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    Re: Star - Star Observations
    From: George Huxtable
    Date: 2010 Mar 9, 23:31 -0000

    I suggest that Brad Morris and Peter Hakel are taking the wrong tack.
    
    Their procedure will work only if the two stars have the same (or opposite) 
    azimuths. Only then can one calculate the angle between them, and then, as 
    the next step, apply the appropriate correction for refraction by simple 
    arithmetic.
    
    But in the general case, the job has to be done differently, to get the 
    right answer.
    
    First, obtain the predicted position of star1, in altitude and azimuth. Add 
    the appropriate refraction correction, to get the apparent altitude. Then do 
    the same for star 2. Now, using those two apparent positions, calculate the 
    angle between them using spherical trig. Then, the result will adjust itself 
    automatically for refraction, depending on  how the two azimuths differ.
    
    There are other ways to make the same calculation, but that' the simplest, 
    conceptually.
    
    It's a similar process to the clearing of a lunar distance, except that it's 
    simpler because there are no semidiametrs and limbs to worry about, nor any 
    effects of parallax to account for.
    
    George.
    
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message ----- 
    From: "Brad Morris" 
    To: 
    Sent: Tuesday, March 09, 2010 9:48 PM
    Subject: [NavList] Star - Star Observations
    
    
    Gentlemen
    
    I have been playing around with star-star observations to determine the 
    accuracy of the sextant arc.  Calculating the star to star distance, without 
    refraction is not a challenge, nor is correcting for refraction when both 
    stars are on the same side as the zenith.  Derive GHA Aries for the 
    observation instant, apply SHA objects, determine instantaneous altitude for 
    both objects using spherical trig, compute refraction correction based on 
    altitude for both objects, create delta refraction correction and finally, 
    subtract from star to star distance to get the observable distance for my 
    location.  It sounds like a lot of work, but I have set up a spreadsheet 
    that uses the Celestron SkyScout as inputs.  I just point at two stars, 
    enter some data from the SkyScout (in Right Ascension & Declination), and 
    the observable distance from my location at a known time is the 
    instantaneous result.  All the mindless tabular work is done by the 
    spreadsheet.  I don’t really even need to know which stars they are, as long 
    as the Celestron does!  Of course, I have checked my spreadsheet against 
    some hand done calculations to check to see if it is working the way I 
    expect it to…and it is.
    
    Here is the dilemma.  When I get to larger angles, I need to go beyond my 
    zenith.  For example, I have been looking at Polaris vs Sirius.  My latitude 
    is about 40 degrees north.  So Sirius is to my south, Polaris, naturally, is 
    to my north.  The nominal distance works out to about 106 degrees 20 odd 
    minutes (forgive me, I don’t have the exact numbers in front of me). 
    Because each object is on either side of my zenith, both objects will appear 
    to be lower in the sky compared to the horizon, due to refraction.  Yet 
    because they oppose each other in azimuth, the observable distance between 
    them should be larger by the sum of the refraction corrections, not reduced 
    by the difference of the refraction corrections.  That is, compute the true 
    distance without refraction.  Since each object is lowered by refraction, 
    but in opposite directions, shouldn’t we add the refraction corrections to 
    the nominal distance to obtain the observable distance?
    
    Best Regards
    Brad
    
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