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    Re: Lunar Distance Puzzle
    From: Frank Reed
    Date: 2011 Aug 19, 09:22 -0700

    Herbert, you wrote:
    "can we leave the limb out of this and replace it by the moon's center or is it essential to your problem? In other words, I just want to confirm that you are not thinking of using differential parallax (augmentation or such), particularly as you are saying the moon is high up."

    Yes, we can leave it out, and yes, I can confirm that I was not thinking of differential parallax.

    In any case, when I thought it through a bit further I got right back to square one. If we limit ourselves to any pair of lunar distances or in my hypothetical case, any pair of stars sitting right on the Moon's limb, the observations uniquely determine the Moon's topocentric position in the sky (well, really there might be two solutions but widely separated so no issue to distinguish them). If we have those distances to the nearest second of arc, then, assuming the distances are in relatively perpendicular directions from the Moon, we can calculate the RA and Dec of the Moon to the nearest second of arc for that moment of time. A third distance, or a fourth or fifth, will merely be consistent with those. It doesn't change the derived position except to the extent that a few more points can improve the quality of the position in the usual statistical way. If we change the time, we will get a different position, or if we change the observer's location on the Earth, we get a different position, but it's an either/or proposition. Either you get GMT from measuring lunar distances or you get latitude and longitude at a known GMT.

    But this still leaves us with the problem that the "black box" solutions say otherwise. Clearly Dave W. and Harri and Peter are solving somehow for GMT and position at the same time, but it's highly sensitive to the exact position data and the exact model specifications. There must be some slowly varying parameter in there. I still can't see what's going on though I wouldn't be surprised if it's staring me right in the face. I hope to spend more time puzzling over it this weekend.

    -FER
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