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I wrote:
> I also solved for time and position:
> 
> 17:05:54.8 S16°30.65' W151°53.78'  Hirose solution

If my solution is accurate, an independent computation of the altitudes
and lunar distances at that time (UT1) and place should agree with the
observations. JPL HORIZONS gives these azimuths, refracted altitudes,
and diameters:

312.4207°  43.1722° 1791.479"  Moon
  79.8985°  12.8457° 1906.867"  Sun

Assume negligible differential refraction between center and limb.
Assume 3'50" dip. Compare the calculated and observed limb altitudes:

43.1722° refracted Moon center
   .2488  semidiameter
   .0639  dip
-------
43.4849  refracted Moon upper limb
43.4833  observed angle
-------
   .0016° difference (= .09')


12.8457° refracted Sun center
   .2648  semidiameter
   .0639° dip
-------
12.6447  refracted Sun lower limb
12.6400  observed angle
-------
   .0047  difference (= .28')


Check lunar distance:

106.2916°  refracted separation angle
    .2488   Moon semidiameter
    .2648   Sun semidiameter
--------
105.7779   limb to limb angle
105.7844   observed angle
--------
   -.0065   difference (= -.39')

I hoped for a better result, but at least this confirms no serious
mathematical error in my solution.

Most of the difference between my computation and HORIZONS is in the
refraction, especially for the Sun. Unrefracted altitudes agree to 
.0002° and the unrefracted lunar distances to .0001° (center of body in 
all cases).


> As for his theory that the altitude observations were not simultaneous 
> with the lunars, the Moon and Sun altitude rates were -10.7 and +14.1 
> '/min, respectively, and the observed - computed were +42.0' and -39.7'. 
> This implies the altitudes were shot 3 or 4 minutes before the mid time 
> of the lunars. But I wonder, were the observers that dumb? Isn't it more 
> logical, and just as easy, to shoot 5 lunars, 2 altitudes, then 5 more 
> lunars?

My time solution (17:05:55 UT1) assumed simultaneous observations. But 
what if the altitudes were actually observed 3 minutes before the lunar 
distance? Then for a precise solution, I should correct the lunar 
distance to the same time as the altitudes.

The topocentric lunar distance rate is -16"/min, so add 48" to the 
observed lunar distance (105°47'04"). With that adjustment, and the same 
altitudes, my new solution is 17:04:10.

If the solution were totally insensitive to altitude, the new one would 
be exactly 3 minutes earlier than the old one. But it's only 1m45s 
earlier. The discrepancy (3m0s - 1m45s = 1m15s) is the error due to not 
observing all three angles at the same time. A 1m15s time error is 
equivalent to 1.25 * 16 = 20" error in lunar distance. That is the 
result of shooting the altitudes 3 minutes before the lunar.

-- 

   

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