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    Re: Lunar Distance Puzzle
    From: David Fleming
    Date: 2011 Aug 12, 09:18 -0700

    My first reaction was that time is easily found from this data but position is not.

    Each lunar distance measurement is a determination of the time. The Vega-Lunar is most important as the moon is moving essentially straight toward Vega, but other lunars will supply time measurements but should be given less weight.

    Data are given in GHA Dec coordinate system. To simplify shift to the celestial sphere where GHA like coordinate is constant. To do that take the 0300 GHA of stars as their position, "gha" and for the moon 0400 subtract 15d 2m 27.9s.

    For a graphical solution plot the moons position 0300 to 0400 on a small area plotting sheet covering "gha" 55d to 75d and Dec -21d 54m to -22d. You have essentially a DR plot on celestial sphere for the moon.

    Take the Lunar distances for the 3 stars and find "gha" for two values of dec, say -21d55.5m and -21d58.5m. Plot those points on the small area ploting sheet and connect the pairs with a straight line thus obtaining lines of position for the lunar measurements.

    The intersection of those LOPs with the moon DR plot will give points. The distance fom the moon 0300 DR divided by the toal distance travelled by the moon 0300->0400 is the time as a fraction of that interval.

    Average the three times with appropriate weights ( how perpendicular LOP is to moon DR plot) to find the best time estimate.

    To find position we are left with examinig the effects of refraction on the lunar distances and more importantly on the effect of parallax on moving the moon observed position. How effectively that can be carried out I'll need to think about further.

    Thanks for the challenge!

    Dave Fleming
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