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    Re: Calculated Altitudes for Lunars
    From: Bruce Stark
    Date: 2002 Oct 22, 15:09 EDT

    This is a continuation of the October 12th "Re: use of Sun Sights . . ."
    posting. In it the navigator, seriously uncertain of his GMT and DR, had
    taken a morning time sight and worked it once with the guessed-at latitude.
    That gave him the approximate local apparent time, so he didn't have to stand
    around forever waiting for the sun to "dip" at the noon latitude observation.
    Once he had the correct latitude he worked the time sight again for accurate
    local apparent time. By comparing this with what the watch had read he knew
    how fast or slow it was on LAT.
    Then he got a sun lunar, including the two altitudes needed to clear it. To
    the GMT found by lunar he applied the equation of time, converting to GAT. To
    the watch time of the lunar he applied the correction found by time sight,
    converting the watch reading to LAT. The difference between GAT and LAT gave
    him the longitude of the place where he took the time sight.
    Now let's suppose you are in a similar situation, but were unable to get the
    If the time sight, noon latitude, and lunar were taken in different places,
    bring both latitude and LAT to the place of the lunar, so you can calculate
    altitudes for that place. For LAT, change the difference of longitude to time
    and add if the place of the time sight was west, else subtract.
    At this point you could, if you chose, go ahead and calculate the sun's
    altitude. LAT past twelve, or until twelve, is the hour angle. Any reasonable
    guess at GMT would be good enough to take out the declination, and you have
    the latitude. But since you need the moon's altitude as well, take a
    different approach.
    Using a rough guess at GMT, take the equation of time from the Almanac and
    apply it, with reverse sign, to change LAT to LMT. Convert your uncertain DR
    longitude to arc. If it's west, add it to LMT. If it's east, subtract. The
    result is the best you can do at present for GMT.
    With that GMT take out the sun's and moon's elements from the Almanac, just
    as you normally would. Now take the difference between the GHA of the sun and
    the GHA of the moon. That tells you how far the moon is east or west of the
    sun. Apply that difference to the sun's hour angle, that is, to LAT from noon
    reduced to arc, and you have the moon's local hour angle. You now have
    everything needed to calculate the altitudes.
    If the distance was taken from a star or planet, find its hour angle the same
    way you did the moon's.
    The advantage of this approach is that only a rough estimate of GMT is needed
    to get an acceptable altitude of any body other than the moon and, with the
    moon, the error in local hour angle cause by an error in GMT is only about
    one-thirtieth what it would be using standard procedures.

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