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    Re: Captain Cook's Sep 07th, 1773 Lunar revisited
    From: Alexandre Eremenko
    Date: 2012 Jul 19, 15:52 -0400

    They most certainly used different instruments.
    (For the observations in Point Venus which I investigated
    they explicitly say this, and which instruments).
    They also say what the index error was.
    Half-degree unaccounted index error I don't believe,
    especially if their latitude is correct.
    See my previous message, and what I propose.
    If there is time which fits both altitudes, we should accept this
    time of observation, and see what the error in the Lunar is.
    If there is no such time, we have to admit either
    a) That we assume incorrect ship position, or
    b) that they made a blunder
    Assuming of course that Kermit made no blunder.
    There is one more possibility which can be checked, if we have a map
    with the place of observation: One has to check using the map and asimuths
    that both Sun and Moon were visible over the sea horizon from their position.
    It could be that one of them (or both) was over land and they took the
    over the land horizon.
    > Alex & Kermit
    > Perhaps(?), they used a different instrument to measure the altitudes vs
    > the lunar distance.
    > This would easily explain the 3/4 offset nicely, index error.
    > More than one?
    > Brad
    > On Jul 19, 2012 1:30 PM, "Antoine Couëtte" <
    > antoine.m.couette---fr> wrote:
    >> Mauritius Island, on Jul 19th, 2012
    >> Dear Aliex,
    >> Yes, I did study lately your work on Cook's Observations in Point Venus
    >> and found it very interesting. Thank you for sharing it with all of us.
    >> *******
    >> Then, this Sep 07th, 1773 Cook Lunar was addressed here :
    >> http://fer3.com/arc/m2.aspx/Sun-Moon-Lunars-155-degrees-Morris-mar-2010-g12562
    >> here :
    >> http://fer3.com/arc/m2.aspx/Sun-Moon-Lunars-155-degrees-K%C3%B6berer-mar-2010-g12571
    >> and here :
    >> http://fer3.com/arc/m2.aspx/Sun-Moon-Lunars-155-degrees-Huxtable-apr-2010-g12645
    >> All three references hereabove started exactly the same thread title and
    >> I
    >> do not want to deprive any of their three Authors of "having started"
    >> such
    >> thread. Down the line came a number of subsequent contributions as you
    >> can
    >> see in the Archives files.
    >> *******
    >> You will find here-enclosed a summary of it all, where at the very
    >> bottom
    >> of some pages, you will be also able to retrieve the "original" web
    >> pages.
    >> Then in order for you to start your computations, just recheck that my
    >> data for Sep 07th, 1773 are faithfully reproduced, or better r=directly
    >> refer to the published data page (the one with many many many numbers
    >> ...).
    >> With all 4 pages of such enclosed document, you know it all and have
    >> everything to recompute such Lunar. At least, everything I have used in
    >> in
    >> there.
    >> *******
    >> Now and finally, to be more specific with the main other point you are
    >> raising.
    >> In my former e-mail I did make mention of " Time by Chronometer # 1 :
    >> 02h08m43s.0 " only for the sake of completeness. However I have not used
    >> this data and have not used any of the formerly unavoidable hassle of
    >> going
    >> through True Local Time, true Greenwich time, Sun height used to
    >> determine
    >> true local time ... GMT as used nowadays is a huge and amazingly
    >> wonderful
    >> simplification of all earlier computations. True : GMT nowadays can be
    >> used
    >> mainly because we have very accurate time-keepers. This does not prevent
    >> me
    >> from thinking that the introduction of GMT in Navigation Courses could
    >> have
    >> come much earlier than before early 19th century, since it would have
    >> been
    >> so much easier to make computations, even without good and reliable
    >> time-keepers. You could even have got rid of using Equation of Time then
    >> !
    >> I am suspecting that here Frank you might (strongly) disagree with this
    >> view point ... keeping my fingers crossed ! :-)
    >> My reasoning - with modern computation power - boils down to the
    >> following
    >> : from a known point (here from S 16°45'33" W151°29'48" on RAIATEA
    >> Island)
    >> and around the date of Sep 07 th, 1773, if you did observe a SUN-MOON
    >> limb
    >> to limb distance (as read directly off your "perfect" sextant) equal to
    >> 105°47'04" (as a result of 10 averaged observations), then with TT-UT =
    >> 16.4s and all the other environment data as indicated, then UT of
    >> Sextant
    >> observed value is UNIQUELY (very close to a few seconds of time to) UT =
    >> 17h07m18s5, as I could determine from own computation. I also have a
    >> quick
    >> excellent independent confirmation from Frank's computer to within 2/30
    >> of
    >> arc minute (i.e. 4 arcseconds) on the computed angles.
    >> Then, starting from both same position and UT, it is easy to work
    >> backwards and "reconstruct" Moon and Sun Altitude's at that specific
    >> time
    >> and from this specific location, whether they be refracted or not
    >> affected
    >> by refraction, and/or whether they be observed from HOE = 17 ft or HOE =
    >> 0
    >> ft, and/or whether they be topocentric or geocentric and whether - if
    >> topocentric - they be upper or lower limb since - of course - all
    >> geocentric heights relate to only body centers.
    >> My ultimate concern also boils down to the following : even if taking in
    >> account all the environmental constraints earlier discussed (including
    >> obstruction of horizon by land masses) whatever "kind of height" might I
    >> consider (refracted one, not refracted one ...) none of the Cook's
    >> published Moon and Sun heights values seem to (adequately) "fit" to any
    >> modern determination of such values. There still remains a (surprisingly
    >> high) unexplained (so far) difference of some 3/4 of a degree ...
    >> Hence my (maybe stupid) question :
    >> Any cue here ? Am I missing something ?
    >> *******
    >> Best Friendly Regards to you Aliex from
    >> Kermit
    >> ----------------------------------------------------------------
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    >> Linked File:
    >> http://www.fer3.com/arc/imgx/Cook-Astronomical-Observatio.zip
    > View and reply to this message: http://fer3.com/arc/m2.aspx?i=120027

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