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    Re: Star - Star Observations
    From: Brad Morris
    Date: 2010 Mar 10, 14:00 -0500
    A big thank you to George and Andres for clarifying the equations.  And I did find my error, so I can now compute
    what the observed distance should be.
     
    To re-iterate,
     
    d = acos{ [cos(D) +cos (H1 + H2)]*cos(h1)*cos(h2) / (cos(H1)*cos(H2)) -cos(h1+h2) }
    where
    H1 is the true altitude of object 1, should refraction not exist
    H2 is the true altitude of object 2, should refraction not exist
    h1 will be the observed altitude of object 1, when refraction is present
    h2 will be the observed altitude of object 2, when refraction is present.
    d is the observed distance, when refraction is present.
    D would be the true distance, should refraction not exist.  
     
    Since all objects rise with the tide
    h1 = H1 + a1
    h2 = H2 + a2
    where
    a1 is the altitude correction for refraction for object 1
    a2 is the altitude correction for refraction for object 2
     
     
    Now for the fun part, I have two objects already selected.
            My location N40d 53.0m  W72d 48.0m
            GMT  10-March-10 00-57-00
            Object 1: RA 6h 45.22m  Dec -16.7175
            Object 2: RA 9h 27.68m  Dec  -8.6678   
    Therefore
            D = 40d 21m 12.41s
            H1 = 28.63501 d
            H2 = 37.80218 d
            a1 = 0.03025 d
            a2 = 0.02135 d
            factor 1 = 0.43592
            factor 2 = 0.02371
    And consequently
            d, Corner Cosines = 40d 22m   1.7s
            d, Youngs             = 40d 24m 45.84s
     
    I find a difference of 2m 44.14s between the two computations. The first assumption is that I erred again (a too often occurrence IMHO) ! 
    The second assumption is that Young's equations are rigorous while the corner cosines are only an approximation, therefore a small
    difference is to be expected and that Young's equations are the ones to follow.
     
     
    Some further commentary would certainly be helpful!
     
    Best Regards
    Brad
     
     
     
     
     

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