to the implied position on the Earth if I change the time by one minute? It seems like there might be a simultaneous determination of time and position if I use one star aligned with the leading or trailing edge and two of the stars at 45 degree angles from the "cardinal points" of position angle.

    -FER


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