NavList:

Anabasis wrote:

A ship is sailing in the East China Sea on 6 January 2009.  The course
is 195 degrees True and
is steaming at 10.5 knots.  The 1530L fix is Lat 34 deg 21.5N';
longitude
128 deg 55.4'E.  IE is 0.8' on the arc, height of eye is 107 feet,
standard temp
and pressure.

Around 1545L (0645 UTC) a 3-body fix is taken.  Determine Latitude and
Longitude
at 1545L.

At 15h 43m Venus is observed at meridian transit with an Hs of 44 deg
25.8'

At 15h 43m 46s the upper limb of the moon is observed with an Hs of
35d 57.0'

At 15h 44m 52s the lower limb of the sun is observed with an Hs of 16d
46.5'

  

I don't know anything about the classical methods but wonder how close I came by direct calculation.  I did not allow for the movement of the ship between the sights or refraction.

Aires = 100.7797  Time offset =      0
Star               Decl     SHA     GHA     Alt   T_Day  D  M Year   T_Year   C_GHA      Aires
venus           -11.458  24.675 231.409  44.258   6.717  6  1 2009  126.717 231.409   206.734
moon             18.982 324.715 171.641  35.644   6.729  6  1 2009  126.729 171.641 206.926
sun             -22.473  72.556 279.758  16.739   6.748  6  1 2009  126.748 279.758    207.202
 
Star1           Star2              Lat1    Lng1    Lat2    Lng2
venus           moon             34.281 230.888 -33.262 187.352
venus           sun              34.282 230.996 -42.148 192.394
moon            sun              34.188 230.888 -29.647 196.834
Average location                 34.2501 230.9240

And on the map



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