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    Re: Captain Cook's Sep 07th, 1773 Lunar revisited
    From: Antoine Couëtte
    Date: 2012 Jul 23, 22:55 -0700

    Dear All,

    As indicated earlier, I have reworked Cook's Lunar from a "reasonable" position both not too far from Ohamaneno harbor, and from which the Sun and Moon Azimuths are not land blocked.

    From (a just slightly revised) position S16°44'W151°35'0, and with all other elements as follows :

    HOE = 15.5 ft T = 77.5°F , on Sep 07th, 1773, with TT-UT = + 16.4s and

    a limb to limb sextant measure of 105°47'04" as a result of 10 measures, (whilst the recorded heights SUN LL = 12°38'24" , MOON UL = 43°29'00" are NOT being used to derive the following results because the position is forced into S16°44'W151°35'0)

    .. we can compute that this Lunar was observed at a time very close from UT = 17h06m58s1 on the 07th of September 1773, with such found date and time being reckoned in our modern acceptance.

    This Lunar is rated by Frank's computer as [QUOTE] Error in Lunar 0'1 , Error in Longitude 0°02'0 [UNQUOTE], no change here and I can interpret these "computer comments" as meaning a difference of 4" between our angular values for the Lunar Distance. These 4" are a quantity definitely well below the best accuracy they could achieve then.

    From such position S16°44'W151°35'0 and time 17h06m58s1, we get :

    SUN LL = 13°08'33" in Azimuth 079°7 and MOON UL = 42°55'25" in Azimuth 312°1

    From this position we can check that the Moon Azimuth was not landblocked. The same holds true for the Sun which appeared over the Sea in the gap between the northern tip of RAIATEA and the southern tip of TAHAA.

    Let us try refining these results in attempting to further resolve the (still a bit) annoying discrepancy on the observed heights as follows. If we want the Sun height become closer to its recorded value of 12°38'04", then we must choose some earlier UT time by about 2 minutes of time. So let's do it and compute the position of Sun and Moon at time 17h05m00s0. From still the same position we get :

    SUN LL = 12°40'51" in Azimuth 079°8 and MOON UL = 43°16'00" in Azimuth 312°5

    Then, these computed altitudes match reasonably well the recorded heights (Difference of 2'27" for the SUN and 13'00" for the MOON). If we want to better match the SUN altitudes, then at UT = 17h04m49s5, SUN LL = 12°38'23"/079°8 (virtually identical height to recorded value now) and at this time MOON UL = 43°17'50"/312°5 with a slightly reduced difference of 11'10" when compared to its recorded value. Not a definite improvement then.

    To finalize our research, and if we admit that this lunar was observed by UT = 17h05m00s (does not seem achievable to do definitely better, Paul, uh ?) from position S16°44'00"W151°35'00", then the lunar distance should have been recorded as : 105°47'29"5, which is 25"5 away from the recorded Lunar Distance of 105°47'04".

    More refined - and tentatively final - conclusions here-under.

    Probably not possible to do much better with available data since :

    As a result of both the lesser quality Octants used for the heights - with the best one(s) being used for the Lunar distances - and the fact that averaged altitudes time and averaged Lunar distances time might have differed by maybe up to 2 minutes of time - ideally they should have occured at the very same time - the recorded altitudes are probably in error by up to 10' and maybe 15'. This seems consistent with Alex's and Paul's earlier remarks here. This specific Lunar also seems quite sensitive to altitude errors , but no time for me now to dig this matter further.

    Given the technical difficulty of correctly "catching/matching" both SUN and MOON Limbs since they had to hold their sextant more or less horizontal for this Lunar, we can certainly understand that - despite the fact that they did increase the number of their distances sightings to 10 measures (the biggest number recorded on that page) - their final Lunar distance could NOT be as accurate as their otherwise excellent Latitude determinations from Sun Heights with their best Octants.

    All in all, I would allocate the remaining errors as follows.

    There seems to be only very limited room to locate Adventure significantly far for assumed position S16°44'W151°35'0. These mains constraints are :
    - Not being too far from Ohamaneno Harbour (6 to 7NM at the most), and
    - Being able to observe the SUN over unobstructed horizon in the (narrow) gap between RAIATEA and TAHAA, i.e. from Adventure one had to see this gap at an Azimuth of 80° +/- a few degrees.

    Therefore, this **** 25"5 **** discrepancy on the Lunar Distance would almost exclusively rely on the following causes : half of these 25"5 might be explained by a sizeable difference between the Lunars Distances Mean Time and the Heights Mean Times in addition to their actual heights sighting errors due to lesser quality octants, and the other half - i.e. some 15" - could be explained by the inaccuracy of their Lunar Distances sightings.

    Not that bad at all, finally ...


    PS : Paul, just before publishing this post, I just checked NavList and I thank you for having published your reply meanwhile. Our results now do differ because I have not adjusted for both time and/or position as you just did. This time I have sticked to a "most probable position" of S16°44'W151°35'0 for the reasons given here-above. I am sure that we would get quite similar results if you were to use the same assumptions ... unless you may prefer me to take off from Adventure on my flying carpet and overfly you just a few minutes after in the vicinity of Bola Bola :-).

    Thanks again Paul, Don and Alex for your GREAT support here.

    Then, LAST BUT NOT LEAST, let us not forget my former "obvious and immediate question" : Any published Cook's Lunar anywhere from a land place which can be (fully and firmly) established to-day ?

    Anyone knows ???

    Any taker on that one ???

    ... so that I can simply start playing the very same game all over again ... :-))

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