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    Re: Star-star distances for arc error
    From: Frank Reed
    Date: 2009 Jun 25, 20:04 -0700

    Douglas, since you've decided to re-subscribe, I suppose I should reply to your recent posts.
    
    You had written previously:
    "Attempting to use star separations to try to determine scale accuracy for 
    example would not be possible due to the variables in the measurements 
    themselves - including the refraction component even if calculated."
    
    And I commented:
    "A sure indication that you have never tried it! "
    
    And you replied:
    "I have tried it and I don't rate it as practical."
    
    Sorry for the confusion. I should have said that this is a sure indication 
    that you HAVE NEVER TRIED IT CORRECTLY --and given your comments in this post 
    and in a later post about the "variables... including the refraction 
    component", that much is plain. There is no mystery to the quantity of 
    refraction. It is not some unknown variable. But if you neglect it when you 
    measure star-to-star distances or if you account for it incorrectly, your 
    results would be disappointing, displaying errors of one minute of arc or 
    more. Your conclusions may result from that error.
    
    And Douglas, you wrote:
    "If accuracy is required, the measurements are difficult to achieve in the 
    first place unless the sextant is clamped. Clamping requires special 
    arrangements for tilting the sextant."
    
    Clamping may help under some circumstances, but it's not required. Personally 
    I don't recommend it from my own experience. It can, however, be useful to 
    prop yourself up against something or to lean your elbows on a rail. 
    Naturally this applies only to sights on land, but since the only purpose for 
    these sights would be to estimate arc error, that's not an issue. You would 
    never do star-star sights on the water.
    
    And you wrote:
    "Also, combining of two stars overlapping, with the inevitable abberrations 
    seen in the telscope image itself preclude this to being within one minute at 
    best."
    
    The "aberrations" in the telescope image can be largely eliminated using a 
    remarkably simple trick which Bill B. and I discussed on NavList a few years 
    ago: don't dark-adapt. The navigational stars are all bright enough to be 
    seen with minimal dark-adaptation. If you don't allow your eyes to 
    dark-adapt, the images of the stars are generally much crisper with fewer 
    "flares" for many observers. As for a limitation of "one minute of arc" in 
    such observations, you should find with a little practice that you can get 
    much better than this with star-star sights. In individual star-star sights, 
    I find errors of about 0.3 minutes of arc, and when I average a set of four, 
    the error is reduced to about 0.2 minutes of arc or slightly less (error = 1 
    s.d.). It's also important to use a higher magnification telescope. I use a 
    7x scope. Since the unaided resolution of the human eye is 1.0 minutes of arc 
    or a little less under good circumstances, the resolution with such a 
    telescope is around 0.14' in the actual angles. If you use lower 
    magnification, you can expect proportionately worse results.
    
    Douglas, you added:
    "Also, the measurement can only be done to an accuracy of the divisions of the 
    sextant which in most cases is one minute of arc."
    
    Most modern sextants can be read to a TENTH of a minute of arc. Even sextants 
    which lack verniers on the micrometer can be read to at worst 0.2'. Of 
    course, this assumes that the instrument has been properly adjusted (mirrors 
    perpendicular to frame, telescope axis parallel to frame, etc.) and has no 
    pathological problems, like a loose micrometer, for example.
     
    and you wrote:
    "the certificate indicates accuracy of max error of 1 minute 30 seconds at points on the scale."
    
    But that is a correctable error. And that's the whole point of finding some 
    non-laboratory method of checking arc error. If you take a good series of 
    star-to-star sights, correct them properly for refraction, and compare them 
    with the correct true distance (which means you should use monthly data from 
    the almanac's star tables in order to correctly deal with aberration), you 
    can re-generate a calibration certificate for your sextant. Then if you find 
    your sextant has an error of +1.5' at 60 degrees, you know that you should 
    subtract 1.5' for every sight taken close to 60 degrees. It's effectively the 
    same as an index correction dependent on observed angle.
    
    And as I have said before, this is only ONE method of checking arc error. 
    Star-star sights work, but if you have time and opportunity, there are other 
    approaches that are even more accurate.
    
    And Douglas, you wrote:
    "and you are suggesting it is OK to measure two stars where the refraction 
    error alone can be greater than the measurement."
    
    Yes, that is EXACTLY what I am suggesting. Refraction is a known quantity. And 
    the fun thing, which is what I was pointing out in the opening message of 
    this thread, is that the refraction correction is nearly proportional to 
    distance for those cases where both stars are above 45 degrees altitude. This 
    is a very convenient result, and even if we don't use it for actual 
    calculation, it has great practical value for planning a round of star-star 
    sights. Below that altitude, by the way, you simply have to do a more 
    complete calculation --which is not difficult by any means, but it requires 
    either the observed altitudes or the data (latitude, hour angle, e.g.) 
    necessary to calculate the observed altitudes.
    
    By the way, just so you know that this isn't "just me" talking about star-star 
    distances, you may want to take a peek at "appendix G: sextant arc error 
    tables" in John Karl's book "Celestial Navigation in the GPS Age". The 
    preface to these tables begins, "The following tables are handy for checking 
    sextant arc error. They give star-star distances adjusted for the 
    refraction..." And for those NavList members who have a copy of this book, if 
    you look at those tables, you can see large blocks in the center of each 
    table where the refracted distance barely changes. Those are the cases where 
    both objects are above 45 degrees and fit the case which I've described in 
    the first message in the thread. I should add that Ken Gebhart, who is 
    co-publisher of John Karl's book and the world's largest distributor of 
    sextants today, considers this the best text in celestial navigation 
    currently on the market. I think it's pretty good, too! :-)
    
    And you wrote:
    "if less than twenty degrees it is 2.6 minutes of arc;  and less than ten 
    degrees  it is over 5 minutes of arc and the unknown effects of barometric 
    pressure and humidity affecting density make low altitudes very suspect 
    indeed."
    
    Below THREE degrees, indeed, you have to be suspicious of the refraction 
    correction, but above that altitude and certainly at ten degrees altitude and 
    above, there is no problem correcting for refraction. After all, we correct 
    for refraction in every celestial sight. Surely you can see that this is no 
    different in principle, only in the details. 
     
    And you wrote:
    "The only proper way is to use a dividing table and collimator where the 
    dividing head is at least accurate to one tenth of a minute of arc at all 
    readings."
    
    But you haven't really tried anything, have you? Have you experimented with 
    measuring a complete set of angles around the horizon (another method of 
    checking arc error)? Have you tried observing lunars (still another method 
    which many people find more successful than star-star disstances)? Ya know, 
    everybody is entitled to an opinion, but opinions should be based on 
    empirical facts, not speculations.
     
    And Douglas, you concluded:
    "It is easy to get carried away with the theory without considering the 
    practical difficulties or potential errors of the measurement itself compared 
    to what one is measuring."
    
    Indeed. I agree with that sentiment. But I have tried all of these things 
    extensively myself. So your speculation that we may be getting "carried away 
    with theory" is not relevant here.
    
    -FER
    
    
    
    
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