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    Re: Lunar Distance Puzzle
    From: Harri Ojanen
    Date: 2011 Aug 13, 12:35 -0700

    Dave,

    Thanks for an interesting puzzle. Here's my approach:

    Given assumed position and assumed time, then for any pair of bodies it is possible to compute apparent lunar distance by reversing the steps in the usual cosine-rule lunar clearing. The necessary apparent altitudes can also be computed in reverse.

    This gives three equations in three unknowns, which can be solved numerically -- of course not always, but in this case there were no problems. I used directly lat, lon, and time for the unknowns (assumed all three LDs were measured at the same time).

    The "reverse lunar clearing" function I already had in my toolbox, and a suitable solver was found in the "Scipy" library: "fsolve", some form of modified Powell's method according to it's docs.

    The solution:

    38°43.4'N 077°01.6'W
    time 3:27:22

    But it seems to be very sensitive to the original lunar distances. To get some idea of this, I solved the problem again for +-1 arc second changes in each of the lunar distances. The results vary a lot: latitude from 38°28'N to 39°02'N, longitude from 075°41'W to 078°31'W, time from 3:24 to 3:30. And all of this is done with a simple refraction model (the same formula as in NA).

    So solving the puzzle is doable in principle, but the results are probably not that useful...

    Cheers,
    Harri

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