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    Re: Moon's angular speed
    From: Ken Gebhart
    Date: 2005 Nov 20, 14:35 -0600

    On 11/20/05 2:22 AM, "Frank Reed"  wrote:
    
    > 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
    >
    Frank,
    
    Don't you mean 13.2? per HOUR instead of per day?
    
    Ken Gebhart
    
    
    

       
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