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    Re: Modern Lunars
    From: Antoine Couëtte
    Date: 2016 Sep 25, 22:07 -0700

    RE g36677

    Dear Paul,

    I'm surprised that you didn't comment on the 0.0002° systematic discrepancy in our topocentric apparent unrefracted Moon position in the 1855 lunar. That's 0.7″.

    Yes, and I noticed it too. I have to wait being back home before I can study it more in depth in late October.

    This systematic discrepancy affects only the Moon and has the same order of Magnitude - it is nonetheless smaller  - than the +0.50"/-0.25" correction earlier mentioned. Did I actually fail to perform it here (I am using a juste recently developped "super accurate" computation mode hooking onto INPOP 2013C results), or did I (rather) perform it twice ? Or some other explanation ? Since it is "systematic" it should be easier to chase and get hold of than if it were a random discrepancy.

    Also are my Apparent Equatorial Coordinates from the Bureau des Longitudes Server the same as the ones you are obtaining on your side ? Maybe this should be the very first point to check again together this time. I am using the following ones (before performing the +0.50"/-0.25" correction earlier mentioned):

    Moon, 1855-09-07T08:05:00.00, i.e. 08h05m00.000 s TT : RA = 08 h 10 m 10.16146 s , DEC = +25 ° 17 ' 31.0209 ", Distance = 0.002701090 UA,

    Hence  HP = 0.904 419 770°(54.26518619’)  and Geocentric SD = 0.246 438 905°(14.78633432‘) with SD = 1,738 km

    and finally also: ARIES GHA = 107.057 931 8 ° (107°03’28”555).

    I have not observed any discrepancy onto Aries GHA, so every source of discrepancy should come from either the coordinates themselves hereabove or their subsequent processing.

    From previous earlier exchanges I am also supposing/assuming that you are performing 3 D computation for deriving local Topocentric coordinates onto WGS84 Ellipsoid, which automatically yields super-accurate parallax computation (mainly for height and also for azimuth). Please be so kind as to confirm this latter point.

    A sextant is readable to 6″, and my goal is 0.6″ accuracy. (There is a rule of thumb in electronics that test equipment should be 10x better than the device under test.)

    Yes, I fully agree with your rule of thumb, and I have always attempted to look into the computation of effects so much smaller than the sextant 6" readability. Except when I directly hook onto INPOP 2013C theory results through "locally" correcting my own computed Ephemeris - which is the case here - I am otherwise using my own Ephemeris accurate to only 4", but I am taking in account any and all other effects to a much greater accuracy ... nonetheless ignoring the Moon Limbs accidental variations due to the Moon mountains  :-)  .

     > I've never seen any evidence that the "modern lunar" has a significant advantage over the traditional solution if you avoid unfavorable altitudes and separation angles. I'm open to the possibility, but skeptical.

    One advantage of modern computation is that you can very accurately compute the ever changing shape of the Limbs points since Refraction constantly changes with time while it is also specific to each pair of equal (ever changing) altitude Limb points. For each instant you can also exactly "mathematically draw" the unique apparent Great Circle perpendicular to each of the everchanging distorted apparent Limbs, then measure a distance alongside such Great Circle (hence mathematically directly comparable to the observed Sextant Refracted Distance). This can be done in one whole overall single  operation, covering all shape distortion ever changing effects, instead of adding some changing corrections to the SD's. I am well aware that this stands significant for apparent distorted Limbs only seen at low altitudes, (say, below 10°), because at higher altitudes these effects quickly become non significant at the accuracy level we are aiming at.

    Second and more definite advantage as I see it: modern software can easily give you "synthetic" sextant distances first derivatives with respect to UT1 which can be very different from their corresponding geocentric distances first derivatives with respect to UT1. Modern Lunars thus give extra and valuable information about the actual "performance" of Lunars in terms of Longitude determination. It gives better insight - and sometimes a totally unexpected one (re: 1955 Fomalhaut Lunar) - than the traditional/classical rule of thumb of avoiding "unfavorable altitudes and separation angles" which you mentioned.

    Thank you again, and

    Best Friendly Lunarian Regards,

    Kermit

       
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