NavList:

Frank,

Since in your 05 Jan 2018 post you cared for indicating that your altitudes are "  (geocentric, body center, =Ho) " , which I have seen as an implicit and kind reference to " Publishing-Heights-values-Couëtte-dec-2017-g41032 ", I decided to take a look at your Exercise.

• First of all, I grabbed my Ephémérides Nautiques pour l'An 1981 from Bureau des Longitudes and on page 420 I attempted to put the Moon close to your picture position. It gave me Moon RA = 08h20m and Moon Dec Close to +19°N
• I then computed the time by end of January 2018 at which the Moon RA is 08h20m. I found that on Jan 31st at 00:00 GMT, Moon RA = 08h20m and Moon Dec = 19°N : Good enough ! Your CelNav Observation Party took place probably slightly before that time since we know that it took place in the Atlantic Ocean at sunset.
• I decided to use your averaged heights as well as the time interval between them, i.e. :
  • UT1 Moon with Ho Moon = 16°07.5'
  • UT1 Sirius = UT1 Moon + 5 s with Ho Sirius = 13°17.0'
  • UT1 Procyon  = UT1 Moon + 7 s with Ho Procyon = 16°20.5'
    • Hence we just need to determine UT1 Moon given our assumption that the date is Jan 30th, 2018 in the evening UT Time.
• The variable I have chosen to look into is the intersection of the 3 plans containing the 3 circles of equal altitudes of the 3 bodies considered, thus simply looking for the time when this intersection - computed here in units of Earth radius - exactly crosses the Sea surface. 
  • First trial with 22h12m03s / 22h12m08s / 22h12m10s - a reasonable start given the environment data - this 3 plan intersection is at D = 1.1631
    • Second trial one half hour later : UT = 22h32m03s / 22h32m08s / 22h32m10s , then D = 0.8133 
      • Since the variation of D is not strictly constant with time I needed 3 iterations to find : UT = 22h19m22S / 22h19m27s / 22h19m29s with D = 0.9999 and N34°29.7' W063°36.5'

Final results :

• At the Moon averaged time, the watch indicates 04h12m03s when UT = 22h19m22s, hence Chronometer correction : + 18h07m19s
• Observer's position : N34°29.7' W063°36.5'
• Course and distance to Bermuda (TXKF Airport) : 203° / 140 NM

Antoine Couëtte

PS : Freezing weather and lot of snow in Conanicut Island ? Well, I can see that .. I did not operate to JFK since my flight got cancelled.