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    Re: Modern Lunars
    From: Paul Hirose
    Date: 2016 Sep 20, 16:08 -0700

    On 2016-09-20 7:43, Antoine Couëtte wrote:
    > Re: LUNAR #2 (re: http://fer3.com/arc/m2.aspx/Modern-Lunars-Couëtte-sep-2016-g36570)
    > One thing puzzles me ... the difference between our Azimuts:
    > For the Moon, you get  85.4227° , while I get: *Moon Z = 85.42280° including 
    a Parallax in Azimut equal to dZ = -14.59022” , which - without the parralax 
    in Azumuth - would put the Moon at 85.4268 °*
    > For the Sun, you get 85.4223°, while I get: *Sun Z = 85.42227°, including a 
    parallax in Azimut equal to dZ = - 0.02538”*
    > Maybe a difference in Aries GHA ? I am computing it at ARIES GHA = 107.057 
    931 8 °, but I am ignoring some higher order cross-terms of the "Equation des 
    Equinoxes".
    
    Below is the complete output of my program for the time and place in
    your document.
    
    Although the program displays sidereal time, it actually uses the "new
    paradigm" introduced in 2000, with the Celestial Intermediate Origin
    instead of the equinox, and Earth rotation angle instead of sidereal
    time. The result should be virtually identical with either method.
    
    Altitude and lunar distance rates ignore refraction, and so in this
    extreme case are not accurate. However, the solution still converges to
    .00001° in 10 iterations.
    
    initial time:
    1855-09-07T08:04:52.320 UT1
    1855-09-07T08:05:00.000 TT (Gregorian)
    2398833.5 + 0.336806 = TT Julian date
    +0m07.680s delta T
    +0.00000° +0.00000° polar motion x, y
    
    initial coordinates:
    +30.11083°  -30.00000° north lat, east lon
                 -30.03209° ephemeris east lon
    0.0 meters (0 feet) above ellipsoid
    +0.00000° +0.00000° deflection of vertical xi, eta
    
    23.9 C (75.0 F) at observer
      985.4 mb (29.10″ Hg) altimeter setting
      985.4 mb (29.10″ Hg) station pressure
    50.0% relative humidity
    0.0002 water vapor partial pressure fraction
    1.0002616 index of refraction at 550 nm
    
    Moon:
       0.00000° dip
      48.87353° apparent lower limb altitude
       0.01306° refraction
      -0.24932° unrefracted semidiameter
      49.10980° unrefracted altitude of center
      49.10989° predicted altitude
      -0.00009° intercept
      85.42269° predicted azimuth
    
    altitude partial derivatives:
    0.080° per ° N latitude
    0.862° per ° E longitude
    0.208° per minute time
    
    Sun:
       0.00000° dip
       4.49557° apparent lower limb altitude
       0.16522° refraction
      -0.26465° unrefracted semidiameter
       4.59500° unrefracted altitude of center
       4.59376° predicted altitude
       0.00123° intercept
      85.42225° predicted azimuth
    
    altitude partial derivatives:
    0.080° per ° N latitude
    0.862° per ° E longitude
    0.216° per minute time
    
    predicted Moon to Sun angle:
       44.51613° center to center, unrefracted
        0.14519° refraction
       44.37094° center to center, refracted
        0.24921° Moon near limb refracted SD
        0.25805° Sun near limb refracted SD
    
       43.86275° observed angle
       43.86369° computed Moon to Sun
       -0.00093° observed - computed
    
    separation angle partial derivatives:
    +0.000960° per ° N latitude
    +0.010420° per ° E longitude
    -0.005044° per minute time
    78% of total angular velocity
    
    DE406 ephemeris
    149597870.691 km per au
    
    BCRS position (km) and velocity (km/day).
    Moon:
    1.451103229e+008 -3.292822757e+007 -1.421809283e+007
    5.026452032e+005 2.244336976e+006 9.749565176e+005
    Sun:
    -9.706259896e+005 -9.457987890e+004 -1.279692556e+004
    -2.457214254e+002 -9.827485677e+002 -4.192286425e+002
    
    GCRS to celestial intermediate matrix
    (IAU 2006-2000B precession-nutation)
    0.9999014 -0.0000010 0.0140430
    -0.0000016 1.0000000 0.0001888
    -0.0140430 -0.0001888 0.9999014
    
    108.90837° Earth rotation angle
      7.137195h Greenwich apparent sidereal time
      5.137195h local apparent sidereal time
    
    23.45805° mean obliquity
    -0.00255° +0.00217° nutation in longitude, obliquity
    
    polar motion matrix:
    1.0000000 0.0000000 0.0000000
    0.0000000 1.0000000 0.0000000
    0.0000000 0.0000000 1.0000000
    
    Moon apparent geocentric place:
    -2.0877426e+005 3.0144303e+005 1.6977604e+005 GCRS
    4.0410580e+005 geometric distance (km)
      8.169499h +25.29193° equinox RA, dec
      8.292861h intermediate RA
    237.45752° SHA
    0.24634° semidiameter
    0.90436° horizontal parallax
    119.22732°  +5.07609° ecliptic true lon, lat
    119.22987° mean lon
    
    Sun apparent geocentric place:
    -1.4628618e+008 3.3148350e+007 1.4380829e+007 GCRS
    1.5068267e+008 geometric distance (km)
    11.024173h  +6.25884° equinox RA, dec
    11.147536h intermediate RA
    194.63740° SHA
    0.26465° semidiameter
    0.00243° horizontal parallax
    164.10755°  +0.00026° ecliptic true lon, lat
    164.11011° mean lon
    
    geocentric separation angle:
       45.10541° center to center
    -0.007558° per minute
    85% of total angular velocity
    
    illumination conditions:
    85.4° 4.6° Sun unrefracted az, el
    180.0° Moon to Sun position angle (0 = zenith)
    135.4° Moon phase angle (0 = full, 180 = new)
    
    position angles:
    180.0° Moon to Sun
    360.0° Sun to Moon
    
    recommended limbs:
    Use Moon lower limb.
    Use Moon near limb.
    
    

       
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