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    Re: Star to Star Distances taken on a Second Hand Sextant
    From: Paul Hirose
    Date: 2019 Dec 6, 16:44 -0800

    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.
    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
      48°54.77' computed unrefracted center altitude
          0.87' refraction
      48°55.63' apparent center altitude
    286°08.11' predicted azimuth
      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
    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 
    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
      17°14.89' computed unrefracted center altitude
          3.17' refraction
      17°18.06' apparent center altitude
      66°10.71' predicted azimuth
      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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