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    Star-to-star distances
    From: Alexandre Eremenko
    Date: 2004 Sep 29, 15:02 -0500

    Subject: star-to-star measurements
    
    I am trying to learn how to use my sextant,
    and to find its instrumental error (as explained in my previous
    message today with "no subject").
    
    I began with taking Sun's altitudes with artificial
    horizon (first a plate with water, then a Davis art horizon).
    These were OK, the average error was approx. 0.3'
    The main problem limiting precision was the motion
    of the water because of the air movement and my own movement.
     When I
    switched
    to Davis art horizon, I found it unusable for the Sun: it is
    heated by the Sun, the water evaporates and covers its
    transparent lids with fog. If I remove lids, the air movement
    hurts again. (A dog passing by also spoils the experiment for
    few minutes:-)
    
    1. I was taking series of 4-10 measurements with about 1 minute
    time intervals. Then I plotted them,
    rejecting one or two which stick
    out too  much from a smooth line. Then I reduced them using the real
    Almanach and "exact" solution of the navigational triangle on my
    computer. (First I tried "Complete on board Celestial Navigator",
    but it gives about 3' error because
    of rounding in the reduction tables.
    Its almanach in the "Complete on Board" is better,
     but still it is less precise
    than the real Almanach or
    Frank's on-line version). My real coordinates were determined
    with online maps (500 meters precision).
    
    The result was the average deviation of 0.3'
    (average of 10 measurements,
    moderate wind), maximal deviation 0.6'. (After discarding
    two of the 10 results BEFORE sight reduction).
    In a second observation,
    the deviations were 0.4', 0.2', 0.2', 0.2' (one discarded before
    sight reduction) in the
    series of
    5 measurements, exceptionally quiet weather.
    I consider this satisfactory, taking into account that the image of
    the sun in the water was oscillating all the time,
    even when there was no wind.
    
    I also tried to determine the index correction
    according to the Russian
    manuals, by comparing the Lower Limb altitude
    with the Upper Limb altitude.
    This gave -0.7' index correction.
    
    2. Then I switched to the stars. Beginning with the index correction.
    After two days of practice I learned how to obtain consistent results
    in a long series of measurements. The index correction was 0.0'
    (literally!).
    I mean that now I can measure distances of a star-to-itself,
    10 times in row,
    and obtain all readings which are less than 0.1' by absolute value.
    Remark: this is much easier to do with a star of 2-nd magnitude than
    with a bright star! A "small" star really looks like a point,
    while the
    image of a bright star has some distorted "shape".
    
    3. Then I started star-to-star distances. First, using the distances
    shown in the Bruce Bauer book, then after Frank's explanation,
    using Frank's formulas
    for the refraction correction. (See his postings
    on April 6, and also Chauvenet, vol. 1,
    where more explanation is given).
    And the results were a complete faillure...
    
    a) My measurements of the same distance taken in a short time
    interval have typical span of about 1'. (Worse than for the
    Sun!)
    b) When I tried to average over series of 3-10 measurements and
    compared with computed distances, the result was erratic error
    of the order of 1' and more, in BOTH directions!
    
    More details.
    The measurements were made late at night, from my balcony.
    The sky was
    clear, the altitudes (for refraction) were determined with the Rude
    starfinder and/or
    with my Star Globe. The sextant was preset for approximate distance;
    (measured directly on the globe!)
    this simplifies very much catching both stars. If the stars are
    not on the same vertical, I had to hold the sextant in an inclined
    or horizontal position, which is very inconvenient.
    But there was no difference in precision between "convenient" pairs
    of stars and "inconvenient" ones.
    Usually when measuring I sit a sturdy chair
    sometimes I had to lay on the floor.
    Here are two typical series:
    
    September 26, GMT 5:41
    Vega-Altair, 4 observations, span 1.1',
    Average measured distance 34d12.5'
    Bauer distance 34d11.9', Corrected distance (Frank's method) 34d11.3'
    
    September 28, GMT 5:00
    Vega-Elthanin, 5 observations, span 0.9',
    Average measured distance 14d31.1'
    Bauer: 14d31.8' Corrected 14d31.5'
    (this was the "best coincidence" I've got).
    
    It total, I measured 8 distances, many of them 10 times and more.
    The table of "instrumental errors" based on these measurements
    looks like this:
    
    Angle: 14d    19d    23d     30d     34d      54d       59d
    Error: +0.4'  +0.2   -0.9    -0.6              -0.9      +2.4
    
    which looks absurd. The unfilled place of 34d corresponds to
    Vega-Altair distance which I measured many times on different
    days and times of the day with the results for the
    sextant correction like: -1.2, -0.2, and -1.2
    What conclusion can I make about my sextant instrumental error?
    I believe my sextant (at least the mechanical part and mirrors)
    is better than that! It feels very tight.
    
    From my point of view, the problems come
    from the difficulty of detecting
    the precise moment when the stars overlap.
    So I am inclined to blame the
    optics for my poor results.
    (With usual binoculars I see the stars much
    better than with any of the two scopes of my sextant).
    
    I will appreciate all advises and suggestions on the matter.
    
    Alex.
    
    
    

       
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