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    Re: Captain Cook's Sep 07th, 1773 Lunar revisited
    From: Alexandre Eremenko
    Date: 2012 Jul 19, 15:45 -0400

    As I understand you used Cook's Lunar to find the GMT time of
    the observation.
    Then you say that Moon and Sun altitudes do not agree with true ones.
    What I recommend is this: try to find the time from the Sun observation.
    If the Moon fits, then we may assume that the altitudes are correct,
    and the Lunar has some (presumably) small error.
    When you do this, make sure that you use the "correct" date:
    they could count the date differently from how we count.
    (Sometimes the date changes in midnight, sometimes at noon!).
    The advantage of my proposal is that the Sun and Moon altitude chenge
    with time more quickly than the Lunar distance, so this permits you to find
    the time more reliably.
    The main question: is it possible to find the time, so that BOTH Sun and
    Moon altitudes fit.
    > 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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    > > > > > > View and reply to this message: http://fer3.com/arc/m2.aspx?i=120026 > > >

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