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    Re: distance with atan2
    From: Paul Hirose
    Date: 2005 Nov 11, 15:44 -0800

    One way to calculate distance (separation angle) on a sphere is to use
    vectors and the atan2 function or rectangular to polar conversion. Set x
    to the dot product of the two vectors, and y to the magnitude of their
    cross product. The separation angle is atan2(y, x), or you can get the
    angle by converting x and y to polar form.
    
    For example, Meeus calculates the separation angle between two stars:
    
    14h 15m 39.7s +19°10′57″
    13h 25m 11.6s -11°09′41″
    
    He uses spherical trig. Using the vector method, start by forming the
    rectanglar coordinates on the celestial sphere:
    
    -.783786 -.526988 .328578
    -.914079 -.356354 -.193573
    
    dot product = .840633 (x)
    cross product magnitude = .541606 (y)
    
    Converting (x, y) to polar form gives angle 32.7930°, which agrees with
    Meeus.
    
    An advantage of the vector method is its accuracy at all angles. A large
    portion of Meeus' chapter on separation angle discusses ways to avoid
    the inaccuracy of the traditional spherical trig formula near 0 or 180
    degrees.
    
    
    

       
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