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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
emergency.

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

Moon:
   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

Sun:
   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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