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    Captain Cook's Sep 07th, 1773 Lunar revisited
    From: Antoine Couëtte
    Date: 2012 Jul 19, 05:45 -0700

    Hello to all,


    Some 2 years ago, and further to our dear George's suggestion, we covered some of the Cook's Lunars which were published for the year 1773.

    Let me get back to the one published for Sep 07th, 1773

    *******

    Here are the published data :

    From "Ohamaneno Harbourg in Ulietea", Sep, 07th, 1773

    Time by Chronometer # 1 : 02h08m43s.0
    Sun to Moon limb to limb distance 105°47'04" (as a result of 10 averaged observations)
    Altitude of the Sun (LL observation) : 12°38'24"
    Altitude of the Moon (UL observation) : 43°29'00"
    Longitude : 208°35'48" East of Greenwich, which equates to W 151°24"12"
    Latitude : S 16°45'30"
    Temperature : 77.5 (Farenheit)
    There is also a specific note stating the following : " it must here be obferved, that all altitudes are put down as they were obferved with Hadley's Sextant, from the fhip's deck, and consequently are to be corrected for the femi-diameter of the object, the refraction, and dip of the horizon, which , on the Adventure, was about 3' 50" ...///...
    From this note here-above and from further indications exchanged on this Forum, we have concluded that it is reasonable to use a Height of Eye equal to 15'5 (4m70)
    And, last but not least, a "historical" nautical chart of the "Ohamaneno Harbourg in Ulietea" was also published by one NavList Member. This chart enables us to ascertain that Adventure's mooring point was on the Western part of the Island.

    *******

    So, as a starting point, I first identified Cook's mooring point with Google Earth (WGS 84). By comparison with the published "historical" chart, they is little doubt that Cook's actual anchorage point was (very) close to the following position : S 16°45'33" W151°29'48" on RAIATEA Island.

    Here we can observe that Cook's Latitude was already extremely accurate (to within 100 yards) while his believed Longitude was (probably) 5 miles off. The position believed by Cook (S 16°45'30" W 151°24"12") might still be considered as a "valid" anchorage point for our research to-day. In fact Google Earth shows that it is lying in the vicinity of the reef which a passage through them. However, such believed position of S 16°45'30" W 151°24"12" - in the eastern coast of RAIETEA - is NOT consistent with the data published on the historical chart which - again - clearly show that "Ohamaneno Harbourg in Ulietea" definitely lies on the western side of this same island.

    *******

    All the above to indicate that - with modern computing tools and using TT-UT = +16.4s - I have reworked this Lunar using the "Ohamaneno Harbourg in Ulietea" coordinates as given by Google Earth, i.e. S 16°45'33" W151°29'48"

    With all the data as indicated here-above, I find that UT of Cook's observation was 17h07m18s5.

    When feeding these data into your Computer, Frank, I get the following grade " Error in Lunar 0'1, error in Longitude 2'0 "

    So there is little doubt that the results here-above constitute (close to) the Best modern reconstruction of this Lunar performed some 240 years ago.

    *******

    THINGS START BEING INTERESTING RIGHT HERE !

    From Frank's computer, we can also get the following data :

    Moon Apparent Altitude at DR 42°28'2 and Moon Altitude Correction -0°39'0 (which yields a Moon Center geocentric altitude of 43°07'2) , and
    Sun Apparent Altitude at DR 13°30'3 and Sun Altitude correction +3'7 (which yields a Sun Center geocentric altitude of 13°26'3), and
    Cleared Distance (i.e. geocentric Moon center to Sun center distance) 105°57'4

    All your values Frank, are exactly the same ones which I am deriving, as long as you published topocentric heights are published for Body centers affected by refraction and with Height of Eye equal to 0ft, which I believe is the actual case , no ?

    The intriguing remark here is that I CAN NOT find any way to reconcile the published height values given by Cook, i.e.

    Altitude of the Sun (LL observation) : 12°38'24"
    Altitude of the Moon (UL observation) : 43°29'00"

    with any of the heights values computed nowadays as showing on your Computer, Frank, ...

    If indeed, we are to understand that the Cook's published values are exactly as stated, i.e. U/L limb with the effect of both Dip and Refraction included, I am therefore computing such data as follows : Sun LL height = 13°17'9 with Sun Az = 079°6, and Moon UL height = 42°47'1 with Moon Az = 311°9 .

    Still no way to reconcile these values with the ones published by Cook.

    Even if considering that SUN/MOON heights determinations are not so critical for accurate Lunars determination (see Frank's lectures on this subject), and even if considering that from (our) currently used position, the horizon was definitely obscured by the close land in the Sun's Direction (and probably not in the Moon's direction since there seems to be a gap between 2 distant islands exactly in the Moon's Azimuth at this time of Observation) it looks DEFINITELY STRANGE that the heights published by Cook might be in error by over three quarters of a degree in this specific example.

    Any cue here ? Am I missing something ?

    Thanks for your Kind understanding and reply(ies)

    Kermit

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