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    Re: nautical almanac information needed
    From: Frank Reed
    Date: 2009 Aug 1, 17:31 -0700

    George, you wrote:
    "1772 October 4, 6h and 9h, (which will be 6pm and 9pm) lunar distances, both
    East and West of the Moon.
    What I'm after is the actual numerical information predicted in that
    Almanac, rather than a modern back-prediction."
    
    No problem. 
    
    The listed lunar distances from the actual, published Nautical Almanac for 
    October 4, 1772 at 6h and 9h are:
    Sun (W) 102.23.14, 103.51.23
    Antares (W) 48.48.3(9), 50.22.24
    Markab (E) 56.6.40, 54.37.1(2)
    
    As usual for the almanacs of that period, the angular format is 
    degrees.minutes.seconds. A digit in parentheses is my way of indicating that 
    it is uncertain/difficult to read. And of course, back then, Markab was 
    actually listed as "alpha Pegasi".
    
    You said you didn't need them, but for general interest, the corresponding 
    "back-predicted" lunar distances which are believed to be accurate to 1" or 
    better are as follows (for 6h and 9h GAT --not GMT):
    Sun (W) 102.22.30, 103.50.39
    Antares (W) 48.47.59, 50.21.45
    Markab (E) 56.7.22, 54.37.53
    
    The differences (NA-true) in seconds of arc are:
    Sun +44, +44
    Antares +40, +39
    Markab -42, -41
    
    This pattern indicates rather well that the ecliptic longitude of the Moon was 
    still the primary source of error at around 42". Also, the pattern suggests 
    that my "uncertain" digits above are probably the correct printed values.
    
    Finally, for those not so familiar with lunars, you can see that these lunar 
    distances are increasing for the objects to the west and decreasing for the 
    object to the east at a rate of about 30 minutes of arc per hour, which is 
    typical. That rate is equal to one second of arc in two seconds of time, so 
    an error of 40 seconds of arc in the predicted distances implies an 
    unavoidable error of 80 seconds in time or about 20 minutes of arc error in 
    longitude. If you're lucky, your observational error will be in the opposite 
    direction. If you're unlucky, it will add onto the error in the predicted 
    distance.
    
    -FER
    
    
    
    
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