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On 2019-12-06 12:46, David Pike wrote:
> Well there was only one thing to do; go out and try it.  Wednesday, 
Thursday, and Friday we were down in the low light pollution area of Norfolk, 
so with great fortitude and determination and the temperature down to 2 
degrees Centigrade, Mrs P and I drove the car onto Kelling Heath (N52.92789 
E1.13489 on Wednesday evening 4^th Dec, taking along ‘Navigator’ on a 
Netbook, and my Hughes Three Circle Mates Sextant No 25410.  First star pair 
was Deneb at roughly Hs= 48.55 and Az= 286 and Vega at Hc= 27.17 and Az= 299 
and a tilt of about 30 off the horizontal.

Your wife must be a good sport. This isn't the first time I've seen you
mention the assistance of "Mrs P."

I guessed the time was about 2000, and your altitudes confirm that's
close enough as makes no difference.

Here is the output (heavily edited) from my Lunar 4.4 program for Windows.
http://sofajpl.com/lunar4_4/index.html


2019-12-04 20:00:00.00 UT1

1°07.80' +52°55.80'  east lon, north lat
0.0 meters (0 feet) above ellipsoid

2.0 C (35.6 F) at observer
1013.3 mb (29.92″ Hg) air pressure
50.0% relative humidity

Deneb
  48°54.77' computed unrefracted center altitude
      0.87' refraction
  48°55.63' apparent center altitude
286°08.11' predicted azimuth

Vega
  27°17.27' computed unrefracted center altitude
      1.93' refraction
  27°19.19' apparent center altitude
299°08.49' predicted azimuth

topocentric apparent Deneb to Vega angle
  23°50.79' center to center, unrefracted
      1.04' refraction
  23°49.76' center to center, refracted

position angles:
209.7° Deneb to Vega
21.5° Vega to Deneb

The position angles are with respect to the zenith. If Deneb is exactly
above Vega, position angle from Vega to Deneb is zero. This angle
increases counterclockwise, which is the same sense as azimuth, though
it seems backward because you're viewing the celestial sphere from the
inside.

With the sextant preset to the expected separation and the position
angle known, it's much easier to acquire both stars. I have found the
correct sextant orientation (about the line of sight) non-obvious unless
the stars are close. A precomputed position angle saves a lot of time in
that respect.

> After about 15 minutes practicing like this, I felt confident enough to put 
the telescope back in and do the job properly.  I found the best method was 
to rock the sextant ever so slightly like rolling the Sun about the sea 
horizon and gradually increasing Hs until the reflected star crashed though 
the index glass star.  I then increased Hs further until the stars separated 
again.

That's what I did, the few times I have tried to observe star separation
angles. A steady superimposition of both bodies doesn't work for me. To
my eye it makes the error more difficult to perceive. I prefer to
repeatedly sweep one star past the other.

> After all that messing around with Vega and Deneb, Orion and the Twins were 
becoming nicely visible and with Betelgeuse at roughly Hc= 17.54 Az= 102 and 
Pollux at Hc=17.42, Az=067, I had two stars horizontal and at a low Hc.

I estimate a time 15 minutes later.

2019-12-04 20:15:00.00 UT1

Pollux
  17°14.89' computed unrefracted center altitude
      3.17' refraction
  17°18.06' apparent center altitude
  66°10.71' predicted azimuth

Betelgeuse
  17°24.40' computed unrefracted center altitude
      3.14' refraction
  17°27.54' apparent center altitude
100°59.93' predicted azimuth

topocentric apparent Pollux to Betelgeuse angle
  33°11.61' center to center, unrefracted
      0.59' refraction
  33°11.02' center to center, refracted

position angles:
275.6° Pollux to Betelgeuse
84.9° Betelgeuse to Pollux

This should torpedo the myth that equal altitudes eliminate the effect
of refraction on separation angle.

Some years ago I encountered this phenomenon when testing some code to
correct semidiameter for refraction. Upper and lower refracted SD were
correct, but SD at the 3 and 9 o'clock positions were not unchanged as I
expected. After much troubleshooting, I realized there was no bug. Every
point on the limb is raised by refraction along great circles which
converge at the zenith. Therefore, refraction reduces SD in every
direction. (This is noted by Meeus in "Astronomical Algorithms.")

   

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