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    Re: Apollo spacecraft sextant
    From: Ken Muldrew
    Date: 2004 May 3, 19:53 -0600

    Frank Reed wrote:
    
    > procedures that would work throughout the Solar System. This would
    > require an almanac with heliocentric coordinates for all of the
    > planets, but that's no problem (the Nautical Almanac from the 1780s
    > included heliocentric latitudes and longitudes, for some odd reason,
    > but not distances).
    
    I think the longitudes and latitudes were to calculate the lunar distances
    using the approximate formula:
    
    D = arcos((cos(long1 - long2)) + (cos(lat1 - lat2)))
    
    for the sun and applying the correction:
    
    10^((5.3144 + log sin(moon's lat) + log sin(star's lat) + log versin(long1 -
    long2) + log csc(D))-40)
    
    for a star (with this correction in seconds). If the latitudes of the the moon
    and star are of the same denomination then the correction is subtracted,
    otherwise it is added. The "-40" is to take out the index from the logs.
    Even with the moon at 5? off the ecliptic and the star at 15? off the
    ecliptic, this rule gives the distance within 10"; the error is reduced in half
    when the star is within 10?.
    
    From Maskelyne's article in the Phil. Trans Roy. Soc. of 1764, p.263-276
    (an approximate method for clearing the distance is also given.
    
    Ken Muldrew.
    
    
    

       
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