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    Star identification via Bygrave formulas
    From: Paul Hirose
    Date: 2018 Jan 12, 08:48 -0800

    In addition to sight reduction, the Bygrave formulas and a slide rule
    can identify a star (compute its SHA and declination) from its azimuth
    and altitude if the observer's position and time are approximately
    known. Simply interchange the pole and observer: latitude retains its
    usual sense, but use azimuth angle (Z) as LHA and altitude as
    declination. Then work the problem as a sight reduction.
    
    For instance, at 2018 Jan 8 10 h UT, 30S 160E, a bright star is observed
    at altitude 61° and estimated azimuth 40°. To identify the star, use
    these parameters:
    
    30 latitude
    61 declination
    140 LHA
    
    Remember that Z is measured from the south in south latitude, so if
    azimuth = 40 then Z (alias "LHA") = 140. (You should have seen how much
    time I wasted because I forgot that.) Latitude and declination are "same
    name" unless altitude is negative.
    
    No great accuracy is necessary, so I won't try to interpolate between
    the graduations on the slide rule.
    
    W = arc tan (tan 61 / cos 140)
    W = 67.0
    
    LHA is between 90 and 270, so replace W with 180 - W:
    
    W = 113.0
    
    X = 90 - 30 + 113.0
    X = 173.0
    
    Z = arc tan (tan 140 * cos 113.0 / cos 173.0)
    Z = 18.3
    
    Hc = arc tan (cos 18.3 * tan 173.0)
    Hc = 6.6
    
    Greenwich hour angle of Aries is 258°. Add east longitude (160),
    subtract 360, and get 58 as the local hour angle of Aries.
    
    Angle Z (18°) from the Bygrave formula is actually the meridian angle of
    the unknown body. It was observed east of the meridian, so right
    ascension = 58 + 18 = 76°. Therefore SHA = 360 - 76 = 284. Hc is the
    declination, -7°.
    
    If you search the stars in the Almanac daily table, Rigel is the only
    one with both coordinates approximately correct. (There are a few
    degrees of error since I intentionally made the azimuth a little
    inaccurate.)
    

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