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    Re: Lunars: Three simultaneous observations
    From: Frank Reed CT
    Date: 2004 Sep 22, 22:47 EDT
    George H wrote:
    "This followed a cyclic pattern over a lunation. Lunar
    distances would show cyclic errors of a similar order. Such errors could
    put a calculated longitude out by 25 arc-minutes, maybe more. With this,
    any observationl error would have to be combined. Presumably the Moon
    predictions were no better in Cook's time. For a lunar, accuracy to 25
    minutes would be considered quite good going.
    When Cook's longitudes happen to coincide rather precisely with modern
    values (and indeed, many do) we have to put at least some of that down to
    luck. "

    One small point: I don't think it would be correct to describe the errors as "cyclic". They went up and down, yes, but the pattern was rather complex. If it had been literally cyclic in any meaningful sense, they would have corrected for it very early along.

    As for Cook's longitudes, consider this: what would have happened if Cook had forgotten his Nautical Almanac at home? Or better yet, consider a slightly different history where the motion of the Moon remains beyond the skill of astronomers and mathematicians to predict to better than, say, 30 minutes of arc (which would apparently imply a 15 degree typical error in longitude and would make lunars essentially useless for navigation). Given this "what if" change in history and leaving every other development in maritime science unchanged, could Cook and Green have done anything useful on their voyage? The answer, of course, is yes. The astronomers back in Greenwich carefully observed the position of the Moon at every opportunity. If they had had no predictive model of the Moon's motion, they would still have had the required positional data after the fact. If (and this is not guaranteed) Cook and Green had carefully observed lunar distances and the other data necessary to clear lunars, always keeping their sextants in perfect adjustment, their observations could have been turned into very exact longitudes when they returned to Britain by comparing them with the lunar positions observed at Greenwhich. Setting aside the "what if" scenario, the real Nautical Almanac was good but not perfect, and the astronomers knew that. They did adjust at least some of the longitudes determined on Cook's voyage by correcting for the almanac inaccuracies after the voyage. I don't know what fraction of the original observations were adjusted based on the observed errors of the Moon's position, but some of them were. And if you re-work the lunars from the voyage of the Endeavour using modern almanac data, it is remarkable how accurate they were.

    Frank R
    [ ] Mystic, Connecticut
    [X] Chicago, Illinois
       
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