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    Re: Modern Lunars
    From: Paul Hirose
    Date: 2016 Sep 19, 23:12 -0700

    Antoine's Lunar #2 is even more difficult than the "difficult lunars" I
    re-computed from Chauvenet. Unrefracted center altitude of the Sun is
    only 4.6°. I'm sure no navigator would shoot such a lunar except in an
    Below is some of the pre-solution and post-solution output from my
    program. Generally, my angles are virtually perfect (within .0001° of
    his document), except the Sun altitude and the separation angle. My time
    solution is 8 seconds different.
    Time and position were adjusted so the calculated angles are equal to
    the observed angles. It required 9 iterations to converge to .0001°
    accuracy. That's an exceptionally large number. Normally it would
    require only about 5 iterations even with one hour error in initial time
    and 10 degrees error in latitude and longitude! Possibly my algorithm is
    not very robust in such unfavorable conditions.
    Lunars #3 and #4 appear much less sensitive to refraction, but I haven't
    worked them yet.
    initial time:
    1855-09-07T08:04:52.32 UT1
    1855-09-07T08:05:00.00 TT (Gregorian)
    2398833.5 + 0.336806 = TT Julian date
    +0m07.68s delta T
    initial coordinates:
    +30.1108°  -30.0000° north lat, east lon
    0.0 meters (0 feet) above ellipsoid
    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
       0.0000° dip
      48.8735° apparent lower limb altitude
       0.0131° refraction
      -0.2493° unrefracted semidiameter
      49.1098° unrefracted altitude of center
      49.1099° predicted altitude
      -0.0001° intercept
      85.4227° predicted azimuth
       0.0000° dip
       4.4956° apparent lower limb altitude
       0.1652° refraction
      -0.2646° unrefracted semidiameter
       4.5950° unrefracted altitude of center
       4.5938° predicted altitude
       0.0012° intercept
      85.4223° predicted azimuth
    predicted Moon to Sun angle:
       44.5161° center to center, unrefracted
        0.1452° refraction
       44.3709° center to center, refracted
        0.2492° Moon near limb refracted SD
        0.2580° Sun near limb refracted SD
       43.8628° observed angle
       43.8637° computed Moon to Sun
       -0.0009° observed - computed
    Solution, after 9 iterations.
    corrected time:
    1855-09-07T08:04:59.98 UT1
    1855-09-07T08:05:07.66 TT (Gregorian)
    geocentric separation angle:
       45.1044° center to center

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