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    Moon's angular speed
    From: Frank Reed CT
    Date: 2005 Nov 20, 03:22 EST

    Here's a little trick that might entertain some of you...
    
    Suppose you want to know how rapidly the Moon's position in the sky is
    changing. The average rate is 13.2 degrees per day or 33.0 minutes of arc per
    hour. But the range is large, running from 29.5 to 38.5 minutes of arc per hour.
    It turns out that you can get a very good estimate of the actual angular speed
     (geocentric!) at any moment by looking at the Moon's HP.
    
    Since the Moon  slows down when it is further from the Earth in accordance
    with Kepler's Second  Law, it might at first seem that the change in angular
    speed would be directly  proportional to the change in horizontal parallax
    relatve to its mean value of  57.0 minutes of arc, but in fact it's double that.
    When the Moon is, for  example, 1% farther from the Earth, its linear speed is
    reduced by 1% and in  addition, since it is visually further away, the angular
    rate is reduced by 1%  more. So if I look up the Moon's HP in an almanac and
    find that it's 60.0',  that's 3 minutes of arc or 5.3% above average. I double
    that percentage to get  10.6% and apply that to the Moon's mean angular rate of
    33 minutes per hour to  get 36.5 minutes per hour. This calculation is
    accurate to +/-1% at worst and  typically accurate to +/-0.5%. Of course, it's not
    complicated to do a really  accurate calculation if you have a computing device
    handy (you can calculate the  actual great circle distance, or you could use
    a formula from Meeus), but  this little method is something that you can do in
    your head if you have  access to the Moon's actual HP for the time in
    question.
    
    Note: I think I've got this all right, but as always, check it out for
    yourself.
    
    -FER
    42.0N 87.7W, or 41.4N  72.1W.
    www.HistoricalAtlas.com/lunars
    
    
    

       
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