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    Position fix : Lunar LOP + Lacrosse 5
    From: Frank Reed
    Date: 2008 Jan 25, 23:24 -0500

    Last Friday, the Moon was rather close to Mars in the early evening, so I
    decided to experiment with my recently-adjusted sextant. It took a set of
    four lunar distances (Moon-Mars Near Limb), corrected for index error, and
    averaged them. The distance was 01d 15.2' at an average time of 01:00:06
    I had checked heavens-above.com earlier in the evening and knew that there
    was a pass of the satellite Lacrosse 5 coming soon after I finished my lunar
    distance observations. So I put down the sextant and grabbed my binoculars.
    The satellite was nice and bright and easy to identify even without the
    binoculars. I tracked it across the sky, and it passed just about
    one-quarter of a degree on the northeast side of alpha Persei around four
    minutes after 7pm (about 0104 GMT).
    Each of these sights yields a line of position. The Moon-Mars lunar distance
    would have been 01d 15.2 (as measured, at the given GMT) at the following
    points: 41 55.2N 88.0W, 41 41.2N 87.5W, 41 27.2N 87.0W. I determined these
    points simply by entering the longitude values and varying the latitude
    until the error in the distance was cleared to zero (using my online lunar
    clearing tool at www.HistoricalAtlas.com/lunars). These three points fall on
    a nice, nearly straight line running roughly southeast to northwest. Of
    course, this line of position is only as accurate as the measured distance
    and if we shift it parallel to itself by about six nautical miles, the
    cleared distance changes by about a tenth of a minute of arc.
    The single observation of Lacrosse 5 without accurate timing information
    also yields a line of position, roughly parallel to the "ground track" of
    the satellite. The distance of closest approach to alpha Persei would have
    been 0.25 degrees at these points: 42.24N 87.25W, 41.87 87.75W. I determined
    these points by trial-and-error through heavens-above.com. This gives a line
    of position running roughly southwest to northeast. This LOP is relatively
    insensitive to errors in estimating the angle since the satellite is close
    to the Earth (almost 500 times closer than the Moon).
    I plotted the two lines of position from the Mars lunar distance and the
    Lacrosse 5 pass, and they met at a point about eight nautical miles from my
    known true position. The satellite LOP passed very close to my true
    position, as expected, so the intrinsically less accurate lunar LOP was the
    primary source of error.
    Notice that neither one of these observations required a visible horizon.
    Also, of course, they do both depend on easy access to a computer or a
    properly programmed calculator. Also, if the "DR" position were really way
    off, say by hundreds of miles, it would be rather difficult to identify
    specific artificial satellites. But hey, how's that for an exotic position
    fix: a lunar distance LOP combined with an artificial satellite observation!
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