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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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