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    3 Lop's
    From: Alexandre Eremenko
    Date: 2004 Nov 14, 23:01 -0500

    Some books consider finding a fix from 3 lines
    of position. This case also popped up in our infinite
    discussion of the Averaging.
    Can anyone explain, under what circumstances one could
    possibly want to determine her position from 3 LOP's?
    It is hard to imagine (for me) such circumstances.
    (Hard but possible).
    1. Three stars (or two stars and the Moon) taken on a short intevral.
    Why would you want to do this?
    If there are two bodies whose azymuths make a decent angle
    (well away from 0 and 180d), and whose altitudes
    are reasonable (away from 0 and 90d) why don't you concentrate
    your attention on these two bodies?
    Twilights are short. Is not it better to take several
    altitudes of these two bodies, rather than distruct your
    attention for the third one?
    If all pairwise angles are "bad", three stars will
    not help much.
    The only case where the choice seems hard is when you see 3
    bodies with all asymuth differences about 120d, and on approx
    the same altitude:-)
    (In which case I would probably still restrict myself with two,
    taking their altitudes carefully).
    2. Sun. We are talking of "running fixes" then.
    If the first two observations are well-spanned,
    why not to derive a fix from these two,
    without waiting for the third?
    The only case when you
    may want to use 3, seems to be the following:
    Suppose 30
    after the first observation, (which was made in some
    "windiw in the clouds") the sky is still cloudy,
    you are afraid you won't be able to get a second LOP today,
    and you don't want
    to wait longer,
    so you make the second observation, 30 minutes after the first.
    The angle difference is too small for a reliable fix.
    Then, 2 hours after, the clouds disappear and you decide to take
    the third altitude. But 1 hour after that, the sky is again
    completely covered by clouds:-)

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