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    Re: Historical Lunars : take in account 'delta-T' or ignore it ?
    From: Antoine Cou�tte
    Date: 2009 Dec 13, 14:08 -0800

    My Dear Friend,
    
    
    
    
    Thank you for your in depth study of the example of our upcoming Lunar covered 
    in [NavList 11087]. Than you in particular also for mentioning the JPL 
    "HORIZON" Server which I was just vaguely aware of before your post.
    
    *******
    
    First of all, I am very sorry for having given you trouble - which you sorted 
    out quite well indeeed ! congratulations !!! - when using a TT-UT value 
    different from the one you had access to. This 66.7 second value was simply 
    the one predicted by the Nasa document referenced in [NavList 11087]. I was 
    just a bit lazy ...
    
    
    Nonetheless, since it is extremely easy for me to recompute this example with 
    a more correct value of 66.06 seconds - any TT-UT value in fact- here are the 
    results accordingly updated.
    
    
    23 Dec 2009   Height of Eye = 17 ' T = 59d F , P = 29.92" HG Estimated UT / 
    Position :  16h58m53.0s / N3707.1W01253.7 - All observations assumed to occur 
    at the same time - Distance SUN-MOON = 77d53'7 , SUNL = 5d50'1 , MOONL = 
    50d05'0 . All sextant measures are corrected for Instrument error (and only 
    instrument error), i.e. all other corrections (dip, refraction, SD, Parallax 
    ... ) need to be performed from the "raw data" hereabove.
    
    
    UPDATED VALUES :
    
    o   With delta-T = 66.06 seconds (current best value for Dec 23, 2009) :
    
        � Lunar Distance UT = 17h00m01.38s - i.e. TT = 17h01m07.44s (unchanged 
    value as expected) - hence UT error = -1m08.38s, cleared distance = 
    78d34.00', and
        � We also get the following position at time of Lunar Distance :
    N3659.9W01300.5 (result of 2 body fix), and
        � Crosscheck with Frank's on-line computer (you need to enter both 
    heights) : Error in Lunar : -0.1', approximate Error in Longitude 03.9',      
     cleared distance = 78d33.9'
    
    *******
    
    NOW, back to the results first published with TT-UT=66.7 seconds.
    
    
    You also took great care in checking the results I published. So on my side, I 
    did some further research on my own to try explaining the minor discrepancy 
    between the published results and the ones you reworked through "HORIZONS" as 
    well as your own software.
    
    First of all, I verified that the planetary coordinates I am using are not 
    "too far off". Comparison was made here with INPOP06 from 
    http://www.imcce.fr/page.php?nav=fr/ephemerides/formulaire/form_ephepos.php. 
    I used TT=17h01m07.4s which is the value I was initially referring to.
    
    I am using the following values :
    
    SUN RA = 18h08m44.2064s, Dec=-23d25'24.5165", Dist=.9836273 UA, yielding SD=0.271005d and HP=8.9405"
    
    Comparison with INPOP06 (extremely close from DE406) shows the following errors in absolute values :
    
    For the SUN :
    
    Coordinates error < 0.08", SD error < 0.005" and HP error < 0.0001"
    
    For the MOON :
    
    Coordinates error < 1.7", SD error < 0.1" and HP error < 0.35"
    
    As a result, the Approximate Ephemeris I am computing are well under the NAL tolerances.
    
    I am also noticing that, compared to HORIZON, I am using exactly the same 
    unrefracted augmented SD's as the ones which you quoted : MOON .25177d 
    (HORIZON : .2517d ) and for the SUN .2710 ( HORIZON : .2710)
    
    
    The difference in corrected altitudes for the MOON is negligible (1.2") and 
    the difference in corrected altitudes for the SUN, although more important 
    (3.6") is not significant since the SUN altitude is only 5.5d and - according 
    to various sources - refractions are not reliably known to such accuracies 
    below 8d or 10d.
    
    Given the geometry - namely the arrival/departure orientations - of the 
    shortest great circle line joining up both apparent limbs, the combined 
    effects of both the difference in the SUN and Moon altitudes (3.6" and 1.2") 
    and the Moon overall inaccuracy (1.9") seem to almost fully explain the 4.8" 
    remaining difference with your own "refined" results taking in account 
    "refracted" semi-diameters.
    
    Just one question here : I am not quite familiar with the definition of 
    "refracted" semi-diameters. They imply some kind of "Center". From which such 
    "center" are they reckoned ? Obviously, given the irregular apparent shape of 
    both bodies - and especially the Sun who is quite low with such a distorted 
    limb - refracted semi-diameters will vary according to the directions in 
    which they are measured. This is a bit intricate to compute, but this can be 
    accurately done with to-day computing power.
    
    However, and from the information you give, I am under the impression that 
    your definition of the "refracted center" might be the apparent point which 
    is the image of the non-refracted center. I would then guess that you compute 
    the great circle distance between both refracted centers and then substract 
    both refracted semidiameters measured alongside the relevant "departure and 
    arrival" directions reckoned alongside this great circle. So far so good, 
    BUT, there seems to be no reason why the great circle joining up both 
    "refracted centers" - as defined hereabove - would be exactly the shortest 
    distance between both apparent limbs. When both bodies are high in the sky 
    and therefore almost undistorted, no problem at all - the line joining the 
    refracted centers is extremely close from the shortest line joining up both 
    limbs - , but when either body or both are quite low on the horizon, are both 
    such lines still "fully merged" / "exactly the same ones" ? Is it a safe and 
    "mathematically correct" assumption to keep considering that they are still 
    "fully merged", and if so, to which accuracy level ?
    
    
    That you for your Kind Attention, and
    
    
    Best Regards
    
    
    Antoine
    
    
    Antoine M. Cou�tte
    
    -- 
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