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    Re: Unexpected USNO height correction precepts
    From: Paul Hirose
    Date: 2018 Dec 24, 15:50 -0800

    Computation of topocentric position angle, Venus to Sun, with respect to
    the true equator and equinox of date.
    
    1977-03-18T00:02:16.99 UT1
    +47.50s delta T
    
    topocenter:
    144.8950° -27.5833° E lon, N lat
    4.6 meters above ellipsoid
    
    Venus topocentric apparent place
       19.8778° +16.3211° RA, dec (true equator & equinox)
    
    Sun topocentric apparent place
      357.5051°  -1.0807° RA, dec
    
    The Sun is 22.4° west of Venus. I will solve for position angle with a
    slide rule and the Bygrave formulas. Angles rounded to .1°. In the
    Bygrave formulas, negative signs are ignored.
    
      W = arc tan(tan 1.1 / cos 22.4)
        = 1.2°
      X = 90 - 16.4 - 1.2
        = 72.4
      Z = arc tan(tan 22.4 * cos 1.2 / cos 72.4)
        = 53.7
    X is less than 90, so replace Z with its supplement: Z = 126.3. Because
    the Sun is west of Venus, position angle = 360 - Z = 233.7 with respect
    to the true pole of date.
    

       
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